https://mathimages.swarthmore.edu/api.php?action=feedcontributions&user=Rebecca&feedformat=atomMath Images - User contributions [en]2022-11-26T18:55:41ZUser contributionsMediaWiki 1.31.1https://mathimages.swarthmore.edu/index.php?title=Pages_Ready_for_Final_Review&diff=26933Pages Ready for Final Review2011-07-22T13:09:37Z<p>Rebecca: /* Sweet Briar Pages */</p>
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'''<font color=darkred> AN IMPORTANT NOTE ABOUT PAGES PUT UP FOR FINAL REVIEW BETWEEN JULY 18TH AND 22ND'''<br />
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'''Anna is going to a training which will keep her extremely busy during that week. Priority for editing will be given to Swarthmore students and any others for whom it is their last week of work on the project (please note if you are NOT at Swarthmore and it is your last week. ''' I will make a big effort to get through everything posted by this weekend, so there isn't a backlog. I will also be completely unavailable for editing August 6th-15th, and will not be reachable during that time. </font> <br />
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'''<font color=olive><font color=green>CHRIS T.</font>, <font color=blue>STEVE C.</font>, and <font color=slateblue>REBECCA</font> will be helping to review pages while Anna is busy.</font>'''<br />
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===Swarthmore Pages===<br />
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*[[Logistic Bifurcation]] by [[User:Dpatton1|Diana]] 17:00 7/7/11<br />
:<font color=green> Chris 7/16 I've put up comments from a "layman's" perspective. </font><br />
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*[[Snell's Law]]<br />
addressing Anna's comment. [[User:Ljeanlo1|Ljeanlo1]] 18:40, 21 July 2011 (UTC) <br />
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*[[Witch of Agnesi]] <br />
addressed Chris' comment. [[User:Ljeanlo1|Ljeanlo1]] 18:39, 21 July 2011 (UTC)<br />
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*[[Dimensions]] by [[User:Htasoff|Htasoff]]<br />
:<font color=green> SteveC 7/20 -- a couple of comments.</font><br />
::<font color=Mediumblue>Confused, Please explain.</font><br />
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===Sweet Briar Pages=== <br />
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*[[Dandelin Spheres Theory]] by [[User:Flora1103|Flora Li]] 15:31, 17 July 2011 (UTC)<br />
:<font color=green> Chris 7.20.11 I've responded to some of your changes and comments. </font><br />
::<font color=plum>Flora 07.20 12:08 I responsed to your suggetions and made a little more changes.</font><br />
:::<font color=green> Chris 7.21.11 I've completed the rest of the page and made comments. </font><br />
::::<font color=plum>Thanks for your suggestion. I have made some change based on your comments. Flora 07.21 12:29</font><br />
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*[[Steiner's Chain]] by [[User:Donko14|Anna]]<br />
:<font color=darkred> comments are up [[User:AnnaP|AnnaP]] 13:35, 21 July 2011 (UTC) </font><br />
::<font color=plum> Thanks for your quick response with comments! I have made the necessary adjustments!!</font><br />
<font color=slateblue> <br />
::[[User:Rebecca|Rebecca]] 13:09, 22 July 2011 (UTC) This page is great! I left a few small comments, but overall very good! </font color><br />
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*[[Parabolic Integration]] by [[User:Donko14|Anna]]<br />
:<font color=darkred> I've suggested a pretty major revision of one section, and I actually think that it might be best to move that section to another page. See my notes [[User:AnnaP|AnnaP]] 05:07, 22 July 2011 (UTC) </font><br />
::<font color=plum>Hi Anna, should I make the corrections to this section and wait for you to approve the page before I move it to the [[Parabola]] page?</font><br />
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===Rensselaer Polytechnic Institute===<br />
[[Polar Equations]] by [[User:Chanj|Chanj]] 21:35, 7 July 2011 (UTC)<br />
:<font color=blue> I have edited my page by putting up new images, more detailed explanations and comments in the discussion reflecting those changes. --[[User:Chanj|Chanj]] 20:48, 15 July 2011 (UTC)</font><br />
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[[DU11]]</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Steiner%27s_Chain&diff=26932Talk:Steiner's Chain2011-07-22T13:06:26Z<p>Rebecca: /* Examples, Calculations, Applications, Proofs */</p>
<hr />
<div>==Messages to the Future==<br />
* Provided precise suggestions for what could be added in the future<br />
* <font color=darkred> '''The applet on the [[Inversion]] Page does something similar to the applet that you want. Did you put up a request on the [[Math Tools Requests]] page?''' </font><br />
<br />
==References and Footnotes==<br />
* Provided references of all websites and articles used at the bottom of the page<br />
* Gave credit to image creators in all circumstances<br />
* Images throughout the page (speaking of those excluding the main image) show how they were created by me by clicking on the image<br />
<br />
==Good Writing==<br />
* Applied all of the suggestions I received for this page<br />
* Went through numerous drafts and had the page reviewed by many students as well as my professor<br />
<br />
===Context===<br />
* Full of context, especially at the beginning of each section as well as between steps in mathematical equations<br />
* I didn't include a "Why it's Interesting" section because I was unable to find any real-world applications of this topic, even though one was suggested to me on this discussion page by a fellow student, I wasn't able to locate any verifiable sources to prove this.<br />
<br />
===Quality of Prose and Page Structuring===<br />
* Provided a purpose for each section and included it in the first few sentences of the section. <br />
* In the "Basic Description" I tried to layout exactly what I was doing for the reader<br />
*<font color=darkred> The paragraph that begins "With these measurements we can say that" is confusing. I suggest breaking all equations onto different lines, since they run into each other right now. Also, try to provide the justification for the equation ''before'' you write the equation instead of after. <br />
'''*I'm having trouble understanding the relevance of the following sentence to the rest of the page: "When two circles are concentric, the area of the annulus in between is the area of the large circle minus the area of the small circle: <math>\text{Area of Annulus} = \pi(R^2 - r^2) </math>" </font>'''<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 13:05, 22 July 2011 (UTC) “Now, a Steiner chain does not always have to consist of a circle inside the other” This is unclear to me. Do you mean “Now, a Steiner chain does not always consist of a collection of circles within one larger circle”?<br />
*“The image on the left, Figure 3, represents a closed annular chain whereas the image on the right, represents the Steiner chain that is obtained by inverting Figure 3 over a circle.” No comma after right. <br />
</font color><br />
<br />
===Integration of Images and Text===<br />
* Used many many images to explain my topic<br />
* Constantly encouraged my reader to refer to my figures<br />
<br />
===Connection to other Mathematical topics===<br />
* Provided one link to another page for readers to refer to for a better explanation of a specific term<br />
*<font color=darkred> We have a page on [[Inversion]] that definitely should be linked by your page. Also, since your algebraic discussion very closely mirrors [[Problem of Apollonius]], that page should also be linked. </font><br />
<br />
===Examples, Calculations, Applications, Proofs===<br />
* Provided numerous thorough examples<br />
* Included proofs where necessary <br />
* Included context between difficult steps in algebra<br />
*<font color=darkred> '''Is there a way to construct other annual steiner's chains by using polygons other than triangles? It'd be great to have a note about whether or not you can use the same process with other regular polygons.<br />
:I didn't see any change related to this comment. '''<br />
*You need to explain a bit more of how you go from this statement "1. We can see that C, B, C', B' form a quadrilateral and one of the most basic theorems about quadrilaterals says that their opposite angles are supplementary." to the angle equality below it. You definitely skip a step of reasoning that should be stated explicitly.</font><br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 13:06, 22 July 2011 (UTC) Your proof for the radii ratio could use some transition sentences like you have in the previous section. What about something like “Multiplying both sides by (R+r) gives us…” after the first equation. Then “Distributing the sin(pi/2)” can go between the next two equations. You get the picture, but I think that would help people be less intimidated if there were transitions instead of just having a block of equations. <br />
</font color><br />
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===Mathematical Accuracy and Precision of Language===<br />
* Tried to clearly explain topics in the most simple words<br />
* Included mouse-overs very often<br />
*<font color=darkred> In your basic description, can you clarify if Steiner's Chains have to have one circle totally inside another? That seems to be the case, but you don't say it explicitly <br />
*This sentence: "points C' and B' are concyclic as are points C and B." is confusing given your definition of concyclic. Points C' and B' don't lie on the same circle as you show in the image, rather one is the center and the other is on the outside. Can you clarify what you mean? </font><br />
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===Layout===<br />
* Organized well, with little white space<br />
* Utilized features such as hide/show as well as mouse-overs<br />
* Organized into understandable sections<br />
*<font color=darkred> '''I'd encourage making this sentence: "By inverting points along all the circles of the Steiner chain, another can be formed that differs slightly from the original but still maintains the properties specific to Steiner chains (which are mentioned above under "Basic Description")". it's own paragraph. That will make the reader pause more after the link to inversion and click the link if they need more information''' </font><br />
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=General comments=<br />
{{hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:20, 28 June 2011 (UTC): You've got some great pictures, and it looks like you know what you're talking about, but you need to do a much better job of defining they key terms (Steiner's Porism, Steiner chains) and of explaining what you're doing and why you're doing it. I read the whole page carefully more than once, and I'm still confused about what's going on.</font><br />
<br />
<font color=orangered><br />
Hey Anna!<br />
<br />
Cool page! One comment that I got a lot from the people who worked on this last summer, was that when I have math writing, like you do with your proofs, to explain what happens from one line to the next.<br />
Like this:<br />
</font><br />
<br />
<math> \sin \frac{\pi}{n}= \frac{R-r}{R+r}</math><br />
<br />
Multiplying both sides by <math>R+r</math> gives us<br />
<br />
<math> \sin \frac{\pi}{n} (R+r)= R-r</math><br />
<br />
Distribution gives us<br />
<br />
<math> R \sin \frac{\pi}{n} + r\sin \frac{\pi}{n} = R - r</math><br />
<br />
After we subtract <math>R, r</math> from both sides, we have<br />
<br />
<font color=orangered><br />
...and so on and so forth.<br />
<br />
Becky left a ton of comments on the the discussion page for [[Law of Sines]] about this in hot pink if you need any reference. That page has a lot of math writing.<br />
<br />
Richard 6/13<br />
<br />
</font><br />
<br />
=Section-specific comments=<br />
==Intro==<br />
<font color=orangered>You mention circles, but your main picture has spheres. Maybe mention spheres in this part? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*You should link to [[Inversion]] in this section. It's not a perfect page, but what's there will definitely help people understand inversion.</font><br />
*<font color=dodgerblue>''A Steiner chain is a figure of tangent circles'' - sounds awkward. Might be better to say it's "made of" tangent circles.</font><br />
*<font color=dodgerblue>This section really doesn't help me understand what a Steiner chain or Steiner porisms are ''at all''. I see that you have a bit more of an explanation in the original caption, but you should really move that down here or at least say the same thing with different words here. Since the caption comes before the TOC, a lot of people tend to skip over it.</font><br />
*<font color=dodgerblue>Also, you need to offer some sort of explanation as to what a "porism" is - is "Steiner's porism" synonymous with "a Steiner chain"? Because the only term you've used so far is "Steiner chain", and I'm very confused as to why the page is called "Steiner's Porism" and not "Steiner chains".</font><br />
*<font color=dodgerblue>You end this bit by saying something about the "properties of a Steiner chain" - what are these properties? You should at least touch on them somewhere in the basic description. This will also help give context to the two construction sections that follow - give me something so that I can kind of see why we're doing what we're doing, and how we know when we've succeeded in creating a Steiner chain. To be honest, I read this whole section and still didn't really know what a Steiner chain was besides a picture involving circles. You need to give some sort of definition, and not just a description of how to make one example.</font><br />
<br />
<font color=orangered>I'm not sure I understand your definition of inversion in this section. And you should say something about reflection fixing the points the same distance from the line as they start out. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
===Creating a Steiner Chain===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*Unsure why you would say "regular triangle" - I think "equilateral triangle" is a much more familiar term for most people.</font><br />
*<font color=dodgerblue>''Using the points of <math>\triangle XYZ</math> as centers, construct tangent circles <math>X,Y,Z</math>…''<br />
::Upon re-reading, I'm pretty sure you mean that XYZ are tangent to each other, but at first I thought you meant that they were tangent to the original circle, which they're not. Consider rewording this sentence.</font><br />
*<font color=dodgerblue>Is the picture at the end of this section a Steiner chain? If so, please say so. If not, what is it? As it is, the section ends rather abruptly.</font><br />
<br />
<br />
*<font color=orangered> By your definition, the main image is not concentric circles. You may want to make sure that this is just one particular way of making a Steiner chain. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
===Creating a Steiner Chain using Inversion===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*''Construct an inversion circle to reflect over the three tangent circles and the two concentric circles. ''<br />
::This sentence confused me. The way you've phrased it sounds as though the new circle you're creating is the one that's going to be reflected - "Construct an inversion circle that will then be reflected over the three tangent circles and the two concentric circles," whereas I'm pretty sure you mean to say "Construct an inversion circle to reflect the three tangent circles and the two concentric circles over." If you're uncomfortable with ending the sentence with a preposition, try "Construct an inversion circle over which the three tangent circles and the two concentric circles will be reflected." Also, there's no need to call that figure "the three tangent circles and the two concentric circles" - call it "the Steiner chain" or "our previous figure" or something.</font><br />
<br />
<br />
*<font color=dodgerblue>The last image in this section is kind of huge. Make sure it's on a different line than your text - it splits the paragraph up weird. And maybe make it a tiny bit smaller?</font><br />
<br />
*<font color=dodgerblue>This may just be part of my general confusion over what Steiner chains actually are, but why do we want to create a new Steiner chain by inversion? What is the purpose of doing this? Just for fun?</font><br />
<br />
*<font color=orangered>I'm not sure that I understand all of the elements of this last picture. Nothing is tangent to the big circle. I assuming you can make a Steiner chain by inversion without being tangent? (I thought they were supposed to be) And why are there different sized circles within the smaller one? Is it a proportional thing? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
==A More Mathematical Explanation==<br />
===Formulas===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*I don't understand why you have this section heading. First of all, it's the wrong size - it's hidden inside the MME, but if you look at the TOC it's not listed as a sub-section of the MME - to fix that you need to add another equals sign on either side of the heading. But there's nothing in the MME that's not also inside Formulas, so it seems to me that all you've done is re-name your MME, which doesn't seem necessary - all of the subheadings say "Formula" in them…</font><br />
<br />
*<font color=dodgerblue>So Steiner's Porism is a ''theorem'' about Steiner chains? You NEED to explain this above, even if you don't want to state the full thing. You just can't have a page about something and not even show what that thing is except for inside a hidden section.</font><br />
<br />
*<font color=dodgerblue>Also, you need to actually ''explain'' the Porism - I'm not stupid, and I have almost no idea what it's actually saying. What is the "starting circle" of a Steiner chain? What does it mean for a Steiner chain to "close"? What are the "loops" of a Steiner chain? Try to rephrase this statement using just the terms you've introduced in the basic description (and then move that simpler statement ''to'' the basic description!). Also, why is it called a "Porism" and not a "theorem"?</font><br />
:::<font color=orangered>I second Kate here. What's a Porism? It's sort of like this is just hanging out here. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
<br />
====Tangent Circles Formula====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*In your first image in this section, the ordered pairs for the points aren't close enough to the arrows showing which points they belong to.</font><br />
*<font color=dodgerblue>What is the point of this section? How are these equations about tangent circles relevant to the rest of the page? If you're just establishing them here so that you can use them later, you need to say that.</font><br />
====Concentric Circles Formula====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): Again, what on earth is the purpose of this section? Give me some context so I'm not so confused! :(</font><br />
====Circle to Circle Inversion====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):</font><br />
*<font color=dodgerblue>First of all, context! Context, context, context! I am so very very confused. Why are we doing any of this????</font><br />
*<font color=dodgerblue> ''Points (C, C'), (B, B') are inverses with respect to J \Rightarrow points C, C', B, B' are concyclic''<br />
::I've gotta question your notation here - I thought that C, C', B, and B' were all points in their own right. Why are you making ordered pairs out of points? Or are they not points after all? If they're not points, what are they?</font><br />
*<font color=dodgerblue>In this whole section, I think you need a little more explanation than just all these arrows - what you've got is technically correct as a proof, but it'd be a lot more readable if you sort of embedded it in explanatory sentences. (This is what Richard was talking about in his earlier comment.)</font><br />
*<font color=dodgerblue>Why did we stop where we did? What is the significance of that result? Also, fix that period that's just sorta chillin by itself at the end here.</font><br />
<br />
*<font color=orangered>What's a cyclic quadrangle? <br />
*Try to add overlines to all of your formulas in this section? <br />
[[User:Rscott3|Richard]] 7/18</font><br />
<br />
====Steiner Chain Construction via Inversion Formulas====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*''An inversion can be done on a symmetrical arrangement of n circles (shown in Figure 3) in a region between two concentric circles, one with radiusR and the other with radius r. ''<br />
::I have no idea what this sentence means. Also, what is the purpose of this section? What are we trying to accomplish in it?</font><br />
*<font color=dodgerblue>''This arrangement is represented by: [math stuff]''<br />
::What arrangement? And where did that math come from? :( :( so confused.</font><br />
*<font color=dodgerblue>Again, you need to provide some explanation with your math. I have no idea what you're trying to do or how you're doing it, and also I don't like this format where you say "X=Y! Therefore, Z=W!" and ''then'' have an expandable section showing how you get from X=Y to Z=W - I think the explanation should come in the middle of the two statements.</font><br />
<font color=orangered>Do you have a figure 1 and 2? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
<br />
<font color=orangered>See my comment from the last time. And also where did you get these formulas? I'm not exactly sure how you got them.<br />
<br />
You've got an "is" "are" problem in the sentence starting with "The lengths of the radii of the tangent circles..."<br />
[[User:Rscott3|Richard]] 7/18</font><br />
<br />
====Types of Steiner Chains====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): This section needs to be at the top of the page! These sections define important terms that I need to understand before I can understand the statement of Steiner's Porism. They should '''not''' be hidden down here! It should go at the top of the MME or even the bottom of the Basic Description - this is actually more important to understand what's going on with the page than the steps to constructing a Steiner Chain are, imo.</font><br />
:::<font color=orangered>Agreed 100%. [[User:Rscott3|Richard]] 7/18</font><br />
=====Closed Steiner Chains=====<br />
=====Open Steiner Chains=====<br />
=====Multicyclic Steiner Chains=====<br />
=====Annular Steiner Chains=====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): I'd like to see an example of a non-annular Steiner Chain in this section, just for contrast.</font><br />
<br />
*<font color=orangered> This type reminds me of a gun cylinder/barrel thing!...Why It's Interesting maybe????? Steiner Chain in real life? http://www.pyramydair.com/blog/images/ar6-cylinder-web.jpg [[User:Rscott3|Richard]] 7/18<br />
</font><br />
<br />
}}</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Steiner%27s_Chain&diff=26931Talk:Steiner's Chain2011-07-22T13:05:32Z<p>Rebecca: /* Quality of Prose and Page Structuring */</p>
<hr />
<div>==Messages to the Future==<br />
* Provided precise suggestions for what could be added in the future<br />
* <font color=darkred> '''The applet on the [[Inversion]] Page does something similar to the applet that you want. Did you put up a request on the [[Math Tools Requests]] page?''' </font><br />
<br />
==References and Footnotes==<br />
* Provided references of all websites and articles used at the bottom of the page<br />
* Gave credit to image creators in all circumstances<br />
* Images throughout the page (speaking of those excluding the main image) show how they were created by me by clicking on the image<br />
<br />
==Good Writing==<br />
* Applied all of the suggestions I received for this page<br />
* Went through numerous drafts and had the page reviewed by many students as well as my professor<br />
<br />
===Context===<br />
* Full of context, especially at the beginning of each section as well as between steps in mathematical equations<br />
* I didn't include a "Why it's Interesting" section because I was unable to find any real-world applications of this topic, even though one was suggested to me on this discussion page by a fellow student, I wasn't able to locate any verifiable sources to prove this.<br />
<br />
===Quality of Prose and Page Structuring===<br />
* Provided a purpose for each section and included it in the first few sentences of the section. <br />
* In the "Basic Description" I tried to layout exactly what I was doing for the reader<br />
*<font color=darkred> The paragraph that begins "With these measurements we can say that" is confusing. I suggest breaking all equations onto different lines, since they run into each other right now. Also, try to provide the justification for the equation ''before'' you write the equation instead of after. <br />
'''*I'm having trouble understanding the relevance of the following sentence to the rest of the page: "When two circles are concentric, the area of the annulus in between is the area of the large circle minus the area of the small circle: <math>\text{Area of Annulus} = \pi(R^2 - r^2) </math>" </font>'''<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 13:05, 22 July 2011 (UTC) “Now, a Steiner chain does not always have to consist of a circle inside the other” This is unclear to me. Do you mean “Now, a Steiner chain does not always consist of a collection of circles within one larger circle”?<br />
*“The image on the left, Figure 3, represents a closed annular chain whereas the image on the right, represents the Steiner chain that is obtained by inverting Figure 3 over a circle.” No comma after right. <br />
</font color><br />
<br />
===Integration of Images and Text===<br />
* Used many many images to explain my topic<br />
* Constantly encouraged my reader to refer to my figures<br />
<br />
===Connection to other Mathematical topics===<br />
* Provided one link to another page for readers to refer to for a better explanation of a specific term<br />
*<font color=darkred> We have a page on [[Inversion]] that definitely should be linked by your page. Also, since your algebraic discussion very closely mirrors [[Problem of Apollonius]], that page should also be linked. </font><br />
<br />
===Examples, Calculations, Applications, Proofs===<br />
* Provided numerous thorough examples<br />
* Included proofs where necessary <br />
* Included context between difficult steps in algebra<br />
*<font color=darkred> '''Is there a way to construct other annual steiner's chains by using polygons other than triangles? It'd be great to have a note about whether or not you can use the same process with other regular polygons.<br />
:I didn't see any change related to this comment. '''<br />
*You need to explain a bit more of how you go from this statement "1. We can see that C, B, C', B' form a quadrilateral and one of the most basic theorems about quadrilaterals says that their opposite angles are supplementary." to the angle equality below it. You definitely skip a step of reasoning that should be stated explicitly.</font><br />
<br />
===Mathematical Accuracy and Precision of Language===<br />
* Tried to clearly explain topics in the most simple words<br />
* Included mouse-overs very often<br />
*<font color=darkred> In your basic description, can you clarify if Steiner's Chains have to have one circle totally inside another? That seems to be the case, but you don't say it explicitly <br />
*This sentence: "points C' and B' are concyclic as are points C and B." is confusing given your definition of concyclic. Points C' and B' don't lie on the same circle as you show in the image, rather one is the center and the other is on the outside. Can you clarify what you mean? </font><br />
<br />
===Layout===<br />
* Organized well, with little white space<br />
* Utilized features such as hide/show as well as mouse-overs<br />
* Organized into understandable sections<br />
*<font color=darkred> '''I'd encourage making this sentence: "By inverting points along all the circles of the Steiner chain, another can be formed that differs slightly from the original but still maintains the properties specific to Steiner chains (which are mentioned above under "Basic Description")". it's own paragraph. That will make the reader pause more after the link to inversion and click the link if they need more information''' </font><br />
<br />
=General comments=<br />
{{hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:20, 28 June 2011 (UTC): You've got some great pictures, and it looks like you know what you're talking about, but you need to do a much better job of defining they key terms (Steiner's Porism, Steiner chains) and of explaining what you're doing and why you're doing it. I read the whole page carefully more than once, and I'm still confused about what's going on.</font><br />
<br />
<font color=orangered><br />
Hey Anna!<br />
<br />
Cool page! One comment that I got a lot from the people who worked on this last summer, was that when I have math writing, like you do with your proofs, to explain what happens from one line to the next.<br />
Like this:<br />
</font><br />
<br />
<math> \sin \frac{\pi}{n}= \frac{R-r}{R+r}</math><br />
<br />
Multiplying both sides by <math>R+r</math> gives us<br />
<br />
<math> \sin \frac{\pi}{n} (R+r)= R-r</math><br />
<br />
Distribution gives us<br />
<br />
<math> R \sin \frac{\pi}{n} + r\sin \frac{\pi}{n} = R - r</math><br />
<br />
After we subtract <math>R, r</math> from both sides, we have<br />
<br />
<font color=orangered><br />
...and so on and so forth.<br />
<br />
Becky left a ton of comments on the the discussion page for [[Law of Sines]] about this in hot pink if you need any reference. That page has a lot of math writing.<br />
<br />
Richard 6/13<br />
<br />
</font><br />
<br />
=Section-specific comments=<br />
==Intro==<br />
<font color=orangered>You mention circles, but your main picture has spheres. Maybe mention spheres in this part? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*You should link to [[Inversion]] in this section. It's not a perfect page, but what's there will definitely help people understand inversion.</font><br />
*<font color=dodgerblue>''A Steiner chain is a figure of tangent circles'' - sounds awkward. Might be better to say it's "made of" tangent circles.</font><br />
*<font color=dodgerblue>This section really doesn't help me understand what a Steiner chain or Steiner porisms are ''at all''. I see that you have a bit more of an explanation in the original caption, but you should really move that down here or at least say the same thing with different words here. Since the caption comes before the TOC, a lot of people tend to skip over it.</font><br />
*<font color=dodgerblue>Also, you need to offer some sort of explanation as to what a "porism" is - is "Steiner's porism" synonymous with "a Steiner chain"? Because the only term you've used so far is "Steiner chain", and I'm very confused as to why the page is called "Steiner's Porism" and not "Steiner chains".</font><br />
*<font color=dodgerblue>You end this bit by saying something about the "properties of a Steiner chain" - what are these properties? You should at least touch on them somewhere in the basic description. This will also help give context to the two construction sections that follow - give me something so that I can kind of see why we're doing what we're doing, and how we know when we've succeeded in creating a Steiner chain. To be honest, I read this whole section and still didn't really know what a Steiner chain was besides a picture involving circles. You need to give some sort of definition, and not just a description of how to make one example.</font><br />
<br />
<font color=orangered>I'm not sure I understand your definition of inversion in this section. And you should say something about reflection fixing the points the same distance from the line as they start out. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
===Creating a Steiner Chain===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*Unsure why you would say "regular triangle" - I think "equilateral triangle" is a much more familiar term for most people.</font><br />
*<font color=dodgerblue>''Using the points of <math>\triangle XYZ</math> as centers, construct tangent circles <math>X,Y,Z</math>…''<br />
::Upon re-reading, I'm pretty sure you mean that XYZ are tangent to each other, but at first I thought you meant that they were tangent to the original circle, which they're not. Consider rewording this sentence.</font><br />
*<font color=dodgerblue>Is the picture at the end of this section a Steiner chain? If so, please say so. If not, what is it? As it is, the section ends rather abruptly.</font><br />
<br />
<br />
*<font color=orangered> By your definition, the main image is not concentric circles. You may want to make sure that this is just one particular way of making a Steiner chain. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
===Creating a Steiner Chain using Inversion===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*''Construct an inversion circle to reflect over the three tangent circles and the two concentric circles. ''<br />
::This sentence confused me. The way you've phrased it sounds as though the new circle you're creating is the one that's going to be reflected - "Construct an inversion circle that will then be reflected over the three tangent circles and the two concentric circles," whereas I'm pretty sure you mean to say "Construct an inversion circle to reflect the three tangent circles and the two concentric circles over." If you're uncomfortable with ending the sentence with a preposition, try "Construct an inversion circle over which the three tangent circles and the two concentric circles will be reflected." Also, there's no need to call that figure "the three tangent circles and the two concentric circles" - call it "the Steiner chain" or "our previous figure" or something.</font><br />
<br />
<br />
*<font color=dodgerblue>The last image in this section is kind of huge. Make sure it's on a different line than your text - it splits the paragraph up weird. And maybe make it a tiny bit smaller?</font><br />
<br />
*<font color=dodgerblue>This may just be part of my general confusion over what Steiner chains actually are, but why do we want to create a new Steiner chain by inversion? What is the purpose of doing this? Just for fun?</font><br />
<br />
*<font color=orangered>I'm not sure that I understand all of the elements of this last picture. Nothing is tangent to the big circle. I assuming you can make a Steiner chain by inversion without being tangent? (I thought they were supposed to be) And why are there different sized circles within the smaller one? Is it a proportional thing? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
==A More Mathematical Explanation==<br />
===Formulas===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*I don't understand why you have this section heading. First of all, it's the wrong size - it's hidden inside the MME, but if you look at the TOC it's not listed as a sub-section of the MME - to fix that you need to add another equals sign on either side of the heading. But there's nothing in the MME that's not also inside Formulas, so it seems to me that all you've done is re-name your MME, which doesn't seem necessary - all of the subheadings say "Formula" in them…</font><br />
<br />
*<font color=dodgerblue>So Steiner's Porism is a ''theorem'' about Steiner chains? You NEED to explain this above, even if you don't want to state the full thing. You just can't have a page about something and not even show what that thing is except for inside a hidden section.</font><br />
<br />
*<font color=dodgerblue>Also, you need to actually ''explain'' the Porism - I'm not stupid, and I have almost no idea what it's actually saying. What is the "starting circle" of a Steiner chain? What does it mean for a Steiner chain to "close"? What are the "loops" of a Steiner chain? Try to rephrase this statement using just the terms you've introduced in the basic description (and then move that simpler statement ''to'' the basic description!). Also, why is it called a "Porism" and not a "theorem"?</font><br />
:::<font color=orangered>I second Kate here. What's a Porism? It's sort of like this is just hanging out here. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
<br />
====Tangent Circles Formula====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*In your first image in this section, the ordered pairs for the points aren't close enough to the arrows showing which points they belong to.</font><br />
*<font color=dodgerblue>What is the point of this section? How are these equations about tangent circles relevant to the rest of the page? If you're just establishing them here so that you can use them later, you need to say that.</font><br />
====Concentric Circles Formula====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): Again, what on earth is the purpose of this section? Give me some context so I'm not so confused! :(</font><br />
====Circle to Circle Inversion====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):</font><br />
*<font color=dodgerblue>First of all, context! Context, context, context! I am so very very confused. Why are we doing any of this????</font><br />
*<font color=dodgerblue> ''Points (C, C'), (B, B') are inverses with respect to J \Rightarrow points C, C', B, B' are concyclic''<br />
::I've gotta question your notation here - I thought that C, C', B, and B' were all points in their own right. Why are you making ordered pairs out of points? Or are they not points after all? If they're not points, what are they?</font><br />
*<font color=dodgerblue>In this whole section, I think you need a little more explanation than just all these arrows - what you've got is technically correct as a proof, but it'd be a lot more readable if you sort of embedded it in explanatory sentences. (This is what Richard was talking about in his earlier comment.)</font><br />
*<font color=dodgerblue>Why did we stop where we did? What is the significance of that result? Also, fix that period that's just sorta chillin by itself at the end here.</font><br />
<br />
*<font color=orangered>What's a cyclic quadrangle? <br />
*Try to add overlines to all of your formulas in this section? <br />
[[User:Rscott3|Richard]] 7/18</font><br />
<br />
====Steiner Chain Construction via Inversion Formulas====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*''An inversion can be done on a symmetrical arrangement of n circles (shown in Figure 3) in a region between two concentric circles, one with radiusR and the other with radius r. ''<br />
::I have no idea what this sentence means. Also, what is the purpose of this section? What are we trying to accomplish in it?</font><br />
*<font color=dodgerblue>''This arrangement is represented by: [math stuff]''<br />
::What arrangement? And where did that math come from? :( :( so confused.</font><br />
*<font color=dodgerblue>Again, you need to provide some explanation with your math. I have no idea what you're trying to do or how you're doing it, and also I don't like this format where you say "X=Y! Therefore, Z=W!" and ''then'' have an expandable section showing how you get from X=Y to Z=W - I think the explanation should come in the middle of the two statements.</font><br />
<font color=orangered>Do you have a figure 1 and 2? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
<br />
<font color=orangered>See my comment from the last time. And also where did you get these formulas? I'm not exactly sure how you got them.<br />
<br />
You've got an "is" "are" problem in the sentence starting with "The lengths of the radii of the tangent circles..."<br />
[[User:Rscott3|Richard]] 7/18</font><br />
<br />
====Types of Steiner Chains====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): This section needs to be at the top of the page! These sections define important terms that I need to understand before I can understand the statement of Steiner's Porism. They should '''not''' be hidden down here! It should go at the top of the MME or even the bottom of the Basic Description - this is actually more important to understand what's going on with the page than the steps to constructing a Steiner Chain are, imo.</font><br />
:::<font color=orangered>Agreed 100%. [[User:Rscott3|Richard]] 7/18</font><br />
=====Closed Steiner Chains=====<br />
=====Open Steiner Chains=====<br />
=====Multicyclic Steiner Chains=====<br />
=====Annular Steiner Chains=====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): I'd like to see an example of a non-annular Steiner Chain in this section, just for contrast.</font><br />
<br />
*<font color=orangered> This type reminds me of a gun cylinder/barrel thing!...Why It's Interesting maybe????? Steiner Chain in real life? http://www.pyramydair.com/blog/images/ar6-cylinder-web.jpg [[User:Rscott3|Richard]] 7/18<br />
</font><br />
<br />
}}</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Steiner%27s_Chain&diff=26930Talk:Steiner's Chain2011-07-22T13:05:07Z<p>Rebecca: /* Quality of Prose and Page Structuring */</p>
<hr />
<div>==Messages to the Future==<br />
* Provided precise suggestions for what could be added in the future<br />
* <font color=darkred> '''The applet on the [[Inversion]] Page does something similar to the applet that you want. Did you put up a request on the [[Math Tools Requests]] page?''' </font><br />
<br />
==References and Footnotes==<br />
* Provided references of all websites and articles used at the bottom of the page<br />
* Gave credit to image creators in all circumstances<br />
* Images throughout the page (speaking of those excluding the main image) show how they were created by me by clicking on the image<br />
<br />
==Good Writing==<br />
* Applied all of the suggestions I received for this page<br />
* Went through numerous drafts and had the page reviewed by many students as well as my professor<br />
<br />
===Context===<br />
* Full of context, especially at the beginning of each section as well as between steps in mathematical equations<br />
* I didn't include a "Why it's Interesting" section because I was unable to find any real-world applications of this topic, even though one was suggested to me on this discussion page by a fellow student, I wasn't able to locate any verifiable sources to prove this.<br />
<br />
===Quality of Prose and Page Structuring===<br />
* Provided a purpose for each section and included it in the first few sentences of the section. <br />
* In the "Basic Description" I tried to layout exactly what I was doing for the reader<br />
*<font color=darkred> The paragraph that begins "With these measurements we can say that" is confusing. I suggest breaking all equations onto different lines, since they run into each other right now. Also, try to provide the justification for the equation ''before'' you write the equation instead of after. <br />
'''*I'm having trouble understanding the relevance of the following sentence to the rest of the page: "When two circles are concentric, the area of the annulus in between is the area of the large circle minus the area of the small circle: <math>\text{Area of Annulus} = \pi(R^2 - r^2) </math>" </font>'''<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 13:05, 22 July 2011 (UTC) “Now, a Steiner chain does not always have to consist of a circle inside the other” This is unclear to me. Do you mean “Now, a Steiner chain does not always consist of a collection of circles within one larger circle”?<br />
</font color><br />
<br />
===Integration of Images and Text===<br />
* Used many many images to explain my topic<br />
* Constantly encouraged my reader to refer to my figures<br />
<br />
===Connection to other Mathematical topics===<br />
* Provided one link to another page for readers to refer to for a better explanation of a specific term<br />
*<font color=darkred> We have a page on [[Inversion]] that definitely should be linked by your page. Also, since your algebraic discussion very closely mirrors [[Problem of Apollonius]], that page should also be linked. </font><br />
<br />
===Examples, Calculations, Applications, Proofs===<br />
* Provided numerous thorough examples<br />
* Included proofs where necessary <br />
* Included context between difficult steps in algebra<br />
*<font color=darkred> '''Is there a way to construct other annual steiner's chains by using polygons other than triangles? It'd be great to have a note about whether or not you can use the same process with other regular polygons.<br />
:I didn't see any change related to this comment. '''<br />
*You need to explain a bit more of how you go from this statement "1. We can see that C, B, C', B' form a quadrilateral and one of the most basic theorems about quadrilaterals says that their opposite angles are supplementary." to the angle equality below it. You definitely skip a step of reasoning that should be stated explicitly.</font><br />
<br />
===Mathematical Accuracy and Precision of Language===<br />
* Tried to clearly explain topics in the most simple words<br />
* Included mouse-overs very often<br />
*<font color=darkred> In your basic description, can you clarify if Steiner's Chains have to have one circle totally inside another? That seems to be the case, but you don't say it explicitly <br />
*This sentence: "points C' and B' are concyclic as are points C and B." is confusing given your definition of concyclic. Points C' and B' don't lie on the same circle as you show in the image, rather one is the center and the other is on the outside. Can you clarify what you mean? </font><br />
<br />
===Layout===<br />
* Organized well, with little white space<br />
* Utilized features such as hide/show as well as mouse-overs<br />
* Organized into understandable sections<br />
*<font color=darkred> '''I'd encourage making this sentence: "By inverting points along all the circles of the Steiner chain, another can be formed that differs slightly from the original but still maintains the properties specific to Steiner chains (which are mentioned above under "Basic Description")". it's own paragraph. That will make the reader pause more after the link to inversion and click the link if they need more information''' </font><br />
<br />
=General comments=<br />
{{hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:20, 28 June 2011 (UTC): You've got some great pictures, and it looks like you know what you're talking about, but you need to do a much better job of defining they key terms (Steiner's Porism, Steiner chains) and of explaining what you're doing and why you're doing it. I read the whole page carefully more than once, and I'm still confused about what's going on.</font><br />
<br />
<font color=orangered><br />
Hey Anna!<br />
<br />
Cool page! One comment that I got a lot from the people who worked on this last summer, was that when I have math writing, like you do with your proofs, to explain what happens from one line to the next.<br />
Like this:<br />
</font><br />
<br />
<math> \sin \frac{\pi}{n}= \frac{R-r}{R+r}</math><br />
<br />
Multiplying both sides by <math>R+r</math> gives us<br />
<br />
<math> \sin \frac{\pi}{n} (R+r)= R-r</math><br />
<br />
Distribution gives us<br />
<br />
<math> R \sin \frac{\pi}{n} + r\sin \frac{\pi}{n} = R - r</math><br />
<br />
After we subtract <math>R, r</math> from both sides, we have<br />
<br />
<font color=orangered><br />
...and so on and so forth.<br />
<br />
Becky left a ton of comments on the the discussion page for [[Law of Sines]] about this in hot pink if you need any reference. That page has a lot of math writing.<br />
<br />
Richard 6/13<br />
<br />
</font><br />
<br />
=Section-specific comments=<br />
==Intro==<br />
<font color=orangered>You mention circles, but your main picture has spheres. Maybe mention spheres in this part? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*You should link to [[Inversion]] in this section. It's not a perfect page, but what's there will definitely help people understand inversion.</font><br />
*<font color=dodgerblue>''A Steiner chain is a figure of tangent circles'' - sounds awkward. Might be better to say it's "made of" tangent circles.</font><br />
*<font color=dodgerblue>This section really doesn't help me understand what a Steiner chain or Steiner porisms are ''at all''. I see that you have a bit more of an explanation in the original caption, but you should really move that down here or at least say the same thing with different words here. Since the caption comes before the TOC, a lot of people tend to skip over it.</font><br />
*<font color=dodgerblue>Also, you need to offer some sort of explanation as to what a "porism" is - is "Steiner's porism" synonymous with "a Steiner chain"? Because the only term you've used so far is "Steiner chain", and I'm very confused as to why the page is called "Steiner's Porism" and not "Steiner chains".</font><br />
*<font color=dodgerblue>You end this bit by saying something about the "properties of a Steiner chain" - what are these properties? You should at least touch on them somewhere in the basic description. This will also help give context to the two construction sections that follow - give me something so that I can kind of see why we're doing what we're doing, and how we know when we've succeeded in creating a Steiner chain. To be honest, I read this whole section and still didn't really know what a Steiner chain was besides a picture involving circles. You need to give some sort of definition, and not just a description of how to make one example.</font><br />
<br />
<font color=orangered>I'm not sure I understand your definition of inversion in this section. And you should say something about reflection fixing the points the same distance from the line as they start out. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
===Creating a Steiner Chain===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*Unsure why you would say "regular triangle" - I think "equilateral triangle" is a much more familiar term for most people.</font><br />
*<font color=dodgerblue>''Using the points of <math>\triangle XYZ</math> as centers, construct tangent circles <math>X,Y,Z</math>…''<br />
::Upon re-reading, I'm pretty sure you mean that XYZ are tangent to each other, but at first I thought you meant that they were tangent to the original circle, which they're not. Consider rewording this sentence.</font><br />
*<font color=dodgerblue>Is the picture at the end of this section a Steiner chain? If so, please say so. If not, what is it? As it is, the section ends rather abruptly.</font><br />
<br />
<br />
*<font color=orangered> By your definition, the main image is not concentric circles. You may want to make sure that this is just one particular way of making a Steiner chain. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
===Creating a Steiner Chain using Inversion===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*''Construct an inversion circle to reflect over the three tangent circles and the two concentric circles. ''<br />
::This sentence confused me. The way you've phrased it sounds as though the new circle you're creating is the one that's going to be reflected - "Construct an inversion circle that will then be reflected over the three tangent circles and the two concentric circles," whereas I'm pretty sure you mean to say "Construct an inversion circle to reflect the three tangent circles and the two concentric circles over." If you're uncomfortable with ending the sentence with a preposition, try "Construct an inversion circle over which the three tangent circles and the two concentric circles will be reflected." Also, there's no need to call that figure "the three tangent circles and the two concentric circles" - call it "the Steiner chain" or "our previous figure" or something.</font><br />
<br />
<br />
*<font color=dodgerblue>The last image in this section is kind of huge. Make sure it's on a different line than your text - it splits the paragraph up weird. And maybe make it a tiny bit smaller?</font><br />
<br />
*<font color=dodgerblue>This may just be part of my general confusion over what Steiner chains actually are, but why do we want to create a new Steiner chain by inversion? What is the purpose of doing this? Just for fun?</font><br />
<br />
*<font color=orangered>I'm not sure that I understand all of the elements of this last picture. Nothing is tangent to the big circle. I assuming you can make a Steiner chain by inversion without being tangent? (I thought they were supposed to be) And why are there different sized circles within the smaller one? Is it a proportional thing? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
==A More Mathematical Explanation==<br />
===Formulas===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*I don't understand why you have this section heading. First of all, it's the wrong size - it's hidden inside the MME, but if you look at the TOC it's not listed as a sub-section of the MME - to fix that you need to add another equals sign on either side of the heading. But there's nothing in the MME that's not also inside Formulas, so it seems to me that all you've done is re-name your MME, which doesn't seem necessary - all of the subheadings say "Formula" in them…</font><br />
<br />
*<font color=dodgerblue>So Steiner's Porism is a ''theorem'' about Steiner chains? You NEED to explain this above, even if you don't want to state the full thing. You just can't have a page about something and not even show what that thing is except for inside a hidden section.</font><br />
<br />
*<font color=dodgerblue>Also, you need to actually ''explain'' the Porism - I'm not stupid, and I have almost no idea what it's actually saying. What is the "starting circle" of a Steiner chain? What does it mean for a Steiner chain to "close"? What are the "loops" of a Steiner chain? Try to rephrase this statement using just the terms you've introduced in the basic description (and then move that simpler statement ''to'' the basic description!). Also, why is it called a "Porism" and not a "theorem"?</font><br />
:::<font color=orangered>I second Kate here. What's a Porism? It's sort of like this is just hanging out here. [[User:Rscott3|Richard]] 7/18</font><br />
<br />
<br />
====Tangent Circles Formula====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*In your first image in this section, the ordered pairs for the points aren't close enough to the arrows showing which points they belong to.</font><br />
*<font color=dodgerblue>What is the point of this section? How are these equations about tangent circles relevant to the rest of the page? If you're just establishing them here so that you can use them later, you need to say that.</font><br />
====Concentric Circles Formula====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): Again, what on earth is the purpose of this section? Give me some context so I'm not so confused! :(</font><br />
====Circle to Circle Inversion====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):</font><br />
*<font color=dodgerblue>First of all, context! Context, context, context! I am so very very confused. Why are we doing any of this????</font><br />
*<font color=dodgerblue> ''Points (C, C'), (B, B') are inverses with respect to J \Rightarrow points C, C', B, B' are concyclic''<br />
::I've gotta question your notation here - I thought that C, C', B, and B' were all points in their own right. Why are you making ordered pairs out of points? Or are they not points after all? If they're not points, what are they?</font><br />
*<font color=dodgerblue>In this whole section, I think you need a little more explanation than just all these arrows - what you've got is technically correct as a proof, but it'd be a lot more readable if you sort of embedded it in explanatory sentences. (This is what Richard was talking about in his earlier comment.)</font><br />
*<font color=dodgerblue>Why did we stop where we did? What is the significance of that result? Also, fix that period that's just sorta chillin by itself at the end here.</font><br />
<br />
*<font color=orangered>What's a cyclic quadrangle? <br />
*Try to add overlines to all of your formulas in this section? <br />
[[User:Rscott3|Richard]] 7/18</font><br />
<br />
====Steiner Chain Construction via Inversion Formulas====<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC):<br />
*''An inversion can be done on a symmetrical arrangement of n circles (shown in Figure 3) in a region between two concentric circles, one with radiusR and the other with radius r. ''<br />
::I have no idea what this sentence means. Also, what is the purpose of this section? What are we trying to accomplish in it?</font><br />
*<font color=dodgerblue>''This arrangement is represented by: [math stuff]''<br />
::What arrangement? And where did that math come from? :( :( so confused.</font><br />
*<font color=dodgerblue>Again, you need to provide some explanation with your math. I have no idea what you're trying to do or how you're doing it, and also I don't like this format where you say "X=Y! Therefore, Z=W!" and ''then'' have an expandable section showing how you get from X=Y to Z=W - I think the explanation should come in the middle of the two statements.</font><br />
<font color=orangered>Do you have a figure 1 and 2? [[User:Rscott3|Richard]] 7/18</font><br />
<br />
<br />
<font color=orangered>See my comment from the last time. And also where did you get these formulas? I'm not exactly sure how you got them.<br />
<br />
You've got an "is" "are" problem in the sentence starting with "The lengths of the radii of the tangent circles..."<br />
[[User:Rscott3|Richard]] 7/18</font><br />
<br />
====Types of Steiner Chains====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): This section needs to be at the top of the page! These sections define important terms that I need to understand before I can understand the statement of Steiner's Porism. They should '''not''' be hidden down here! It should go at the top of the MME or even the bottom of the Basic Description - this is actually more important to understand what's going on with the page than the steps to constructing a Steiner Chain are, imo.</font><br />
:::<font color=orangered>Agreed 100%. [[User:Rscott3|Richard]] 7/18</font><br />
=====Closed Steiner Chains=====<br />
=====Open Steiner Chains=====<br />
=====Multicyclic Steiner Chains=====<br />
=====Annular Steiner Chains=====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:17, 28 June 2011 (UTC): I'd like to see an example of a non-annular Steiner Chain in this section, just for contrast.</font><br />
<br />
*<font color=orangered> This type reminds me of a gun cylinder/barrel thing!...Why It's Interesting maybe????? Steiner Chain in real life? http://www.pyramydair.com/blog/images/ar6-cylinder-web.jpg [[User:Rscott3|Richard]] 7/18<br />
</font><br />
<br />
}}</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Inscribed_figures&diff=26905Talk:Inscribed figures2011-07-22T04:21:08Z<p>Rebecca: /* General Comments */</p>
<hr />
<div>=General Comments=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:53, 18 July 2011 (UTC): The page is looking a little messy right now, there's a lot of text floating around in the top left. I think it's because you left your first couple of balloons empty?</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:17, 18 July 2011 (UTC): In general, this page needs a lot more actual geometry in it. The mosaic is nice to look at, and the Eye is kinda cool, but a page about inscribed figures should really have some classic geometry and proofs. For example, you mention that inscribed figures can be used to prove the Pythagorean Theorem - why don't you put that proof in?</font><br />
<br />
<font color=orangered>[[User:Rscott3|Richard]] 7/6 Gave Dayo a hand getting the page started.</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): Your main image is a little grainy - are there any higher quality images available? Or could you maybe make the image a little smaller?</font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:05, 9 July 2011 (UTC) Nice work Dayo. This is a really good start to a page. I'd challenge you to finish this page by the end of the summer. You'll have to really commit your time to it because you're getting started late, but it is a great topic for an image page.<br />
</font color><br />
<br />
<font color=red><br />
*[[User:Rebecca|Rebecca]] 01:54, 22 July 2011 (UTC) Dayo and I discussed some ideas for this page on Wednesday. Essentially he will be adding more to the section on the London Eye. <br />
*[[User:Rebecca|Rebecca]] 04:21, 22 July 2011 (UTC) Dayo- I finally had the chance to read through your page in its entirety again. I think you should forget about making a new main image and spend Friday and whatever makeup days you have on finishing the London Eye section. I realized that your main image is more connected than I originally thought, and this page really needs some more content. <br />
</font color><br />
<br />
=Section specific comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): Typo! ''It is considered one of the finest examples of ceramic inlay,radiative geometry, and use of inscribed figures in art.''<br />
::(you need a space between "inlay," and "radiative".)</font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 00:59, 9 July 2011 (UTC) You need to add mouseovers for ceramic inlay, radiative geometry, inscribed.<br />
</font color><br />
<br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:59, 18 July 2011 (UTC):<br />
*''An inscribed or "cyclic" figure is one which fits "snugly" into another larger shape;''<br />
::Looks to me like you're defining "inscribed" and "cyclic" here, so to follow our established conventions for definitions, you should bold them:<br />
:::''An '''inscribed'' or '''cyclic''' figure is…<br />
</font><br />
<br />
*<font color=dodgerblue>The separate subsection for "Applications" looks weird to me, maybe you should consider just having that be a second paragraph without another header.</font><br />
<br />
*<font color=dodgerblue>It seems wrong to me to say that inscribed figures ''are'' a proof of the Pythagorean theorem, because it's an application, not a definition or necessary characteristic. I'd much rather it said that inscribed figures ''can be used to prove'' the Pythagorean theorem.</font><br />
<br />
*<font color=dodgerblue>I really think this section needs some small pictures showing simple inscribed figures. Maybe three or four 150px by 150 px images showing like, a square in a circle, a triangle in a square, etc…</font><br />
<br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:01, 9 July 2011 (UTC) This is a good way to start the page, but you should make a picture that is simpler and shows how a figured is inscribed. For example, a square with a circle inside. You could even cut this section out and just put this sentence in the mouseover for "inscribed" along with the picture. <br />
* If you don't decide to just put this section in a mouseover, it might be nice to expand on it a bit.<br />
</font color><br />
<br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): <br />
*''For a a breakdown of the image: see below. ''<br />
::Punctuation isn't quite right, try "For a breakdown of the image, see below:"</font><br />
<br />
*<font color=dodgerblue>I know you're just getting off the ground, but make sure that when you write this up, you provide words to go with the pictures! Tell the reader what they're supposed to be observing.</font><br />
<br />
==More Mathematical Explanation==<br />
===Inscribed Figures applications===<br />
==="Example 1: constructing a star and The Walls of The Salon del Trono"===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:13, 18 July 2011 (UTC):<br />
*This section heading seems weird to me, I think it should be a subsection of "Inscribed Figures applications" not on an equal level. Also, there shouldn't be quotation marks around the header, and your capitalization is weird. I'd write: ''Example 1: Constructing a star and the walls of the Salon del Trono''</font><br />
<br />
*<font color=dodgerblue>You should proofread this section. There are a couple sentences that aren't capitalized, and there's one place where you say "orig" when I think you mean "origin". </font><br />
<br />
*<font color=dodgerblue>Your explanation of what's going on in the pictures is pretty clear, but what's not clear is the connection to inscribed figures. You need to make a bigger deal of it at the start of the section, explicitly state that the picture was constructed using inscribed figures and now you're going to walk through the construction.</font><br />
<br />
==="Example 2: The London Eye"===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:13, 18 July 2011 (UTC):<br />
*Again, I don't think the section heading should be in quotation marks here.</font><br />
*<font color=dodgerblue>I assume you're going to expand this section, when you do, make sure you explain what the Eye is, in case readers haven't heard of it, and try and find a picture of it to include. Also, it'd be great if you could tie this in to some geometry - are there any cool proofs that involve pentagons?</font><br />
<br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:02, 9 July 2011 (UTC) You should remove the sentence "proof of pythagorean theorem using Ptolemy's Theorem. That's not what you're doing in this section. Instead, why don't you introduce the fact that you will construct a star using inscribed figures.<br />
* You need to add another paragraph after the one beginning with "example 1: constructing a star...". In this paragraph you can explain in more detail how the squares are inscribed. Then refer to the picture so that readers can see. <br />
* "At every place where the inscriptions’ extended edges meet the edges of the original rectangle, a point is made." What about if you change this to "Each corner of the inscribed squares touches the side of a larger square. At these intersections, a point is made." What you said originally isn't exactly true because the smallest inscribed square's corners touch the middle sized square's edges, not the original squares edges like you said. <br />
* You jump from an image where there are points on the edge of the biggest square as well as inside of that square to a new image where all the points are on the outside. You need to explain this transition and probably add more pictures in between. <br />
* There's no reason to label the points of the star and the squares if you're not going to refer to them. It just clutters the images. <br />
* I think you need another image to illustrate one ray connecting a quarter mark to the nearest perpendicular halfway mark. You should label these points and show a blue line going through them. Then you can jump to the images where you have all these blue lines and the star is generated. Also, are these lines actually rays like you said? Or are they just lines? <br />
* "Connecting the edges of the star with every other edge yields the outermost points of the central star." This doesn't really make sense. I don't think it's what you're doing actually. You're drawing lines from the points of the star to the intersections of the blue lines, right? When you're explaining the images, the best thing to keep in mind is that someone should be able to follow your directions and execute the step without the image. This sentence is too vague for anyone to be able to do that. <br />
* Nice images.<br />
* I'm excited to read about the London Eye (capitalize both London and Eye). This will be your second example by the way, not example three like you have written. <br />
</font color></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=S11&diff=26900S112011-07-22T02:06:39Z<p>Rebecca: /* Dayo's Projects */</p>
<hr />
<div>__TOC__<br />
<br />
== Announcements ==<br />
For public-type help questions, see [[Help:Contents|Help]]. For Swat-specific ones, see [[Swarthmore summer research orientation]].<br />
<br />
<b>Remember to keep your projects sections short and up to date; only the last week of status changes should be mentioned. [[User:Smaurer1|Smaurer1]]</b><br />
<br />
===Group Discussion Questions===<br />
<br />
* [[Topics for conversations through Skype with RPI, SB, and/or Drexel]] Started 6/29.<br />
* [[Who are we writing for?]] Started 6/29.<br />
* [[Possibly expanding student Math Image roles]], to be addressed 7/6.<br />
<br />
===Questions:===<br />
*Things that are listed as Helper Pages but use the Image Page template<br />
:We need to decide whether these pages should be on the Helper Page template, the Image Page template, or both: {{Hide|1=<br />
:*[[Change of Coordinate Systems]] - Image template only; image template live<br />
:*[[Conic Section]] - both templates; image template not live<br />
:*[[Differentiability]] - both templates; image template not live<br />
:*[[Dot Product]] - Image template only; image template not live<br />
:*[[Gradients and Directional Derivatives]] - Image template only; image template not live<br />
:*[[Hyperbolic Geometry]] - Image template only; image template not live<br />
:*[[Inversion]] - Image template only; image template not live<br />
:*[[Iterated Functions]] - Image template only; image template not live<br />
:*[[Parametric Equations]] - Image template only; image template live<br />
:*[[Taylor Series]] - Image template only; image template not live<br />
:*[[Volume of Revolution]] - Image template only; image template live<br />
<br />
:<font color=dodgerblue>''(List complied by [[User:Kderosier|Kate]], June 16)''</font><br />
}}<br />
<br />
<br />
Older questions: {{Hide|1=<br />
*Harrison's question about text being cut off on Cross-cap: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 14:16, 8 June 2011 (UTC)<br />
**The text in MME on the [[Cross-cap]] page is getting truncated when viewed through edit with form, but still appears on the page.<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 00:49, 14 June 2011 (UTC): When I've encountered this problem previously, it's been because a set of double curly brackets wasn't closed.</font><br />
}}<br />
<br />
*Harrison's question about creating a list of not-yet-existent Helper Pages: {{Hide|1=<br />
Harrison, 5/26/11:<br />
:*<s>We need a list of empty pages: Penrose Tiles is only linked to one, now two, pages. Empty pages like this could well fade into obscurity.</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:09, 7 June 2011 (UTC): Such a list has been created. See [[Existing_Pages_Needing_Work#Empty_.28but_linked_to.29_Pages|here]].</font><br />
}}<br />
<br />
*Spam conversation: {{Hide|1=<br />
<font color=dodgerblue><br />
*[[User:Kderosier|Kate]] 14:38, 27 May 2011 (UTC): '''We have some new users who are creating a bunch of pages with links to illegally download or watch movies.''' At first, we though it might be someone from Sweet Briar practicing wiki-syntax, but now it's just starting to look like spam:<br />
**[[Watch_Sniper:_Reloaded_film_in_hd|This is the type of page I'm talking about]]<br />
**[[Special:Contributions/Calrivenick|List of pages created by Calrivenick]]<br />
**[[Special:Contributions/Cadedesi|List of pages created by Cadedesi]]<br />
</font><br />
:Let's talk about what to do this afternoon. [[User:Gene|Gene]] 15:19, 27 May 2011 (UTC)<br />
:<font color=dodgerblue>This problem has continued over the weekend. Someone spammed the talk page for Fun Topology with comments about buying Cialis and stuff. They also posted a lot more movie download pages under the Cadedesi username. I'm going to go through and delete again.</font><br />
:<font color=dodgerblue>The spam comments on Fun Topology were coming from this computer's IP address. </font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 14:34, 6 June 2011 (UTC): Haven't seen any more spam activity for a few days. I assume some computer people have handled the issue? I'm going to hide this conversation so that it's not taking up space on S11.</font><br />
}}<br />
<br />
*Citations/footnotes conversation: {{Hide|1=<br />
:I spent a really long time wandering around MediaWiki and Wikipedia this morning trying to figure out how to do footnotes/citations the way I wanted to - now that I know how, should I add instructions to one of the many help mages on Math Images? If so, which page? (Kate, 5/17)<br />
<br />
:<font color=red> Answer: put it here at [[Help:Wiki_Tricks|Wiki Tricks]] (XD, 5/17) </font><br />
<br />
:[[User:Smaurer1|Smaurer1]] 19:43, 17 May 2011 (UTC) Well, it's not clear that webarticles should have footnotes, although Wikipedia does. In text references may be better. This is surely something we should discuss as a group, and find out what last year's group decided, if they did. If there are footnotes, there has got to be a way to get back seamlessly to where you were before you jumped to the footnote.<br />
<br />
:Also, as for citations, we should be uniform in their format.<br />
<br />
:Finally, you can use 4 tildes to put your username and time stamp on your comments, and 3 tildes for just your username. <br />
<br />
:<font color=dodgerblue>Well, I wasn't doing comment-y type footnotes, I just wanted specific sentences to link to items in my References section. I think that format is better than full intext-citations, because it brings you to the source if that's what you're interested in, but it takes up less space if you're not. The references template we have comes equipped with little links to jump you back up, too- if you look at the [[Quipu#References|Quipu]] page, you can see that it lists each of the sections that reference is linked from, and those links bring you to the reference in that section. All in all, I think it's a clear and intuitive way to do references for both the writer and the reader (although, like most things, it doesn't play well with our hidden sections), and I'm going to go ahead and put the instructions up in WikiTricks. -[[User:Kderosier|Kate]] </font><br />
<br />
{{Hide|1=<br />
*What the help pages say now:<br />
**[[Tour_the_Math_Images_Project#Anatomy_of_a_page|The Tour page's "Anatomy of a page" section]]<br />
**[[Checklist_for_writing_pages#References_and_footnotes|The "References and footnotes" section on the checklist for writing pages]]<br />
*The way to do Wikipedia-like references:<br />
**[[Wiki_Tricks#How_to_do_Citations|Wiki Tricks - Citations section]]<br />
}}<br />
<br />
}}<br />
<br />
*Invisible Comments conversation: {{Hide|1= One of you asked "How do you put invisible comments in the source code?"<br />
<br />
:Answer: Same way you do in html, like this <nowiki><br />
:<!-- hidden stuff --><br />
:</nowiki><br />
:However, if you want to make comments about an article for its author, the comments are more likely to be seen if you either<br />
:* put it in the discussion page, or<br />
:* if it is important to put it right by the material commented on, put it in the article in color with your username and time stamp included.<br />
<br />
:Hidden comments in the source code are likely to be overlooked, except perhaps if they are written by the author him/herself, as a note for further development.<br />
}}<br />
}}<br />
<br />
== Current Individual Projects ==<br />
<br />
===Steve M (aka Prof Maurer)'s Role===<br />
{{Hide|1=<br />
My role is 2-fold:<br />
<br />
<ol><br />
<li> Come see me to sound me out (if you wish) on the mathematical appropriateness of an idea for a page, or for possible references.<br />
<br />
<li> Once you have a reasonable amount written, and want feedback on the quality and correctness of the mathematical exposition, ask me to look it over and then we will have a conference. (Abram and the oldies are as good as I am at discussion general organization and clarity issues.) <br />
</ol><br />
<br />
We have agreed to put a record on this S11 page of what we are doing and what help we want from others, but in addition tell me in person or by email if you want to conference with me.<br />
}}<br />
<br />
===Harrison's Projects===<br />
<br />
[[Harrison's detritus]]<br />
<br />
*[[User:Htasoff|Htasoff]] 23:44, 13 July 2011 (UTC) Pages will be submitted for final review in 1 - 3 days. A few, final comments are welcome. Real Projective Plane is still in the works, though.<br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:19, 14 July 2011 (UTC): Hey Harrison, do you know if that one picture in inverse trig that you got from somewhere on the internet is a picture we can use? Can you check please?</font><br />
<br />
[[Rope around the Earth]]<br />
:<font color=darkred> Approved </font><br />
<br />
<font color=darkred> I have one small suggested wording comment for you on [[Congruent triangles]], then it's good to go. [[User:AnnaP|AnnaP]] 13:48, 21 July 2011 (UTC)</font><br />
<br />
===Richard's Projects===<br />
<br />
<br />
<font color=orangered> <br />
<br />
:APPLET INFO:<br />
:{{Hide|1=<br />
<br />
[[User:Alimurreza|Alimurreza]] 02:53, 6 July 2011 (UTC)I am working on your applet. Check this out here @([http://mathforum.org/mathimages/index.php/DU11 Reza's work]).<br />
:APPLET UPDATE:[[User:Alimurreza|Alimurreza]] 02:41, 15 July 2011 (UTC)I am done with Ambiguous Case applet. Please, check the applet. Feel free to send me any feedback or change-request.<br />
What i want mine to look like, but http://www.mccsc.edu/~aterwill/ambiguouscaseapplet/Ambiguous_Case_applet.html doesn't show the completed triangles.<br />
<br />
I like how this one shows the completed triangles<br />
http://www.mnwest.edu/fileadmin/static/website/dmatthews/Geogebra/AmbiguousCase01.html<br />
<br />
}}<br />
<br />
'''Completed Pages'''<br />
*[[Ambiguous Case]] [[User:Rscott3|Richard]] 7/19<br />
<br />
*[[Law of cosines]]<font color=orangered> [[User:Rscott3|Richard]] 6/23</font><br />
<br />
*[[Law of Sines]] [[User:AnnaP|AnnaP]] 7/7<br />
<br />
*[[Solving Triangles]] 7/12<br />
<br />
:Other ideas: {{Hide|1=<br />
*inscribed angles?<br />
<br />
*Normal Distribution?<br />
<br />
*Birthday Paradox?<br />
}}<br />
</font><br />
<br />
===Dayo's Projects===<br />
Current projects<br />
*[[Inscribed figures]] : there's a [[Compass & Straightedge Construction and the Impossible Constructions]] page, but I think that inscribed figures deserves its' own page. What do others think? <br />
::<font color=slateblue> [[User:Rebecca|Rebecca]] 01:07, 9 July 2011 (UTC) I left comments on the discussion page. </font color><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 15:23, 18 July 2011 (UTC): I left you some comments!</font><br />
::<font color=slateblue> [[User:Rebecca|Rebecca]] 02:06, 22 July 2011 (UTC) Dayo has suggestions from me from Wednesday night </font color><br />
<br />
Future Projects: {{Hide|1=<br />
*[[Mathematics in architecture]]:make changes akin to [[Math for Computer Graphics and Computer Vision]], including:<br />
<br />
::*[[Cross sections]]: calculus application page, including examples of Tokyo international Forum, Suransuns Bridge, and other structures which could be thought of and put together easily in terms of their cross sections <br />
::*[[Torus]] edits, additions concerning the Torus in construction and architecture<br />
::*[[Domes]]:conic sections, arches, parabolas<br />
::*[[The Henderson Waves Bridge]]: sinusoids in architecture, parametric design<br />
::*[[Catenary]]: More real world examples: namely bridges<br />
::*[[Bridge of Peace]]: The equation(s) used to generate the surface, possibly words from the architect, very new, may be hard to get concrete technical information <br />
::*[[Kurilpa Bridge]]: Everyone have a look at the image and tell me what kind of actual subjects you could find in it, namely in the cables and tubes.<br />
::*Teaching Materials(6/30): ''growing up with science: projects'' could be the sort of activities we're looking for. I used these with a class, and think people should look at them.<br />
<br />
<br />
<br />
<br />
}}<br />
<br />
on hold: <br />
*[[Parametric Equations]]: integrating Xingda's page from [[S10]] into page.<br />
<br />
===Diana's Projects===<br />
<br />
====Current====<br />
*[[String Art Calculus]]<br />
<br />
*[[Logistic Bifurcation]]<br />
:<font color=darkred> I've put up comments. There are a few places that could use some work. [[User:AnnaP|AnnaP]] 7/10 </font> <br />
:<font color=slateblue> [[User:Rebecca|Rebecca]] 02:26, 16 July 2011 (UTC) This is a very impressive page. I put up a few small suggestions on the discussion page. </font color><br />
<br />
*[[Markus-Lyapunov Fractals]]<br />
:<font color=darkred> Approved [[User:AnnaP|AnnaP]] 7/14 </font><br />
<br />
====Ideas for later projects====<br />
{{Hide|1=<br />
*Chirikov-Taylor Maps<br />
**This seems like a natural extension of the Markus-Lyapunov Fractals page, but maybe the math involved in the two is too similar?<br />
*This aspect of pendular motion:<br />
**[[http://www.youtube.com/watch?v=yVkdfJ9PkRQ&feature=player_embedded|Varied-Length Pendulums]]<br />
**I'm not sure how or whether to use this -- does a ''moving'' image count as a "math image"? -- But it's incredible, and I'd love to explore it.<br />
*Kuen Surface<br />
**It's just really cool.<br />
}}<br />
<br />
===Kate's Projects===<br />
*[[Anne Burns' Mathscapes]] (Scrapped out of [[Mountains In Spring|three]] [[Mathscape|other]] [[Fractal Scene I|pages]]):<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:29, 18 July 2011 (UTC): As soon as I get confirmation that Anne Burns doesn't mind us using her images, I'll submit this for final review.</font><br />
<br />
*Finished pages: {{Hide|1=<br />
*[[Perko pair knots]]:<br />
:<font color=darkred> Approved </font><br />
<br />
:*[[Critical Points]]:<br />
::<font color=darkred> Approved, but I did have one note on whether or not you intended to add something. It's fine as is, but I wanted to put up a suggestion. [[User:AnnaP|AnnaP]] 16:24, 15 July 2011 (UTC) </font><br />
:::<font color=dodgerblue>I responded to that note.</font><br />
<br />
:*[[Summation Notation]]:<br />
::<font color=darkred> Approved [[User:AnnaP|AnnaP]] 16:24, 15 July 2011 (UTC) </font><br />
<br />
:*[[Bases]]:<br />
:: <font color=dodgerblue>[[User:Kderosier|Kate]] 17:31, 11 July 2011 (UTC): Changed things in response to Chris' comments.</font><br />
<br />
:* [[Quipu]]:<br />
::<font color=darkred> Put up as ready for the public 6/30 [[User:AnnaP|AnnaP]] </font><br />
<br />
:* [[Basic Trigonometric Functions]]:<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 18:11, 30 June 2011 (UTC): Changed the the things that were bolded.</font><br />
<br />
<br />
}}<br />
<br />
===Leah's Projects===<br />
*[[Bedsheet Problem]]<br />
going to do last edits [[User:Ljeanlo1|Ljeanlo1]] 23:57, 20 July 2011 (UTC) <br />
<br />
*[[Boy's Surface]] <br />
: take a look on this tomorrow. [[User:Ljeanlo1|Ljeanlo1]] 23:57, 20 July 2011 (UTC) <br />
: <font color=slateblue> [[User:Rebecca|Rebecca]] 01:34, 22 July 2011 (UTC) I left comments on the discussion page </font color><br />
<br />
*[[Snell's Law]] <br />
-feedback page<br />
up for final review [[User:Ljeanlo1|Ljeanlo1]] 20:04, 21 July 2011 (UTC)<br />
<br />
*[[Witch of Agnesi]] <br />
up for final review [[User:Ljeanlo1|Ljeanlo1]] 20:05, 20 July 2011 (UTC) <br />
<br />
*[[Dot Product]] <font color=darkred> Approved, 7/14 </font><br />
<br />
*[[Vector]] <font color=darkred> Approved, 7/10 </font><br />
<br />
==Requests to S10 Students==<br />
<br />
<br />
*<s>Can XD do a demo for MATLAB?</s> Done - [[Demo of MATLAB using the example of Bifurcation]]<br />
<br />
==Useful Links==<br />
[[S10]]<br />
<br />
[[SB11]]<br />
<br />
[[RPI11]]<br />
<br />
[[DU11]]<br />
<br />
[[Pages Ready for Final Review]]<br />
<br />
[[Feedback Requests]]<br />
<br />
[[Sample discussion page]]<br />
<br />
[[Math Tools Requests]] ''This page is a place where students whose primary focus is writing pages can post requests for applets, animations, and new images that they'd like to see the computer science students create.''<br />
<br />
[[Page Building Help]]<br />
<br />
[[Help:Wiki Tricks|Wiki Tricks]]<br />
<br />
[[From a Bunch of Old Timers]]<br />
<br />
[[List of summer 2010 pages]]<br />
<br />
http://en.wikipedia.org/wiki/Help:Displaying_a_formula<br />
<br />
[[PartnerHome]]<br />
<br />
[[Existing Pages Needing Work]]<br />
<br />
[[Site programming questions]]<br />
<br />
== Current Group Projects ==</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Inscribed_figures&diff=26899Talk:Inscribed figures2011-07-22T01:55:51Z<p>Rebecca: /* General Comments */</p>
<hr />
<div>=General Comments=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:53, 18 July 2011 (UTC): The page is looking a little messy right now, there's a lot of text floating around in the top left. I think it's because you left your first couple of balloons empty?</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:17, 18 July 2011 (UTC): In general, this page needs a lot more actual geometry in it. The mosaic is nice to look at, and the Eye is kinda cool, but a page about inscribed figures should really have some classic geometry and proofs. For example, you mention that inscribed figures can be used to prove the Pythagorean Theorem - why don't you put that proof in?</font><br />
<br />
<font color=orangered>[[User:Rscott3|Richard]] 7/6 Gave Dayo a hand getting the page started.</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): Your main image is a little grainy - are there any higher quality images available? Or could you maybe make the image a little smaller?</font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:05, 9 July 2011 (UTC) Nice work Dayo. This is a really good start to a page. I'd challenge you to finish this page by the end of the summer. You'll have to really commit your time to it because you're getting started late, but it is a great topic for an image page.<br />
<br />
*[[User:Rebecca|Rebecca]] 01:54, 22 July 2011 (UTC) Dayo and I discussed some ideas for this page on Wednesday. Essentially he will be adding more to the section on the London Eye. <br />
<br />
<br />
</font color><br />
<br />
=Section specific comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): Typo! ''It is considered one of the finest examples of ceramic inlay,radiative geometry, and use of inscribed figures in art.''<br />
::(you need a space between "inlay," and "radiative".)</font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 00:59, 9 July 2011 (UTC) You need to add mouseovers for ceramic inlay, radiative geometry, inscribed.<br />
</font color><br />
<br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:59, 18 July 2011 (UTC):<br />
*''An inscribed or "cyclic" figure is one which fits "snugly" into another larger shape;''<br />
::Looks to me like you're defining "inscribed" and "cyclic" here, so to follow our established conventions for definitions, you should bold them:<br />
:::''An '''inscribed'' or '''cyclic''' figure is…<br />
</font><br />
<br />
*<font color=dodgerblue>The separate subsection for "Applications" looks weird to me, maybe you should consider just having that be a second paragraph without another header.</font><br />
<br />
*<font color=dodgerblue>It seems wrong to me to say that inscribed figures ''are'' a proof of the Pythagorean theorem, because it's an application, not a definition or necessary characteristic. I'd much rather it said that inscribed figures ''can be used to prove'' the Pythagorean theorem.</font><br />
<br />
*<font color=dodgerblue>I really think this section needs some small pictures showing simple inscribed figures. Maybe three or four 150px by 150 px images showing like, a square in a circle, a triangle in a square, etc…</font><br />
<br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:01, 9 July 2011 (UTC) This is a good way to start the page, but you should make a picture that is simpler and shows how a figured is inscribed. For example, a square with a circle inside. You could even cut this section out and just put this sentence in the mouseover for "inscribed" along with the picture. <br />
* If you don't decide to just put this section in a mouseover, it might be nice to expand on it a bit.<br />
</font color><br />
<br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): <br />
*''For a a breakdown of the image: see below. ''<br />
::Punctuation isn't quite right, try "For a breakdown of the image, see below:"</font><br />
<br />
*<font color=dodgerblue>I know you're just getting off the ground, but make sure that when you write this up, you provide words to go with the pictures! Tell the reader what they're supposed to be observing.</font><br />
<br />
==More Mathematical Explanation==<br />
===Inscribed Figures applications===<br />
==="Example 1: constructing a star and The Walls of The Salon del Trono"===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:13, 18 July 2011 (UTC):<br />
*This section heading seems weird to me, I think it should be a subsection of "Inscribed Figures applications" not on an equal level. Also, there shouldn't be quotation marks around the header, and your capitalization is weird. I'd write: ''Example 1: Constructing a star and the walls of the Salon del Trono''</font><br />
<br />
*<font color=dodgerblue>You should proofread this section. There are a couple sentences that aren't capitalized, and there's one place where you say "orig" when I think you mean "origin". </font><br />
<br />
*<font color=dodgerblue>Your explanation of what's going on in the pictures is pretty clear, but what's not clear is the connection to inscribed figures. You need to make a bigger deal of it at the start of the section, explicitly state that the picture was constructed using inscribed figures and now you're going to walk through the construction.</font><br />
<br />
==="Example 2: The London Eye"===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:13, 18 July 2011 (UTC):<br />
*Again, I don't think the section heading should be in quotation marks here.</font><br />
*<font color=dodgerblue>I assume you're going to expand this section, when you do, make sure you explain what the Eye is, in case readers haven't heard of it, and try and find a picture of it to include. Also, it'd be great if you could tie this in to some geometry - are there any cool proofs that involve pentagons?</font><br />
<br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:02, 9 July 2011 (UTC) You should remove the sentence "proof of pythagorean theorem using Ptolemy's Theorem. That's not what you're doing in this section. Instead, why don't you introduce the fact that you will construct a star using inscribed figures.<br />
* You need to add another paragraph after the one beginning with "example 1: constructing a star...". In this paragraph you can explain in more detail how the squares are inscribed. Then refer to the picture so that readers can see. <br />
* "At every place where the inscriptions’ extended edges meet the edges of the original rectangle, a point is made." What about if you change this to "Each corner of the inscribed squares touches the side of a larger square. At these intersections, a point is made." What you said originally isn't exactly true because the smallest inscribed square's corners touch the middle sized square's edges, not the original squares edges like you said. <br />
* You jump from an image where there are points on the edge of the biggest square as well as inside of that square to a new image where all the points are on the outside. You need to explain this transition and probably add more pictures in between. <br />
* There's no reason to label the points of the star and the squares if you're not going to refer to them. It just clutters the images. <br />
* I think you need another image to illustrate one ray connecting a quarter mark to the nearest perpendicular halfway mark. You should label these points and show a blue line going through them. Then you can jump to the images where you have all these blue lines and the star is generated. Also, are these lines actually rays like you said? Or are they just lines? <br />
* "Connecting the edges of the star with every other edge yields the outermost points of the central star." This doesn't really make sense. I don't think it's what you're doing actually. You're drawing lines from the points of the star to the intersections of the blue lines, right? When you're explaining the images, the best thing to keep in mind is that someone should be able to follow your directions and execute the step without the image. This sentence is too vague for anyone to be able to do that. <br />
* Nice images.<br />
* I'm excited to read about the London Eye (capitalize both London and Eye). This will be your second example by the way, not example three like you have written. <br />
</font color></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Inscribed_figures&diff=26898Talk:Inscribed figures2011-07-22T01:54:56Z<p>Rebecca: /* General Comments */</p>
<hr />
<div>=General Comments=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:53, 18 July 2011 (UTC): The page is looking a little messy right now, there's a lot of text floating around in the top left. I think it's because you left your first couple of balloons empty?</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:17, 18 July 2011 (UTC): In general, this page needs a lot more actual geometry in it. The mosaic is nice to look at, and the Eye is kinda cool, but a page about inscribed figures should really have some classic geometry and proofs. For example, you mention that inscribed figures can be used to prove the Pythagorean Theorem - why don't you put that proof in?</font><br />
<br />
<font color=orangered>[[User:Rscott3|Richard]] 7/6 Gave Dayo a hand getting the page started.</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): Your main image is a little grainy - are there any higher quality images available? Or could you maybe make the image a little smaller?</font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:05, 9 July 2011 (UTC) Nice work Dayo. This is a really good start to a page. I'd challenge you to finish this page by the end of the summer. You'll have to really commit your time to it because you're getting started late, but it is a great topic for an image page.<br />
<br />
*[[User:Rebecca|Rebecca]] 01:54, 22 July 2011 (UTC) Dayo and I discussed some ideas for this page on Wednesday. I won't write them, but to summarize: He is going to add more explanation of the London Eye example. <br />
<br />
<br />
<br />
</font color><br />
<br />
=Section specific comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): Typo! ''It is considered one of the finest examples of ceramic inlay,radiative geometry, and use of inscribed figures in art.''<br />
::(you need a space between "inlay," and "radiative".)</font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 00:59, 9 July 2011 (UTC) You need to add mouseovers for ceramic inlay, radiative geometry, inscribed.<br />
</font color><br />
<br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:59, 18 July 2011 (UTC):<br />
*''An inscribed or "cyclic" figure is one which fits "snugly" into another larger shape;''<br />
::Looks to me like you're defining "inscribed" and "cyclic" here, so to follow our established conventions for definitions, you should bold them:<br />
:::''An '''inscribed'' or '''cyclic''' figure is…<br />
</font><br />
<br />
*<font color=dodgerblue>The separate subsection for "Applications" looks weird to me, maybe you should consider just having that be a second paragraph without another header.</font><br />
<br />
*<font color=dodgerblue>It seems wrong to me to say that inscribed figures ''are'' a proof of the Pythagorean theorem, because it's an application, not a definition or necessary characteristic. I'd much rather it said that inscribed figures ''can be used to prove'' the Pythagorean theorem.</font><br />
<br />
*<font color=dodgerblue>I really think this section needs some small pictures showing simple inscribed figures. Maybe three or four 150px by 150 px images showing like, a square in a circle, a triangle in a square, etc…</font><br />
<br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:01, 9 July 2011 (UTC) This is a good way to start the page, but you should make a picture that is simpler and shows how a figured is inscribed. For example, a square with a circle inside. You could even cut this section out and just put this sentence in the mouseover for "inscribed" along with the picture. <br />
* If you don't decide to just put this section in a mouseover, it might be nice to expand on it a bit.<br />
</font color><br />
<br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:53, 6 July 2011 (UTC): <br />
*''For a a breakdown of the image: see below. ''<br />
::Punctuation isn't quite right, try "For a breakdown of the image, see below:"</font><br />
<br />
*<font color=dodgerblue>I know you're just getting off the ground, but make sure that when you write this up, you provide words to go with the pictures! Tell the reader what they're supposed to be observing.</font><br />
<br />
==More Mathematical Explanation==<br />
===Inscribed Figures applications===<br />
==="Example 1: constructing a star and The Walls of The Salon del Trono"===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:13, 18 July 2011 (UTC):<br />
*This section heading seems weird to me, I think it should be a subsection of "Inscribed Figures applications" not on an equal level. Also, there shouldn't be quotation marks around the header, and your capitalization is weird. I'd write: ''Example 1: Constructing a star and the walls of the Salon del Trono''</font><br />
<br />
*<font color=dodgerblue>You should proofread this section. There are a couple sentences that aren't capitalized, and there's one place where you say "orig" when I think you mean "origin". </font><br />
<br />
*<font color=dodgerblue>Your explanation of what's going on in the pictures is pretty clear, but what's not clear is the connection to inscribed figures. You need to make a bigger deal of it at the start of the section, explicitly state that the picture was constructed using inscribed figures and now you're going to walk through the construction.</font><br />
<br />
==="Example 2: The London Eye"===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 15:13, 18 July 2011 (UTC):<br />
*Again, I don't think the section heading should be in quotation marks here.</font><br />
*<font color=dodgerblue>I assume you're going to expand this section, when you do, make sure you explain what the Eye is, in case readers haven't heard of it, and try and find a picture of it to include. Also, it'd be great if you could tie this in to some geometry - are there any cool proofs that involve pentagons?</font><br />
<br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:02, 9 July 2011 (UTC) You should remove the sentence "proof of pythagorean theorem using Ptolemy's Theorem. That's not what you're doing in this section. Instead, why don't you introduce the fact that you will construct a star using inscribed figures.<br />
* You need to add another paragraph after the one beginning with "example 1: constructing a star...". In this paragraph you can explain in more detail how the squares are inscribed. Then refer to the picture so that readers can see. <br />
* "At every place where the inscriptions’ extended edges meet the edges of the original rectangle, a point is made." What about if you change this to "Each corner of the inscribed squares touches the side of a larger square. At these intersections, a point is made." What you said originally isn't exactly true because the smallest inscribed square's corners touch the middle sized square's edges, not the original squares edges like you said. <br />
* You jump from an image where there are points on the edge of the biggest square as well as inside of that square to a new image where all the points are on the outside. You need to explain this transition and probably add more pictures in between. <br />
* There's no reason to label the points of the star and the squares if you're not going to refer to them. It just clutters the images. <br />
* I think you need another image to illustrate one ray connecting a quarter mark to the nearest perpendicular halfway mark. You should label these points and show a blue line going through them. Then you can jump to the images where you have all these blue lines and the star is generated. Also, are these lines actually rays like you said? Or are they just lines? <br />
* "Connecting the edges of the star with every other edge yields the outermost points of the central star." This doesn't really make sense. I don't think it's what you're doing actually. You're drawing lines from the points of the star to the intersections of the blue lines, right? When you're explaining the images, the best thing to keep in mind is that someone should be able to follow your directions and execute the step without the image. This sentence is too vague for anyone to be able to do that. <br />
* Nice images.<br />
* I'm excited to read about the London Eye (capitalize both London and Eye). This will be your second example by the way, not example three like you have written. <br />
</font color></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=S11&diff=26897S112011-07-22T01:34:11Z<p>Rebecca: /* Leah's Projects */</p>
<hr />
<div>__TOC__<br />
<br />
== Announcements ==<br />
For public-type help questions, see [[Help:Contents|Help]]. For Swat-specific ones, see [[Swarthmore summer research orientation]].<br />
<br />
<b>Remember to keep your projects sections short and up to date; only the last week of status changes should be mentioned. [[User:Smaurer1|Smaurer1]]</b><br />
<br />
===Group Discussion Questions===<br />
<br />
* [[Topics for conversations through Skype with RPI, SB, and/or Drexel]] Started 6/29.<br />
* [[Who are we writing for?]] Started 6/29.<br />
* [[Possibly expanding student Math Image roles]], to be addressed 7/6.<br />
<br />
===Questions:===<br />
*Things that are listed as Helper Pages but use the Image Page template<br />
:We need to decide whether these pages should be on the Helper Page template, the Image Page template, or both: {{Hide|1=<br />
:*[[Change of Coordinate Systems]] - Image template only; image template live<br />
:*[[Conic Section]] - both templates; image template not live<br />
:*[[Differentiability]] - both templates; image template not live<br />
:*[[Dot Product]] - Image template only; image template not live<br />
:*[[Gradients and Directional Derivatives]] - Image template only; image template not live<br />
:*[[Hyperbolic Geometry]] - Image template only; image template not live<br />
:*[[Inversion]] - Image template only; image template not live<br />
:*[[Iterated Functions]] - Image template only; image template not live<br />
:*[[Parametric Equations]] - Image template only; image template live<br />
:*[[Taylor Series]] - Image template only; image template not live<br />
:*[[Volume of Revolution]] - Image template only; image template live<br />
<br />
:<font color=dodgerblue>''(List complied by [[User:Kderosier|Kate]], June 16)''</font><br />
}}<br />
<br />
<br />
Older questions: {{Hide|1=<br />
*Harrison's question about text being cut off on Cross-cap: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 14:16, 8 June 2011 (UTC)<br />
**The text in MME on the [[Cross-cap]] page is getting truncated when viewed through edit with form, but still appears on the page.<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 00:49, 14 June 2011 (UTC): When I've encountered this problem previously, it's been because a set of double curly brackets wasn't closed.</font><br />
}}<br />
<br />
*Harrison's question about creating a list of not-yet-existent Helper Pages: {{Hide|1=<br />
Harrison, 5/26/11:<br />
:*<s>We need a list of empty pages: Penrose Tiles is only linked to one, now two, pages. Empty pages like this could well fade into obscurity.</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:09, 7 June 2011 (UTC): Such a list has been created. See [[Existing_Pages_Needing_Work#Empty_.28but_linked_to.29_Pages|here]].</font><br />
}}<br />
<br />
*Spam conversation: {{Hide|1=<br />
<font color=dodgerblue><br />
*[[User:Kderosier|Kate]] 14:38, 27 May 2011 (UTC): '''We have some new users who are creating a bunch of pages with links to illegally download or watch movies.''' At first, we though it might be someone from Sweet Briar practicing wiki-syntax, but now it's just starting to look like spam:<br />
**[[Watch_Sniper:_Reloaded_film_in_hd|This is the type of page I'm talking about]]<br />
**[[Special:Contributions/Calrivenick|List of pages created by Calrivenick]]<br />
**[[Special:Contributions/Cadedesi|List of pages created by Cadedesi]]<br />
</font><br />
:Let's talk about what to do this afternoon. [[User:Gene|Gene]] 15:19, 27 May 2011 (UTC)<br />
:<font color=dodgerblue>This problem has continued over the weekend. Someone spammed the talk page for Fun Topology with comments about buying Cialis and stuff. They also posted a lot more movie download pages under the Cadedesi username. I'm going to go through and delete again.</font><br />
:<font color=dodgerblue>The spam comments on Fun Topology were coming from this computer's IP address. </font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 14:34, 6 June 2011 (UTC): Haven't seen any more spam activity for a few days. I assume some computer people have handled the issue? I'm going to hide this conversation so that it's not taking up space on S11.</font><br />
}}<br />
<br />
*Citations/footnotes conversation: {{Hide|1=<br />
:I spent a really long time wandering around MediaWiki and Wikipedia this morning trying to figure out how to do footnotes/citations the way I wanted to - now that I know how, should I add instructions to one of the many help mages on Math Images? If so, which page? (Kate, 5/17)<br />
<br />
:<font color=red> Answer: put it here at [[Help:Wiki_Tricks|Wiki Tricks]] (XD, 5/17) </font><br />
<br />
:[[User:Smaurer1|Smaurer1]] 19:43, 17 May 2011 (UTC) Well, it's not clear that webarticles should have footnotes, although Wikipedia does. In text references may be better. This is surely something we should discuss as a group, and find out what last year's group decided, if they did. If there are footnotes, there has got to be a way to get back seamlessly to where you were before you jumped to the footnote.<br />
<br />
:Also, as for citations, we should be uniform in their format.<br />
<br />
:Finally, you can use 4 tildes to put your username and time stamp on your comments, and 3 tildes for just your username. <br />
<br />
:<font color=dodgerblue>Well, I wasn't doing comment-y type footnotes, I just wanted specific sentences to link to items in my References section. I think that format is better than full intext-citations, because it brings you to the source if that's what you're interested in, but it takes up less space if you're not. The references template we have comes equipped with little links to jump you back up, too- if you look at the [[Quipu#References|Quipu]] page, you can see that it lists each of the sections that reference is linked from, and those links bring you to the reference in that section. All in all, I think it's a clear and intuitive way to do references for both the writer and the reader (although, like most things, it doesn't play well with our hidden sections), and I'm going to go ahead and put the instructions up in WikiTricks. -[[User:Kderosier|Kate]] </font><br />
<br />
{{Hide|1=<br />
*What the help pages say now:<br />
**[[Tour_the_Math_Images_Project#Anatomy_of_a_page|The Tour page's "Anatomy of a page" section]]<br />
**[[Checklist_for_writing_pages#References_and_footnotes|The "References and footnotes" section on the checklist for writing pages]]<br />
*The way to do Wikipedia-like references:<br />
**[[Wiki_Tricks#How_to_do_Citations|Wiki Tricks - Citations section]]<br />
}}<br />
<br />
}}<br />
<br />
*Invisible Comments conversation: {{Hide|1= One of you asked "How do you put invisible comments in the source code?"<br />
<br />
:Answer: Same way you do in html, like this <nowiki><br />
:<!-- hidden stuff --><br />
:</nowiki><br />
:However, if you want to make comments about an article for its author, the comments are more likely to be seen if you either<br />
:* put it in the discussion page, or<br />
:* if it is important to put it right by the material commented on, put it in the article in color with your username and time stamp included.<br />
<br />
:Hidden comments in the source code are likely to be overlooked, except perhaps if they are written by the author him/herself, as a note for further development.<br />
}}<br />
}}<br />
<br />
== Current Individual Projects ==<br />
<br />
===Steve M (aka Prof Maurer)'s Role===<br />
{{Hide|1=<br />
My role is 2-fold:<br />
<br />
<ol><br />
<li> Come see me to sound me out (if you wish) on the mathematical appropriateness of an idea for a page, or for possible references.<br />
<br />
<li> Once you have a reasonable amount written, and want feedback on the quality and correctness of the mathematical exposition, ask me to look it over and then we will have a conference. (Abram and the oldies are as good as I am at discussion general organization and clarity issues.) <br />
</ol><br />
<br />
We have agreed to put a record on this S11 page of what we are doing and what help we want from others, but in addition tell me in person or by email if you want to conference with me.<br />
}}<br />
<br />
===Harrison's Projects===<br />
<br />
[[Harrison's detritus]]<br />
<br />
*[[User:Htasoff|Htasoff]] 23:44, 13 July 2011 (UTC) Pages will be submitted for final review in 1 - 3 days. A few, final comments are welcome. Real Projective Plane is still in the works, though.<br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:19, 14 July 2011 (UTC): Hey Harrison, do you know if that one picture in inverse trig that you got from somewhere on the internet is a picture we can use? Can you check please?</font><br />
<br />
[[Rope around the Earth]]<br />
:<font color=darkred> Approved </font><br />
<br />
<font color=darkred> I have one small suggested wording comment for you on [[Congruent triangles]], then it's good to go. [[User:AnnaP|AnnaP]] 13:48, 21 July 2011 (UTC)</font><br />
<br />
===Richard's Projects===<br />
<br />
<br />
<font color=orangered> <br />
<br />
:APPLET INFO:<br />
:{{Hide|1=<br />
<br />
[[User:Alimurreza|Alimurreza]] 02:53, 6 July 2011 (UTC)I am working on your applet. Check this out here @([http://mathforum.org/mathimages/index.php/DU11 Reza's work]).<br />
:APPLET UPDATE:[[User:Alimurreza|Alimurreza]] 02:41, 15 July 2011 (UTC)I am done with Ambiguous Case applet. Please, check the applet. Feel free to send me any feedback or change-request.<br />
What i want mine to look like, but http://www.mccsc.edu/~aterwill/ambiguouscaseapplet/Ambiguous_Case_applet.html doesn't show the completed triangles.<br />
<br />
I like how this one shows the completed triangles<br />
http://www.mnwest.edu/fileadmin/static/website/dmatthews/Geogebra/AmbiguousCase01.html<br />
<br />
}}<br />
<br />
'''Completed Pages'''<br />
*[[Ambiguous Case]] [[User:Rscott3|Richard]] 7/19<br />
<br />
*[[Law of cosines]]<font color=orangered> [[User:Rscott3|Richard]] 6/23</font><br />
<br />
*[[Law of Sines]] [[User:AnnaP|AnnaP]] 7/7<br />
<br />
*[[Solving Triangles]] 7/12<br />
<br />
:Other ideas: {{Hide|1=<br />
*inscribed angles?<br />
<br />
*Normal Distribution?<br />
<br />
*Birthday Paradox?<br />
}}<br />
</font><br />
<br />
===Dayo's Projects===<br />
Current projects<br />
*[[Inscribed figures]] : there's a [[Compass & Straightedge Construction and the Impossible Constructions]] page, but I think that inscribed figures deserves its' own page. What do others think? <br />
::<font color=slateblue> [[User:Rebecca|Rebecca]] 01:07, 9 July 2011 (UTC) I left comments on the discussion page. </font color><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 15:23, 18 July 2011 (UTC): I left you some comments!</font><br />
<br />
Future Projects: {{Hide|1=<br />
*[[Mathematics in architecture]]:make changes akin to [[Math for Computer Graphics and Computer Vision]], including:<br />
<br />
::*[[Cross sections]]: calculus application page, including examples of Tokyo international Forum, Suransuns Bridge, and other structures which could be thought of and put together easily in terms of their cross sections <br />
::*[[Torus]] edits, additions concerning the Torus in construction and architecture<br />
::*[[Domes]]:conic sections, arches, parabolas<br />
::*[[The Henderson Waves Bridge]]: sinusoids in architecture, parametric design<br />
::*[[Catenary]]: More real world examples: namely bridges<br />
::*[[Bridge of Peace]]: The equation(s) used to generate the surface, possibly words from the architect, very new, may be hard to get concrete technical information <br />
::*[[Kurilpa Bridge]]: Everyone have a look at the image and tell me what kind of actual subjects you could find in it, namely in the cables and tubes.<br />
::*Teaching Materials(6/30): ''growing up with science: projects'' could be the sort of activities we're looking for. I used these with a class, and think people should look at them.<br />
<br />
<br />
<br />
<br />
}}<br />
<br />
on hold: <br />
*[[Parametric Equations]]: integrating Xingda's page from [[S10]] into page.<br />
<br />
===Diana's Projects===<br />
<br />
====Current====<br />
*[[String Art Calculus]]<br />
<br />
*[[Logistic Bifurcation]]<br />
:<font color=darkred> I've put up comments. There are a few places that could use some work. [[User:AnnaP|AnnaP]] 7/10 </font> <br />
:<font color=slateblue> [[User:Rebecca|Rebecca]] 02:26, 16 July 2011 (UTC) This is a very impressive page. I put up a few small suggestions on the discussion page. </font color><br />
<br />
*[[Markus-Lyapunov Fractals]]<br />
:<font color=darkred> Approved [[User:AnnaP|AnnaP]] 7/14 </font><br />
<br />
====Ideas for later projects====<br />
{{Hide|1=<br />
*Chirikov-Taylor Maps<br />
**This seems like a natural extension of the Markus-Lyapunov Fractals page, but maybe the math involved in the two is too similar?<br />
*This aspect of pendular motion:<br />
**[[http://www.youtube.com/watch?v=yVkdfJ9PkRQ&feature=player_embedded|Varied-Length Pendulums]]<br />
**I'm not sure how or whether to use this -- does a ''moving'' image count as a "math image"? -- But it's incredible, and I'd love to explore it.<br />
*Kuen Surface<br />
**It's just really cool.<br />
}}<br />
<br />
===Kate's Projects===<br />
*[[Anne Burns' Mathscapes]] (Scrapped out of [[Mountains In Spring|three]] [[Mathscape|other]] [[Fractal Scene I|pages]]):<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:29, 18 July 2011 (UTC): As soon as I get confirmation that Anne Burns doesn't mind us using her images, I'll submit this for final review.</font><br />
<br />
*Finished pages: {{Hide|1=<br />
*[[Perko pair knots]]:<br />
:<font color=darkred> Approved </font><br />
<br />
:*[[Critical Points]]:<br />
::<font color=darkred> Approved, but I did have one note on whether or not you intended to add something. It's fine as is, but I wanted to put up a suggestion. [[User:AnnaP|AnnaP]] 16:24, 15 July 2011 (UTC) </font><br />
:::<font color=dodgerblue>I responded to that note.</font><br />
<br />
:*[[Summation Notation]]:<br />
::<font color=darkred> Approved [[User:AnnaP|AnnaP]] 16:24, 15 July 2011 (UTC) </font><br />
<br />
:*[[Bases]]:<br />
:: <font color=dodgerblue>[[User:Kderosier|Kate]] 17:31, 11 July 2011 (UTC): Changed things in response to Chris' comments.</font><br />
<br />
:* [[Quipu]]:<br />
::<font color=darkred> Put up as ready for the public 6/30 [[User:AnnaP|AnnaP]] </font><br />
<br />
:* [[Basic Trigonometric Functions]]:<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 18:11, 30 June 2011 (UTC): Changed the the things that were bolded.</font><br />
<br />
<br />
}}<br />
<br />
===Leah's Projects===<br />
*[[Bedsheet Problem]]<br />
going to do last edits [[User:Ljeanlo1|Ljeanlo1]] 23:57, 20 July 2011 (UTC) <br />
<br />
*[[Boy's Surface]] <br />
: take a look on this tomorrow. [[User:Ljeanlo1|Ljeanlo1]] 23:57, 20 July 2011 (UTC) <br />
: <font color=slateblue> [[User:Rebecca|Rebecca]] 01:34, 22 July 2011 (UTC) I left comments on the discussion page </font color><br />
<br />
*[[Snell's Law]] <br />
-feedback page<br />
up for final review [[User:Ljeanlo1|Ljeanlo1]] 20:04, 21 July 2011 (UTC)<br />
<br />
*[[Witch of Agnesi]] <br />
up for final review [[User:Ljeanlo1|Ljeanlo1]] 20:05, 20 July 2011 (UTC) <br />
<br />
*[[Dot Product]] <font color=darkred> Approved, 7/14 </font><br />
<br />
*[[Vector]] <font color=darkred> Approved, 7/10 </font><br />
<br />
==Requests to S10 Students==<br />
<br />
<br />
*<s>Can XD do a demo for MATLAB?</s> Done - [[Demo of MATLAB using the example of Bifurcation]]<br />
<br />
==Useful Links==<br />
[[S10]]<br />
<br />
[[SB11]]<br />
<br />
[[RPI11]]<br />
<br />
[[DU11]]<br />
<br />
[[Pages Ready for Final Review]]<br />
<br />
[[Feedback Requests]]<br />
<br />
[[Sample discussion page]]<br />
<br />
[[Math Tools Requests]] ''This page is a place where students whose primary focus is writing pages can post requests for applets, animations, and new images that they'd like to see the computer science students create.''<br />
<br />
[[Page Building Help]]<br />
<br />
[[Help:Wiki Tricks|Wiki Tricks]]<br />
<br />
[[From a Bunch of Old Timers]]<br />
<br />
[[List of summer 2010 pages]]<br />
<br />
http://en.wikipedia.org/wiki/Help:Displaying_a_formula<br />
<br />
[[PartnerHome]]<br />
<br />
[[Existing Pages Needing Work]]<br />
<br />
[[Site programming questions]]<br />
<br />
== Current Group Projects ==</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Pages_Ready_for_Final_Review&diff=26896Pages Ready for Final Review2011-07-22T01:31:03Z<p>Rebecca: /* Swarthmore Pages */</p>
<hr />
<div>=Pages Ready for Final Review=<br />
Once your page has gone through several cycles of feedback and you (the author) feel that it is ready for the public:<br />
*Go through either the [[Checklist for writing pages]] or the [[Checklist for writing helper pages]] one last time<br />
*Take a few minutes and type up a response to the issues brought up by the checklist by writing 1-3 sentences in response to the bold headings on the checklist. (Check out the [[Sample Response to Checklist]])<br />
*Link the page here. <br />
<br />
Your page will be reviewed by one of the designated final reviewers who will either give you further feedback or mark the page as "ready for the public."<br />
<br />
Please put your name by your page so that we can contact you with questions.<br />
<br />
<br />
<br />
<br />
'''<font color=darkred> AN IMPORTANT NOTE ABOUT PAGES PUT UP FOR FINAL REVIEW BETWEEN JULY 18TH AND 22ND'''<br />
<br />
'''Anna is going to a training which will keep her extremely busy during that week. Priority for editing will be given to Swarthmore students and any others for whom it is their last week of work on the project (please note if you are NOT at Swarthmore and it is your last week. ''' I will make a big effort to get through everything posted by this weekend, so there isn't a backlog. I will also be completely unavailable for editing August 6th-15th, and will not be reachable during that time. </font> <br />
<br />
'''<font color=olive><font color=green>CHRIS T.</font>, <font color=blue>STEVE C.</font>, and <font color=slateblue>REBECCA</font> will be helping to review pages while Anna is busy.</font>'''<br />
<br />
===Swarthmore Pages===<br />
<br />
*[[Logistic Bifurcation]] by [[User:Dpatton1|Diana]] 17:00 7/7/11<br />
:<font color=green> Chris 7/16 I've put up comments from a "layman's" perspective. </font><br />
<br />
*[[Snell's Law]]<br />
addressing Anna's comment. [[User:Ljeanlo1|Ljeanlo1]] 18:40, 21 July 2011 (UTC) <br />
<br />
*[[Witch of Agnesi]] <br />
addressed Chris' comment. [[User:Ljeanlo1|Ljeanlo1]] 18:39, 21 July 2011 (UTC)<br />
<br />
*[[Dimensions]] by [[User:Htasoff|Htasoff]]<br />
:<font color=green> SteveC 7/20 -- a couple of comments.</font><br />
::<font color=Mediumblue>Confused, Please explain.</font><br />
<br />
*[[Cross-cap]] by [[User:Htasoff|Htasoff]]<br />
:<s><font color=slateblue>[[User:Rebecca|Rebecca]] 02:14, 21 July 2011 (UTC) I left a few comments on the checklist. Overall the page is great, and I will approve it as soon as you address these last few things </font color><br />
::<font color=Mediumblue>CHECK</font></s> <font color=slateblue> This page no longer says it is a work in progress. Is there anything else I need to do to approve it? </font color><br />
<br />
===Sweet Briar Pages=== <br />
<br />
*[[Dandelin Spheres Theory]] by [[User:Flora1103|Flora Li]] 15:31, 17 July 2011 (UTC)<br />
:<font color=green> Chris 7.20.11 I've responded to some of your changes and comments. </font><br />
::<font color=plum>Flora 07.20 12:08 I responsed to your suggetions and made a little more changes.</font><br />
:::<font color=green> Chris 7.21.11 I've completed the rest of the page and made comments. </font><br />
::::<font color=plum>Thanks for your suggestion. I have made some change based on your comments. Flora 07.21 12:29</font><br />
<br />
*[[Steiner's Chain]] by [[User:Donko14|Anna]]<br />
:<font color=darkred> comments are up [[User:AnnaP|AnnaP]] 13:35, 21 July 2011 (UTC) </font><br />
::<font color=orange> Thanks for your quick response with comments! I have made the necessary adjustments!!</font><br />
<br />
*[[Parabolic Integration]] by [[User:Donko14|Anna]]<br />
<br />
===Rensselaer Polytechnic Institute===<br />
[[Polar Equations]] by [[User:Chanj|Chanj]] 21:35, 7 July 2011 (UTC)<br />
:<font color=blue> I have edited my page by putting up new images, more detailed explanations and comments in the discussion reflecting those changes. --[[User:Chanj|Chanj]] 20:48, 15 July 2011 (UTC)</font><br />
<br />
===Drexel Pages===<br />
<br />
=Approved Pages=<br />
<br />
Once an editor moves the link to your page here, they have marked it as ready for the public!<br />
<br />
===Swarthmore Pages===<br />
*[[Vector]]<br />
*[[Law of Cosines]]<br />
*[[Law of Sines]]<br />
*[[Quipu]]<br />
*[[Basic Trigonometric Functions]]<br />
*[[Solving Triangles]]<br />
*[[Bases]]<br />
*[[Markus-Lyapunov Fractals]]<br />
*[[Dot Product]]<br />
*[[Summation Notation]]<br />
*[[Critical Points]]<br />
*[[Ambiguous Case]]<br />
*[[Rope around the Earth]]<br />
*[[Perko pair knots]]<br />
*[[Radians]]<br />
*[[Congruent triangles]]<br />
<br />
===Sweet Briar Pages===<br />
*[[Arbelos]]<br />
*[[Euclidean Algorithm]]<br />
*[[Waves]]<br />
*[[Dihedral Groups]]<br />
*[[Pigeonhole Principle]]<br />
<br />
===Rensselaer Polytechnic Institute===<br />
<br />
===Drexel Pages===<br />
<br />
<br />
==Other Links==<br />
<br />
[[S11]]<br />
<br />
[[SB11]]<br />
<br />
[[RPI11]]<br />
<br />
[[DU11]]</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Pages_Ready_for_Final_Review&diff=26895Pages Ready for Final Review2011-07-22T01:28:56Z<p>Rebecca: /* Swarthmore Pages */</p>
<hr />
<div>=Pages Ready for Final Review=<br />
Once your page has gone through several cycles of feedback and you (the author) feel that it is ready for the public:<br />
*Go through either the [[Checklist for writing pages]] or the [[Checklist for writing helper pages]] one last time<br />
*Take a few minutes and type up a response to the issues brought up by the checklist by writing 1-3 sentences in response to the bold headings on the checklist. (Check out the [[Sample Response to Checklist]])<br />
*Link the page here. <br />
<br />
Your page will be reviewed by one of the designated final reviewers who will either give you further feedback or mark the page as "ready for the public."<br />
<br />
Please put your name by your page so that we can contact you with questions.<br />
<br />
<br />
<br />
<br />
'''<font color=darkred> AN IMPORTANT NOTE ABOUT PAGES PUT UP FOR FINAL REVIEW BETWEEN JULY 18TH AND 22ND'''<br />
<br />
'''Anna is going to a training which will keep her extremely busy during that week. Priority for editing will be given to Swarthmore students and any others for whom it is their last week of work on the project (please note if you are NOT at Swarthmore and it is your last week. ''' I will make a big effort to get through everything posted by this weekend, so there isn't a backlog. I will also be completely unavailable for editing August 6th-15th, and will not be reachable during that time. </font> <br />
<br />
'''<font color=olive><font color=green>CHRIS T.</font>, <font color=blue>STEVE C.</font>, and <font color=slateblue>REBECCA</font> will be helping to review pages while Anna is busy.</font>'''<br />
<br />
===Swarthmore Pages===<br />
<br />
*[[Logistic Bifurcation]] by [[User:Dpatton1|Diana]] 17:00 7/7/11<br />
:<font color=green> Chris 7/16 I've put up comments from a "layman's" perspective. </font><br />
<br />
*[[Snell's Law]]<br />
addressing Anna's comment. [[User:Ljeanlo1|Ljeanlo1]] 18:40, 21 July 2011 (UTC) <br />
<br />
*[[Witch of Agnesi]] <br />
addressed Chris' comment. [[User:Ljeanlo1|Ljeanlo1]] 18:39, 21 July 2011 (UTC)<br />
<br />
*[[Dimensions]] by [[User:Htasoff|Htasoff]]<br />
:<font color=green> SteveC 7/20 -- a couple of comments.</font><br />
::<font color=Mediumblue>Confused, Please explain.</font><br />
<br />
*[[Cross-cap]] by [[User:Htasoff|Htasoff]]<br />
:<s><font color=slateblue>[[User:Rebecca|Rebecca]] 02:14, 21 July 2011 (UTC) I left a few comments on the checklist. Overall the page is great, and I will approve it as soon as you address these last few things </font color><br />
::<font color=Mediumblue>CHECK</font></s><br />
<br />
===Sweet Briar Pages=== <br />
<br />
*[[Dandelin Spheres Theory]] by [[User:Flora1103|Flora Li]] 15:31, 17 July 2011 (UTC)<br />
:<font color=green> Chris 7.20.11 I've responded to some of your changes and comments. </font><br />
::<font color=plum>Flora 07.20 12:08 I responsed to your suggetions and made a little more changes.</font><br />
:::<font color=green> Chris 7.21.11 I've completed the rest of the page and made comments. </font><br />
::::<font color=plum>Thanks for your suggestion. I have made some change based on your comments. Flora 07.21 12:29</font><br />
<br />
*[[Steiner's Chain]] by [[User:Donko14|Anna]]<br />
:<font color=darkred> comments are up [[User:AnnaP|AnnaP]] 13:35, 21 July 2011 (UTC) </font><br />
::<font color=orange> Thanks for your quick response with comments! I have made the necessary adjustments!!</font><br />
<br />
*[[Parabolic Integration]] by [[User:Donko14|Anna]]<br />
<br />
===Rensselaer Polytechnic Institute===<br />
[[Polar Equations]] by [[User:Chanj|Chanj]] 21:35, 7 July 2011 (UTC)<br />
:<font color=blue> I have edited my page by putting up new images, more detailed explanations and comments in the discussion reflecting those changes. --[[User:Chanj|Chanj]] 20:48, 15 July 2011 (UTC)</font><br />
<br />
===Drexel Pages===<br />
<br />
=Approved Pages=<br />
<br />
Once an editor moves the link to your page here, they have marked it as ready for the public!<br />
<br />
===Swarthmore Pages===<br />
*[[Vector]]<br />
*[[Law of Cosines]]<br />
*[[Law of Sines]]<br />
*[[Quipu]]<br />
*[[Basic Trigonometric Functions]]<br />
*[[Solving Triangles]]<br />
*[[Bases]]<br />
*[[Markus-Lyapunov Fractals]]<br />
*[[Dot Product]]<br />
*[[Summation Notation]]<br />
*[[Critical Points]]<br />
*[[Ambiguous Case]]<br />
*[[Rope around the Earth]]<br />
*[[Perko pair knots]]<br />
*[[Radians]]<br />
*[[Congruent triangles]]<br />
<br />
===Sweet Briar Pages===<br />
*[[Arbelos]]<br />
*[[Euclidean Algorithm]]<br />
*[[Waves]]<br />
*[[Dihedral Groups]]<br />
*[[Pigeonhole Principle]]<br />
<br />
===Rensselaer Polytechnic Institute===<br />
<br />
===Drexel Pages===<br />
<br />
<br />
==Other Links==<br />
<br />
[[S11]]<br />
<br />
[[SB11]]<br />
<br />
[[RPI11]]<br />
<br />
[[DU11]]</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26892Talk:Boy's Surface2011-07-22T01:10:36Z<p>Rebecca: /* General Comments */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
<font color=slateblue>[[User:Rebecca|Rebecca]] 01:10, 22 July 2011 (UTC) Nice collaboration! This page is a great addition to the site. </font color><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
</font color><br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:03, 22 July 2011 (UTC) I think you need to rearrange the basic description. My suggestions are below:<br />
:* I would start the section with ...<br />
::: Boy's Surface is:<br />
::::*A <b>non-orientable</b> surface. Nonorientable means (definition).<br />
::::* An <b> immersion </b> of [[the real projective plane]] in 3 dimensional space. This means..... (explanation).<br />
::::* One possible parametrization of the surface obtained by sewing a Mobius strip to the edge of a disk. <br />
* I think this a better way to do it than to explain things before you give the definitions- people wont be able to follow what you're saying without the definitions anyway.<br />
* Then I think you should move this to after the bullets. "Boy's surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. This probably sounds like a whole new language, but below the Boy's surface will be described in much detail. We will provide definitions as well as examples of vital terms!<br />
Boy's Surface was discovered in 1901 by German mathematician Werner Boy when he was asked by his advisor, David Hilbert, to prove that an immersion of the projective plane in 3-space was impossible. Today, a large model of Boy's Surface is displayed outside of the Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany. The model was constructed as well as donated by Mercedes-Benz."<br />
</font color><br />
<br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:04, 22 July 2011 (UTC) Manifold should be bolded.<br />
*The tossed blanket example is helpful and well explained. Nice work!<br />
</font color><br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
<font color=slateblue><br />
* If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.<br />
* I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right. </font color><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:08, 22 July 2011 (UTC) If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.<br />
* I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right.<br />
* "Straight forward" should be "straightforward"<br />
* You say that non-continuous means that every input has only one output. Your picture of non-continuous doesn't show this though. It shows two inputs mapping to one output, not one input mapping two outputs. I'm not sure which is actually true, but they should be consistent. <font color><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
</font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:09, 22 July 2011 (UTC) I think that the video should definitely be moved up to the basic description. It was very helpful to be able to see Boy's Surface more clearly, and the video is much less complicated that the manifolds/surfaces section. We advise people to put the easier material up at the top of the page. <br />
* I agree with Harrison- The video could use a short explanation as well. This could be added to the basic description.<br />
</font color><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26889Talk:Boy's Surface2011-07-22T01:09:46Z<p>Rebecca: /* Constructing Boy's Surface */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
</font color><br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:03, 22 July 2011 (UTC) I think you need to rearrange the basic description. My suggestions are below:<br />
:* I would start the section with ...<br />
::: Boy's Surface is:<br />
::::*A <b>non-orientable</b> surface. Nonorientable means (definition).<br />
::::* An <b> immersion </b> of [[the real projective plane]] in 3 dimensional space. This means..... (explanation).<br />
::::* One possible parametrization of the surface obtained by sewing a Mobius strip to the edge of a disk. <br />
* I think this a better way to do it than to explain things before you give the definitions- people wont be able to follow what you're saying without the definitions anyway.<br />
* Then I think you should move this to after the bullets. "Boy's surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. This probably sounds like a whole new language, but below the Boy's surface will be described in much detail. We will provide definitions as well as examples of vital terms!<br />
Boy's Surface was discovered in 1901 by German mathematician Werner Boy when he was asked by his advisor, David Hilbert, to prove that an immersion of the projective plane in 3-space was impossible. Today, a large model of Boy's Surface is displayed outside of the Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany. The model was constructed as well as donated by Mercedes-Benz."<br />
</font color><br />
<br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:04, 22 July 2011 (UTC) Manifold should be bolded.<br />
*The tossed blanket example is helpful and well explained. Nice work!<br />
</font color><br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
<font color=slateblue><br />
* If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.<br />
* I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right. </font color><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:08, 22 July 2011 (UTC) If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.<br />
* I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right.<br />
* "Straight forward" should be "straightforward"<br />
* You say that non-continuous means that every input has only one output. Your picture of non-continuous doesn't show this though. It shows two inputs mapping to one output, not one input mapping two outputs. I'm not sure which is actually true, but they should be consistent. <font color><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
</font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:09, 22 July 2011 (UTC) I think that the video should definitely be moved up to the basic description. It was very helpful to be able to see Boy's Surface more clearly, and the video is much less complicated that the manifolds/surfaces section. We advise people to put the easier material up at the top of the page. <br />
* I agree with Harrison- The video could use a short explanation as well. This could be added to the basic description.<br />
</font color><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26887Talk:Boy's Surface2011-07-22T01:08:09Z<p>Rebecca: /* Immersion, The Real Projective Plane, and Embedding */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
</font color><br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:03, 22 July 2011 (UTC) I think you need to rearrange the basic description. My suggestions are below:<br />
:* I would start the section with ...<br />
::: Boy's Surface is:<br />
::::*A <b>non-orientable</b> surface. Nonorientable means (definition).<br />
::::* An <b> immersion </b> of [[the real projective plane]] in 3 dimensional space. This means..... (explanation).<br />
::::* One possible parametrization of the surface obtained by sewing a Mobius strip to the edge of a disk. <br />
* I think this a better way to do it than to explain things before you give the definitions- people wont be able to follow what you're saying without the definitions anyway.<br />
* Then I think you should move this to after the bullets. "Boy's surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. This probably sounds like a whole new language, but below the Boy's surface will be described in much detail. We will provide definitions as well as examples of vital terms!<br />
Boy's Surface was discovered in 1901 by German mathematician Werner Boy when he was asked by his advisor, David Hilbert, to prove that an immersion of the projective plane in 3-space was impossible. Today, a large model of Boy's Surface is displayed outside of the Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany. The model was constructed as well as donated by Mercedes-Benz."<br />
</font color><br />
<br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:04, 22 July 2011 (UTC) Manifold should be bolded.<br />
*The tossed blanket example is helpful and well explained. Nice work!<br />
</font color><br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
<font color=slateblue><br />
* If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.<br />
* I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right. </font color><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 01:08, 22 July 2011 (UTC) If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.<br />
* I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right.<br />
* "Straight forward" should be "straightforward"<br />
* You say that non-continuous means that every input has only one output. Your picture of non-continuous doesn't show this though. It shows two inputs mapping to one output, not one input mapping two outputs. I'm not sure which is actually true, but they should be consistent. <font color><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26886Talk:Boy's Surface2011-07-22T01:06:19Z<p>Rebecca: /* Non Orientable */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
</font color><br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:03, 22 July 2011 (UTC) I think you need to rearrange the basic description. My suggestions are below:<br />
:* I would start the section with ...<br />
::: Boy's Surface is:<br />
::::*A <b>non-orientable</b> surface. Nonorientable means (definition).<br />
::::* An <b> immersion </b> of [[the real projective plane]] in 3 dimensional space. This means..... (explanation).<br />
::::* One possible parametrization of the surface obtained by sewing a Mobius strip to the edge of a disk. <br />
* I think this a better way to do it than to explain things before you give the definitions- people wont be able to follow what you're saying without the definitions anyway.<br />
* Then I think you should move this to after the bullets. "Boy's surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. This probably sounds like a whole new language, but below the Boy's surface will be described in much detail. We will provide definitions as well as examples of vital terms!<br />
Boy's Surface was discovered in 1901 by German mathematician Werner Boy when he was asked by his advisor, David Hilbert, to prove that an immersion of the projective plane in 3-space was impossible. Today, a large model of Boy's Surface is displayed outside of the Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany. The model was constructed as well as donated by Mercedes-Benz."<br />
</font color><br />
<br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:04, 22 July 2011 (UTC) Manifold should be bolded.<br />
*The tossed blanket example is helpful and well explained. Nice work!<br />
</font color><br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
<font color=slateblue><br />
* If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.<br />
* I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right. </font color><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26885Talk:Boy's Surface2011-07-22T01:04:55Z<p>Rebecca: /* Basic Description */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
</font color><br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:03, 22 July 2011 (UTC) I think you need to rearrange the basic description. My suggestions are below:<br />
:* I would start the section with ...<br />
::: Boy's Surface is:<br />
::::*A <b>non-orientable</b> surface. Nonorientable means (definition).<br />
::::* An <b> immersion </b> of [[the real projective plane]] in 3 dimensional space. This means..... (explanation).<br />
::::* One possible parametrization of the surface obtained by sewing a Mobius strip to the edge of a disk. <br />
* I think this a better way to do it than to explain things before you give the definitions- people wont be able to follow what you're saying without the definitions anyway.<br />
* Then I think you should move this to after the bullets. "Boy's surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. This probably sounds like a whole new language, but below the Boy's surface will be described in much detail. We will provide definitions as well as examples of vital terms!<br />
Boy's Surface was discovered in 1901 by German mathematician Werner Boy when he was asked by his advisor, David Hilbert, to prove that an immersion of the projective plane in 3-space was impossible. Today, a large model of Boy's Surface is displayed outside of the Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany. The model was constructed as well as donated by Mercedes-Benz."<br />
</font color><br />
<br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:04, 22 July 2011 (UTC) Manifold should be bolded.<br />
*The tossed blanket example is helpful and well explained. Nice work!<br />
</font color><br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26884Talk:Boy's Surface2011-07-22T01:04:31Z<p>Rebecca: /* Manifolds/Surfaces */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
</font color><br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:04, 22 July 2011 (UTC) Manifold should be bolded.<br />
*The tossed blanket example is helpful and well explained. Nice work!<br />
</font color><br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26883Talk:Boy's Surface2011-07-22T01:03:30Z<p>Rebecca: /* Manifolds/Surfaces */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
</font color><br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 01:03, 22 July 2011 (UTC) I think you need to rearrange the basic description. My suggestions are below:<br />
:* I would start the section with ...<br />
::: Boy's Surface is:<br />
::::*A <b>non-orientable</b> surface. Nonorientable means (definition).<br />
::::* An <b> immersion </b> of [[the real projective plane]] in 3 dimensional space. This means..... (explanation).<br />
::::* One possible parametrization of the surface obtained by sewing a Mobius strip to the edge of a disk. <br />
* I think this a better way to do it than to explain things before you give the definitions- people wont be able to follow what you're saying without the definitions anyway.<br />
* Then I think you should move this to after the bullets. "Boy's surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. This probably sounds like a whole new language, but below the Boy's surface will be described in much detail. We will provide definitions as well as examples of vital terms!<br />
Boy's Surface was discovered in 1901 by German mathematician Werner Boy when he was asked by his advisor, David Hilbert, to prove that an immersion of the projective plane in 3-space was impossible. Today, a large model of Boy's Surface is displayed outside of the Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany. The model was constructed as well as donated by Mercedes-Benz."<br />
</font color><br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26882Talk:Boy's Surface2011-07-22T01:02:49Z<p>Rebecca: /* Intro */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
</font color><br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Boy%27s_Surface&diff=26881Talk:Boy's Surface2011-07-22T01:01:59Z<p>Rebecca: /* Intro */</p>
<hr />
<div>==General Comments==<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found ''immersion'' to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)<br />
<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!</font><br />
<br />
*<font color=salmon> I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...</font><br />
<br />
==Intro==<br />
*<font color=salmon>[[User:PhoebeJiang|Phoebe]] 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after. </font><br />
<br />
* [[User:Gene|Gene]] Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "<s>The</s>[this "The" ain't needed] Boy’s Surface is an immersion <s>on</s> of the projective plane in three-dimensional space."<br />
<font color=slateblue><br />
<br />
*[[User:Rebecca|Rebecca]] 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?<br />
* I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges." <br />
* "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."<br />
<br />
==Basic Description==<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."<br />
** This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.<br />
*<font color=salmon>It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing. </font><br />
<br />
===Manifolds/Surfaces===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.<br />
<br />
*<font color=salmon> I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot. </font><br />
<br />
* [[User:Gene|Gene]] <s>The</s> Boy''''s''' surface is one of the shapes that is well known in Topology,<s>. Topology is</s> a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]<br />
<br />
===Non Orientable===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.<br />
<br />
*<font color=salmon>I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image. </font><br />
<br />
===Immersion, The Real Projective Plane, and Embedding===<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.<br />
<br />
*[[User:Htasoff|Htasoff]] 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to ''immersion'', ''embedding'', ect. that was provided.<br />
<br />
:<font color=salmon> Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.</font><br />
<br />
I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me). <br /><br />
:: [[User:Nordhr|Nordhr] 18::44 27 Jun 2011 <br /><br /><br />
<br />
<br />
Hey Anna, what would you like to do with this: <br />
"The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."<br />
<br />
Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding?<br />
[[User:Ljeanlo1|Ljeanlo1]] 17:32, 1 July 2011 (UTC)<br />
<br />
* <font color=salmon> About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.</font><br />
<br />
* <font color=salmon> I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation. </font><br />
<br />
==Constructing Boy's Surface==<br />
<br />
* <font color=salmon> For the last sentence in the second para: ''Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.'' <br />
<br />
::1. ''Like the graph.'' Which graph?<br />
::2. Found five commas in this sentence. You break this sentences into too many parts. <br />
::3. Despite those two points, you made it clear why you go back to the starting point.<br />
<br />
* Last sentence before the video: ''By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. '' I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )? <br />
<br />
* Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me. <br />
</font><br />
<br />
==Parametrization==<br />
<font color=salmon><br />
* Explain to us what complex number means via the mouse over in case other people are not familiar with it.<br />
<br />
* As for the parametrization equations, make sure you explain how you get <math>X = \frac{g_1}{g} </math>, <math>Y = \frac{g_2}{g}, </math> and <math>Z = \frac{g_3}{g} </math> and tell us what <math>Im, Re</math> mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.<br />
</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Pages_Ready_for_Final_Review&diff=26647Pages Ready for Final Review2011-07-21T03:15:19Z<p>Rebecca: /* Swarthmore Pages */</p>
<hr />
<div>=Pages Ready for Final Review=<br />
Once your page has gone through several cycles of feedback and you (the author) feel that it is ready for the public:<br />
*Go through either the [[Checklist for writing pages]] or the [[Checklist for writing helper pages]] one last time<br />
*Take a few minutes and type up a response to the issues brought up by the checklist by writing 1-3 sentences in response to the bold headings on the checklist. (Check out the [[Sample Response to Checklist]])<br />
*Link the page here. <br />
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Your page will be reviewed by one of the designated final reviewers who will either give you further feedback or mark the page as "ready for the public."<br />
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Please put your name by your page so that we can contact you with questions.<br />
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'''<font color=darkred> AN IMPORTANT NOTE ABOUT PAGES PUT UP FOR FINAL REVIEW BETWEEN JULY 18TH AND 22ND'''<br />
<br />
'''Anna is going to a training which will keep her extremely busy during that week. Priority for editing will be given to Swarthmore students and any others for whom it is their last week of work on the project (please note if you are NOT at Swarthmore and it is your last week. ''' I will make a big effort to get through everything posted by this weekend, so there isn't a backlog. I will also be completely unavailable for editing August 6th-15th, and will not be reachable during that time. </font> <br />
<br />
'''<font color=olive><font color=green>CHRIS T.</font> and <font color=blue>STEVE C.</font> will be helping to review pages while Anna is busy.</font>'''<br />
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===Swarthmore Pages===<br />
*[[Perko pair knots]] by [[User:Kderosier|Kate]] 19:48, 20 July 2011 (UTC)<br />
:<font color=slateblue>[[User:Rebecca|Rebecca]] 03:15, 21 July 2011 (UTC)This page is great. I made two suggestions, but they're both optional. This page is approved. </font color><br />
<br />
*[[Logistic Bifurcation]] by [[User:Dpatton1|Diana]] 17:00 7/7/11<br />
:<font color=green> Chris 7/16 I've put up comments from a "layman's" perspective. </font><br />
<br />
*[[Radians]] by [[User:Htasoff|Htasoff]]<br />
:<font color=green> Chris 7/18. I've made a few comments. </font><br />
::<font color=Mediumblue>Check</font><br />
<br />
*[[Snell's Law]] [[User:Ljeanlo1|Ljeanlo1]] 16:14, 18 July 2011 (UTC) <br />
:<font color=darkred> I had a bit of unexpected time, so I added one more comment. I think that's all the comments I have for now! </font> <br />
<br />
*[[Witch of Agnesi]] <br />
new draft for final [[User:Ljeanlo1|Ljeanlo1]] 20:07, 20 July 2011 (UTC)<br />
<br />
*[[Congruent triangles]] by [[User:Htasoff|Htasoff]]<br />
:Is fully developed and has instructions for future editors based on Steve's comments.<br />
<br />
*[[Dimensions]] by [[User:Htasoff|Htasoff]]<br />
:<font color=green> SteveC 7/20 -- a couple of comments.</font><br />
::<font color=Mediumblue>Confused, Please explain.</font><br />
<br />
*[[Cross-cap]] by [[User:Htasoff|Htasoff]]<br />
:<font color=slateblue>[[User:Rebecca|Rebecca]] 02:14, 21 July 2011 (UTC) I left a few comments on the checklist. Overall the page is great, and I will approve it as soon as you address these last few things </font color><br />
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===Sweet Briar Pages=== <br />
<br />
*[[Dandelin Spheres Theory]] by [[User:Flora1103|Flora Li]] 15:31, 17 July 2011 (UTC)<br />
:<font color=green> Chris 7.20.11 I've responded to some of your changes and comments. </font><br />
::<font color=plum>Flora 07.20 12:08 I responsed to your suggetions and made a little more changes.</font><br />
<br />
*[[Dihedral Groups]] by [[User:Flora1103|Flora Li]] 18:27, 18 July 2011 (UTC)<br />
:<font color=plum> I make some change, and responsed to your comments. Flora 07.20 11:44</font><br />
::<font color=darkred> a couple more tiny comments to address, then it's good to go </font><br />
:::<font color=plum>Flora 07.20 4:59 Fixed images' titles and the links.</font> <br />
::::<font color=darkred> I clarified one comment. Please take a look [[User:AnnaP|AnnaP]] 02:57, 21 July 2011 (UTC)</font><br />
<br />
*[[Pigeonhole Principle]] by [[User:PhoebeJiang|Phoebe]]<br />
:<font color=green> Chris 7.20.11 I've put up comments on this. </font><br />
::<font color=salmon> Thank you Chris. I've made some changes according to your comments. Also responded to some concerns you may have. Phoebe 7/20</font><br />
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*[[Application of the Euclidean Algorithm]] by [[User:PhoebeJiang|Phoebe]]<br />
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*[[Steiner's Chain]] by [[User:Donko14|Anna]]<br />
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===Rensselaer Polytechnic Institute===<br />
[[Polar Equations]] by [[User:Chanj|Chanj]] 21:35, 7 July 2011 (UTC)<br />
:<font color=blue> I have edited my page by putting up new images, more detailed explanations and comments in the discussion reflecting those changes. --[[User:Chanj|Chanj]] 20:48, 15 July 2011 (UTC)</font><br />
<br />
===Drexel Pages===<br />
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=Approved Pages=<br />
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Once an editor moves the link to your page here, they have marked it as ready for the public!<br />
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[[DU11]]</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Perko_pair_knots&diff=26646Talk:Perko pair knots2011-07-21T03:07:13Z<p>Rebecca: /* Integration of Images and Text */</p>
<hr />
<div><font color=blue>Richard Scott</font> likes this.<br />
<br />
=Response to Checklist=<br />
Original response to checklist, in black, completed by [[User:Kderosier|Kate]] 19:42, 20 July 2011 (UTC)<br />
<br />
==References and footnotes==<br />
*All images cited on click-through<br />
*Footnotes and references used<br />
<br />
==Good writing==<br />
===Context===<br />
*Basic description and Why It's Interesting give historical context and connection to science<br />
<br />
===Quality of prose and page structuring===<br />
*Section headings and first sentences explain purpose of each section<br />
*Relevance of each section is clear<br />
*More complicated math is hidden and/or placed near end of MME <br />
<br />
===Integration of Images and Text===<br />
*Images are referred to explicitly<br />
*Captions and text explain the purpose of each image<br />
*The main proof is a series of images<br />
*<font color=slateblue> [[User:Rebecca|Rebecca]] 03:07, 21 July 2011 (UTC)Is there some picture you could add to the Why It's Interesting section? It's probably OK the way it is, I just think a picture might draw people eyes to the section more. </font color><br />
<br />
===Connections to other mathematical topics===<br />
*I didn't see anywhere to make relevant connections - there is nothing else on the site about knot theory<br />
<br />
===Examples, Calculations, Applications, Proofs===<br />
*The main content of the page is the proof that the two knots are the same<br />
*Examples are given and explained in the Dowker notation section<br />
*Applications of knot theory in general are explained very generally in Why It's Interesting, I don't know of any applications for these specific knots<br />
<br />
===Mathematical Accuracy and precision of language===<br />
*All statements are accurate to the best of my knowledge<br />
*Unfamiliar terms are defined (Two of the 3 sections in the MME are devoted to explaining terminology/notation that readers unfamiliar with knot theory can't be expected to know)<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 03:04, 21 July 2011 (UTC) "Belief in ether soon faded, but interest in identifying and cataloging different types of knots stayed. " maybe "remained" instead of "stayed"? </font color><br />
<br />
===Layout===<br />
*Paragraphs are short, many images are used<br />
*Page has been viewed in a variety of window sizes, spacing and layout seems as good as it can get given the information that needs to be displayed<br />
*Hide/shows used in several places to prevent intimidation<br />
<br />
=Pre-final review comments=<br />
{{Hide|1=<br />
==General Comments==<br />
*<font color=orangered>This page is really good and really clear. It's very easy to follow. There's not a ton of info, but that's okay. The one problem is that you say some things a couple of times. Right now, the page is short enough that these redundancies are fresh in the reader's mind, but after the proof is complete, this may not be so noticeable. [[User:Rscott3|Richard]] 7/14</font><br />
<br />
*<font color=orangered>Are the Reidemeister moves a method of solving "knot problems" or are they tools you use to solve them? To me, it sounds like you're using the word as both, which may be right for all I know. [[User:Rscott3|Richard]] 7/14</font><br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 20:53, 14 July 2011 (UTC): I don't really understand what you're asking. Can we talk about it tomorrow?</font><br />
<br />
==Basic Description==<br />
:<font color=red>xd 18:33, 12 June 2011 (UTC) I think you need a better transition between "To say that two knots are the same is to say that one can be deformed into the other without breaking the knot or passing it through itself." and the next one about the projection. I don't quite see the link between them. Since you have an explanation about projection in the Reidemeister moves section, I think you can get rid of this part.<br />
</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:09, 14 June 2011 (UTC): I really wanted to have projections explained in the basic description section, because they're important and not ''that'' hard to understand, so I changed it around. Does it read better now?</font><br />
<br />
==Reidemeister moves==<br />
:<font color=red>xd 18:33, 12 June 2011 (UTC) I don't understand the part of "projection of a knot was printed on very stretchy rubber" and you can stretch and none of the crossings are affected. How is that so?</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 13:17, 13 June 2011 (UTC): Thanks for pointing that out, I'll try and think of a better way to explain it. Personally, I think of those pictures printed on fruit roll-ups - you can stretch them all over the place, but you're only warping the image, not "really" changing it.</font><font color=red>xd 20:37, 13 June 2011 (UTC) ok. if you can find a way, then all the better, if not, i think you can avoid mentioning that.</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:08, 14 June 2011 (UTC):Yeah, I'm not going to bring up Fruit Roll-ups, but I really do need to explain planar isotopies, because I'm going to be using them in my proof, so hopefully I'll think of a way to elaborate on that explanation.</font><br />
<br />
*<s><font color=orangered>First redundncy: you already mentioned the projection in the Basic Description. You basically state the same info again, but this time you do introduce new ideas about the projection in this section. I think it's fine, just something to look out for. [[User:Rscott3|Richard]] 7/14</font></s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Good point, changed it.</font><br />
<br />
*<s><font color=orangered>Typo: "...or after moving the knot '''trough''' any ambient isotopy." [[User:Rscott3|Richard]] 7/14</font></s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Made irrelevant by change in response to previous comment.</font><br />
<br />
==Provong that the perko knots are equivalent==<br />
*<s><font color=orangered>Title of this section: pair is singular. So should it be "is" not "are"? Don't get mad at me it's just that I don't know and it sounds kind of funny and I'm sorry I'm trying to fix your grammar just trying to help but maybe you could add the word "knots" to this title to make it all better dont hate me? [[User:Rscott3|Richard]] 7/14</font></s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Hahaha! I didn't notice I did that, but I think it happened because it's weird to say that something "is" equivalent - equivalent to what? I changed it to "knots are".</font><br />
<br />
*<s><font color=orangered>Typo: "...Kenneth Perko provided an '''abridge''' proof..." [[User:Rscott3|Richard]] 7/14</font></s><br />
<br />
*<font color=orangered>I think it'd be cool if you labeled which is perko a and perko b in the picture. [[User:Rscott3|Richard]] 7/14</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Actually, the only places where I've seen them labeled that way have been projections that don't match mine, so I'll just remove those two names.</font><br />
<br />
*<s><font color=orangered>You say "Reiemeister images" here. I'd stay consistent with "moves". [[User:Rscott3|Richard]] 7/14</font></s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Oops! I didn't even know that happened, Reidemeister images aren't a thing…</font><br />
<br />
==Why it's interesting==<br />
*<font color=orangered>Second Redundancy: The guy wrote the book in 1899. This one like I said above might not be so bad with the extended proof. [[User:Rscott3|Richard]] 7/14</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): I think I'm going to keep this because if you expanded the MME the old date occurred a long time ago.</font><br />
<br />
*<font color=orangered>TI think you could have waaaaaaaaay more fun with this part. You could do something that shows an ambient isotopy to a shoe tying knot or something. You could link to the Spongebob shoe tying song (This suggestion not so much.) And I'm serious when I say you should maybe link to entanglement--a knot game... [[User:Rscott3|Richard]] 7/14</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Those are some good suggestions, I'll think about it and try and figure out something to add.</font><br />
}}</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Perko_pair_knots&diff=26645Talk:Perko pair knots2011-07-21T03:04:05Z<p>Rebecca: /* Good writing */</p>
<hr />
<div><font color=blue>Richard Scott</font> likes this.<br />
<br />
=Response to Checklist=<br />
Original response to checklist, in black, completed by [[User:Kderosier|Kate]] 19:42, 20 July 2011 (UTC)<br />
<br />
==References and footnotes==<br />
*All images cited on click-through<br />
*Footnotes and references used<br />
<br />
==Good writing==<br />
===Context===<br />
*Basic description and Why It's Interesting give historical context and connection to science<br />
<br />
===Quality of prose and page structuring===<br />
*Section headings and first sentences explain purpose of each section<br />
*Relevance of each section is clear<br />
*More complicated math is hidden and/or placed near end of MME <br />
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===Integration of Images and Text===<br />
*Images are referred to explicitly<br />
*Captions and text explain the purpose of each image<br />
*The main proof is a series of images<br />
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===Connections to other mathematical topics===<br />
*I didn't see anywhere to make relevant connections - there is nothing else on the site about knot theory<br />
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===Examples, Calculations, Applications, Proofs===<br />
*The main content of the page is the proof that the two knots are the same<br />
*Examples are given and explained in the Dowker notation section<br />
*Applications of knot theory in general are explained very generally in Why It's Interesting, I don't know of any applications for these specific knots<br />
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===Mathematical Accuracy and precision of language===<br />
*All statements are accurate to the best of my knowledge<br />
*Unfamiliar terms are defined (Two of the 3 sections in the MME are devoted to explaining terminology/notation that readers unfamiliar with knot theory can't be expected to know)<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 03:04, 21 July 2011 (UTC) "Belief in ether soon faded, but interest in identifying and cataloging different types of knots stayed. " maybe "remained" instead of "stayed"? </font color><br />
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===Layout===<br />
*Paragraphs are short, many images are used<br />
*Page has been viewed in a variety of window sizes, spacing and layout seems as good as it can get given the information that needs to be displayed<br />
*Hide/shows used in several places to prevent intimidation<br />
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=Pre-final review comments=<br />
{{Hide|1=<br />
==General Comments==<br />
*<font color=orangered>This page is really good and really clear. It's very easy to follow. There's not a ton of info, but that's okay. The one problem is that you say some things a couple of times. Right now, the page is short enough that these redundancies are fresh in the reader's mind, but after the proof is complete, this may not be so noticeable. [[User:Rscott3|Richard]] 7/14</font><br />
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*<font color=orangered>Are the Reidemeister moves a method of solving "knot problems" or are they tools you use to solve them? To me, it sounds like you're using the word as both, which may be right for all I know. [[User:Rscott3|Richard]] 7/14</font><br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 20:53, 14 July 2011 (UTC): I don't really understand what you're asking. Can we talk about it tomorrow?</font><br />
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==Basic Description==<br />
:<font color=red>xd 18:33, 12 June 2011 (UTC) I think you need a better transition between "To say that two knots are the same is to say that one can be deformed into the other without breaking the knot or passing it through itself." and the next one about the projection. I don't quite see the link between them. Since you have an explanation about projection in the Reidemeister moves section, I think you can get rid of this part.<br />
</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:09, 14 June 2011 (UTC): I really wanted to have projections explained in the basic description section, because they're important and not ''that'' hard to understand, so I changed it around. Does it read better now?</font><br />
<br />
==Reidemeister moves==<br />
:<font color=red>xd 18:33, 12 June 2011 (UTC) I don't understand the part of "projection of a knot was printed on very stretchy rubber" and you can stretch and none of the crossings are affected. How is that so?</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 13:17, 13 June 2011 (UTC): Thanks for pointing that out, I'll try and think of a better way to explain it. Personally, I think of those pictures printed on fruit roll-ups - you can stretch them all over the place, but you're only warping the image, not "really" changing it.</font><font color=red>xd 20:37, 13 June 2011 (UTC) ok. if you can find a way, then all the better, if not, i think you can avoid mentioning that.</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:08, 14 June 2011 (UTC):Yeah, I'm not going to bring up Fruit Roll-ups, but I really do need to explain planar isotopies, because I'm going to be using them in my proof, so hopefully I'll think of a way to elaborate on that explanation.</font><br />
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*<s><font color=orangered>First redundncy: you already mentioned the projection in the Basic Description. You basically state the same info again, but this time you do introduce new ideas about the projection in this section. I think it's fine, just something to look out for. [[User:Rscott3|Richard]] 7/14</font></s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Good point, changed it.</font><br />
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*<s><font color=orangered>Typo: "...or after moving the knot '''trough''' any ambient isotopy." [[User:Rscott3|Richard]] 7/14</font></s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Made irrelevant by change in response to previous comment.</font><br />
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==Provong that the perko knots are equivalent==<br />
*<s><font color=orangered>Title of this section: pair is singular. So should it be "is" not "are"? Don't get mad at me it's just that I don't know and it sounds kind of funny and I'm sorry I'm trying to fix your grammar just trying to help but maybe you could add the word "knots" to this title to make it all better dont hate me? [[User:Rscott3|Richard]] 7/14</font></s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Hahaha! I didn't notice I did that, but I think it happened because it's weird to say that something "is" equivalent - equivalent to what? I changed it to "knots are".</font><br />
<br />
*<s><font color=orangered>Typo: "...Kenneth Perko provided an '''abridge''' proof..." [[User:Rscott3|Richard]] 7/14</font></s><br />
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*<font color=orangered>I think it'd be cool if you labeled which is perko a and perko b in the picture. [[User:Rscott3|Richard]] 7/14</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Actually, the only places where I've seen them labeled that way have been projections that don't match mine, so I'll just remove those two names.</font><br />
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*<s><font color=orangered>You say "Reiemeister images" here. I'd stay consistent with "moves". [[User:Rscott3|Richard]] 7/14</font></s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Oops! I didn't even know that happened, Reidemeister images aren't a thing…</font><br />
<br />
==Why it's interesting==<br />
*<font color=orangered>Second Redundancy: The guy wrote the book in 1899. This one like I said above might not be so bad with the extended proof. [[User:Rscott3|Richard]] 7/14</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): I think I'm going to keep this because if you expanded the MME the old date occurred a long time ago.</font><br />
<br />
*<font color=orangered>TI think you could have waaaaaaaaay more fun with this part. You could do something that shows an ambient isotopy to a shoe tying knot or something. You could link to the Spongebob shoe tying song (This suggestion not so much.) And I'm serious when I say you should maybe link to entanglement--a knot game... [[User:Rscott3|Richard]] 7/14</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 20:21, 14 July 2011 (UTC): Those are some good suggestions, I'll think about it and try and figure out something to add.</font><br />
}}</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Pages_Ready_for_Final_Review&diff=26630Pages Ready for Final Review2011-07-21T02:14:16Z<p>Rebecca: /* Swarthmore Pages */</p>
<hr />
<div>=Pages Ready for Final Review=<br />
Once your page has gone through several cycles of feedback and you (the author) feel that it is ready for the public:<br />
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*Take a few minutes and type up a response to the issues brought up by the checklist by writing 1-3 sentences in response to the bold headings on the checklist. (Check out the [[Sample Response to Checklist]])<br />
*Link the page here. <br />
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Your page will be reviewed by one of the designated final reviewers who will either give you further feedback or mark the page as "ready for the public."<br />
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'''<font color=darkred> AN IMPORTANT NOTE ABOUT PAGES PUT UP FOR FINAL REVIEW BETWEEN JULY 18TH AND 22ND'''<br />
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'''Anna is going to a training which will keep her extremely busy during that week. Priority for editing will be given to Swarthmore students and any others for whom it is their last week of work on the project (please note if you are NOT at Swarthmore and it is your last week. ''' I will make a big effort to get through everything posted by this weekend, so there isn't a backlog. I will also be completely unavailable for editing August 6th-15th, and will not be reachable during that time. </font> <br />
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'''<font color=olive><font color=green>CHRIS T.</font> and <font color=blue>STEVE C.</font> will be helping to review pages while Anna is busy.</font>'''<br />
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===Swarthmore Pages===<br />
*[[Perko pair knots]] by [[User:Kderosier|Kate]] 19:48, 20 July 2011 (UTC)<br />
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*[[Logistic Bifurcation]] by [[User:Dpatton1|Diana]] 17:00 7/7/11<br />
:<font color=green> Chris 7/16 I've put up comments from a "layman's" perspective. </font><br />
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*[[Radians]] by [[User:Htasoff|Htasoff]]<br />
:<font color=green> Chris 7/18. I've made a few comments. </font><br />
::<font color=Mediumblue>Check</font><br />
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*[[Snell's Law]] [[User:Ljeanlo1|Ljeanlo1]] 16:14, 18 July 2011 (UTC) <br />
:<font color=darkred> I had a bit of unexpected time, so I added one more comment. I think that's all the comments I have for now! </font> <br />
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*[[Witch of Agnesi]] <br />
new draft for final [[User:Ljeanlo1|Ljeanlo1]] 20:07, 20 July 2011 (UTC)<br />
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*[[Congruent triangles]] by [[User:Htasoff|Htasoff]]<br />
:Is fully developed and has instructions for future editors based on Steve's comments.<br />
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*[[Dimensions]] by [[User:Htasoff|Htasoff]]<br />
:<font color=green> SteveC 7/20 -- a couple of comments.</font><br />
::<font color=Mediumblue>Confused, Please explain.</font><br />
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*[[Cross-cap]] by [[User:Htasoff|Htasoff]]<br />
:<font color=slateblue>[[User:Rebecca|Rebecca]] 02:14, 21 July 2011 (UTC) I left a few comments on the checklist. Overall the page is great, and I will approve it as soon as you address these last few things </font color><br />
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===Sweet Briar Pages=== <br />
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*[[Waves]] by [[User:Flora1103|Flora Li]] 20:25, 13 July 2011 (UTC)<br />
:<font color=darkred> Just one ''tiny'' comment left [[User:AnnaP|AnnaP]] 19:42, 20 July 2011 (UTC) </font><br />
::<font color=plum>Flora 07.20 17:09 I have motified that point. Thanks for your work.</font><br />
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*[[Dandelin Spheres Theory]] by [[User:Flora1103|Flora Li]] 15:31, 17 July 2011 (UTC)<br />
:<font color=green> Chris 7.20.11 I've responded to some of your changes and comments. </font><br />
::<font color=plum>Flora 07.20 12:08 I responsed to your suggetions and made a little more changes.</font><br />
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*[[Dihedral Groups]] by [[User:Flora1103|Flora Li]] 18:27, 18 July 2011 (UTC)<br />
:<font color=plum> I make some change, and responsed to your comments. Flora 07.20 11:44</font><br />
::<font color=darkred> a couple more tiny comments to address, then it's good to go </font><br />
:::<font color=plum>Flora 07.20 4:59 Fixed images' titles and the links.</font> <br />
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*[[Pigeonhole Principle]] by [[User:PhoebeJiang|Phoebe]]<br />
:<font color=green> Chris 7.20.11 I've put up comments on this. </font><br />
::<font color=salmon> Thank you Chris. I've made some changes according to your comments. Also responded to some concerns you may have. Phoebe 7/20</font><br />
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*[[Application of the Euclidean Algorithm]] by [[User:PhoebeJiang|Phoebe]]<br />
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*[[Steiner's Chain]] by [[User:Donko14|Anna]]<br />
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===Rensselaer Polytechnic Institute===<br />
[[Polar Equations]] by [[User:Chanj|Chanj]] 21:35, 7 July 2011 (UTC)<br />
:<font color=blue> I have edited my page by putting up new images, more detailed explanations and comments in the discussion reflecting those changes. --[[User:Chanj|Chanj]] 20:48, 15 July 2011 (UTC)</font><br />
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===Drexel Pages===<br />
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=Approved Pages=<br />
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Once an editor moves the link to your page here, they have marked it as ready for the public!<br />
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*[[Vector]]<br />
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===Sweet Briar Pages===<br />
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==Other Links==<br />
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[[DU11]]</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Cross-cap&diff=26629Talk:Cross-cap2011-07-21T02:09:00Z<p>Rebecca: /* Good writing */</p>
<hr />
<div>==Final Review==<br />
<br />
<br />
=== Messages to the Future ===<br />
<br />
* No comments seemed necessary.<br />
<br />
=== References and footnotes ===<br />
<br />
* All images are properly attributed in the page you see when you click on the image. Attributions include original source and remarks if you've modified.<br />
* No direct quotes are used.<br />
* References for text are at the end of the page, with option links to the footnotes within the text.<br />
<br />
=== Good writing ===<br />
<br />
The following items are just meant to be reminders. If one of these items needs clarification, or seems like a great idea that you don't know how to implement, see [[What_Makes_a_Good_Math_Images_Page%3F| What Makes a Good Math Images Page?]].<br />
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'''Context (aka Generating interest aka Who cares?)'''<br />
<br />
* I explain the one-sidedness and non-orientability. The Why It's Interesting section mostly points out that the Cross-cap is interesting as it is a model of the Real Projective Plane.<br />
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<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:08, 21 July 2011 (UTC) If you have time, I'd like to see more about how it's used to model human vision. You could even just add it to future directions for the page. </font color><br />
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'''Quality of prose and page structuring'''<br />
<br />
* The beginning paragraph(s) of the page introduce the cross-capped disk. I realize that they are a bit technical, however I have done my best to explain the terminology I use and provide links.<br />
* Although it is a bit conceptual, I included a discussion of dimensions in the Basic Description as I believe it is crucial to understanding the self intersection of the Cross-cap that often frustrates people.<br />
* I placed the equations that parametrize the Cross-capped disk toward the end of the More Mathematical Explanation, and had the explanation and construction of the Cross-cap at the beginning. The<br />
<br />
'''Integration of Images and Text'''<br />
<br />
* Wherever an image or animation is used to help with an explanation, the reader is explicitly instructed to refer to the image.<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:07, 21 July 2011 (UTC) The applets are so cool and it's nice that they're hidden because they slow the page down a bit. You might want to add a disclaimer "This applet may take up to a minute to load" or something along those lines so people don't give up on it. It just took a while (20 seconds?) on my computer. </font color><br />
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'''Connections to other mathematical topics'''<br />
<br />
* This page is heavily tied to the Mobius strip and Real Projective Plane. <br />
* Fluidly links to such topics as [[Dimensions]], [[Mobius Strip]], [Real Projective Plane]], [[Parametric Equations]], and [[Topology Glossary]].<br />
<br />
'''Examples, Calculations, Applications, Proofs'''<br />
<br />
* I introduce new ideas with explanations and analogies.<br />
* Most of the proofs on this page are visual of conceptual, and are explained step by step.<br />
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'''Mathematical Accuracy and precision of language'''<br />
<br />
* In terms of the mathematical and technical accuracy of the page: I sent it to Don Shimmomoto for review, and he approved it with a few comments, which I have since addressed.<br />
* I try to make my statements as precise as they can be without overwhelming the reader with too many words or dense symbols. I realize that some parts of the page are slightly denser than others, and did my best to thin technical heavy parts into slightly longer, less dense sections. <br />
* I have many explanations, analogies, mouse-overs, and links to aid readers with new terms and concepts .<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:05, 21 July 2011 (UTC) "Surface that is non-orientable, and has only one side." - no comma<br />
* Consider bolding "4 embeddable"<br />
</font color><br />
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'''Layout'''<br />
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* Text is in short paragraphs, and broken up by relevant images throughout.<br />
* Hide and mouse-over features are used as appropriate to reduce clutter and scariness. <br />
** I did hide a second method of constructing of the Cross-cap. The interactive applets are also hidden, as they take up a lot of page space.<br />
** I did not hide the parametrization section. I figured that it was unnecessary as the ME section is already hidden at the start.<br />
* To whatever extent possible, pages do not have large, awkward chunks of white space.<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:06, 21 July 2011 (UTC) The layout of your pictures is pretty spaced out in my window. Did you consider making image 8 and 10 smaller? </font color><br />
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==Harrison's Notes to Self==<br />
<br />
[[User:Htasoff|Htasoff]] 14:15, 8 June 2011 (UTC)<br />
<br />
Accuracy of the article<br />
<br />
*There is virtually nothing in the article (other than the lovely graphics) that is not false. Starting with the misguided attempt to roughly define a cross-cap in the first sentence.<br />
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* First of all, a cross-cap is never topologically equivalent to a Moebius strip. It is a continuous image by a certain type of map of the (closed) Moebius strip into 3-space, a map that has an open interval's worth of double-points.<br />
<br />
* As a topological subspace of 3-space, it is the space obtained by starting with a closed disk D2, choosing an interval in the disk's interior -- say the image of [-1,1] via an embedding h: [-1,1] → int(D2) -- and then identifying the points h(x) and h(-x) with each other for all x in (0,1].<br />
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* A cross-cap may have a boundary that is a round (perfect) circle, but is required only to have a boundary that is an unknotted simple closed curve.<br />
<br />
* Further, there are continuous deformations of the usual picture of a Moebius band to a picture that is still topologically a Moebius band embedded in 3-space (i.e., with no self-intersections), such that its boundary is a perfect circle. So this perfect-circle-boundary property in no way characterizes a cross-cap.<br />
<br />
* The word cross-cap has been erroneously used to mean a cross-cap with a disk glued on to its boundary (making a continuous image of a projective plane). But this is an error, and it should not be perpetuated in this article. Rather, the article should warn people to avoid this misuse of the word.Daqu 00:53, 4 December 2006 (UTC)Daqu 01:18, 4 December 2006 (UTC)<br />
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http://en.wikipedia.org/wiki/Talk:Cross-cap<br />
<br />
Text in MME is getting truncated when viewed through edit with form, but still appears on the page.<br />
<br />
Note to self: f: X --> Y means X is a subspace of the original Y.<br />
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[[User:Htasoff|Htasoff]] 20:09, 2 June 2011 (UTC)<br />
Need the mathematical accuracy of this simplification to be checked: <balloon title="Finite and without edges.">closed surface</balloon><br />
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http://vmm.math.uci.edu/3D-XplorMath/j/applets/en/tree/FullTree.html<br />
Useful?<br />
<br />
=General Comments=<br />
'''Jenn Chan (chanj)'''<br><br />
Hey, I noticed that you have a request for an applet for the cross-cap page, and I found this web site that has what you're looking for.<br><br />
http://3d-xplormath.org/j/applets/en/index.html <br>Cross-cap is on the list.<br><br><font color=Mediumblue>Thank you. I have seen that one and it is really nice. Reza at Drexel made some applets for me that display the exact figures defined by the parametrization on the page, which I made in Mathematica. So all is well.</font><br />
<font color=orangered> Your capital letters seem funky to me. Should "Cross-cap" be capitalized? What about "Real Projective Plane"? -Richard 6/9</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:27, 9 June 2011 (UTC): Agreed.</font><br />
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=Section-specific comments=<br />
==Intro==<br />
<font color=orangered> I don't exactly know our policy on this, but do we want links to other pages in our opening sentence/paragraph? I almost think it's better to wait to link til you introduce the word in the basic description. -Richard 6/9</font><br />
<br />
<br />
==Basic Description==<br />
<font color=orangered> <br />
*The closed-surface mouseover seems incomplete to me. It's just adjectives, not a definition?<font color=Mediumblue>CHECK</font><br />
<br />
*Second paragraph: would it be better to talk about the main image first? I'm getting confused here with all of "the upper surface of the outside of the Cross-cap" It's hard to keep track.<br />
:* what if you start out by saying I'll refer to this part as ceiling, this part as floor, this part as roof/top and this part as the bottom. Maybe with a diagram?<font color=Mediumblue>CHECK, added Labels to image.</font><br />
<br />
*Repeated "the". </font>"So '''the the''' top of the Cross-cap..."<br />
<font color=orangered><font color=Mediumblue>CHECK</font><br />
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*You sound very informal.<font color=Mediumblue>Rectified</font><br />
:*"Here is why."<br />
:*Now to explain..."<br />
<br />
* When you talk about seeing the cross-cap in the fourth dimension, I really like your description. Might it also be helpful if you used an example with time at the fourth dimension?<br />
:* At time t = 1, you could be at (8,7,6) for one parametrization and at the same point when t=5 for another parametrization. These intersect in 3 dimensions, but not 4.<font color=Mediumblue>I had been thinking about that, and have yet to figure out the best way to convey this. The proper animation would be great, but is beyond my knowledge of how to put together. If someone could hunt down how to do this, it would be great.</font><br />
<br />
*What's "4 embeddable"?????? Maybe a mouseover here if the definition is already on another page.<font color=Mediumblue>Switched the order of the sentence to, hopefully, improve clarity.</font><br />
<br />
-Richard 6/9<br />
</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Most of this section does a good job of being as basic as possible, but your first paragraph is really intimidating, mostly because it sort of starts off with all this terminology that a reader might never have seen before.</font><br />
<br />
<font color=dodgerblue><br />
*''Unlike another, more well-known, one-sided object, the Mobius strip, the Cross-cap is a closed surface, and, as a result, 3 dimensional models of it intersect, or pass through, themselves.''<font color=Mediumblue>CHECK</font><br />
:*This sentence has way too many commas in it. Most of them aren't incorrect, but it took me several read-throughs to figure that out. I'd try and rephrase it so it's simpler, even if that takes two sentences.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*The discussion of why it self-intersects made sense, but I think it'd be even clearer if you had a picture illustrating the ball example. </font><font color=Mediumblue>CHECK</font><br />
:<font color=dodgerblue>Yup, picture helps a lot.</font><br />
<br />
<font color=dodgerblue><br />
*This section has a lot of text at once. I think it'd be good if you broke it up with sub-sections, and maybe added more images. (Perhaps an image showing what you mean by floor and ceiling would be helpful.)</font><font color=Mediumblue>CHECK</font><br />
<br />
==A More Mathematical Explanation==<br />
<br />
<font color=orangered> <br />
Maybe make "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" and "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" be in math writing.<font color=Mediumblue>CHECK</font><br />
-Richard 6/9</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Putting the domain for your parametrizations as bullet points under the equations doesn't make sense to me.<br />
</font><font color=Mediumblue>I did away with the bullet point. Hopefully this will avoid confusion.</font><br />
:<font color=dodgerblue>Yes, I find it much less confusing now.<br />
<br />
<font color=dodgerblue><br />
*Both generate the same shape, they merely construct it in a different orientation. The following parametrization''',''' generates '''a the''' Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<br />
:*I would suggest changing this to:<br />
::Both '''sets of equations''' generate the same shape, they merely construct it in a different orientation. The following parametrization generates a Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*Can you put in images for the different parametrizations, so I can see how they differ from each other? <br />
</font><font color=Mediumblue>I left a note to the Rensselaer people asking if they could help me upload 3D graphics.</font><br />
<br />
<font color=dodgerblue><br />
*Typo: ''Sitching the cos(u)…'' - should be "Switching"<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*I think it would be much more helpful to have a bubble on homeomorphic than a red link.<font color=Mediumblue>CHECK</font><br />
</font><font color=Mediumblue><s>It's a big idea that I don't think can be summarized in a bubble.</s></font><br />
:<font color=dodgerblue>Even just saying "Two forms/shapes/things are homeomorphic if they are considered topologically the same" would be more helpful than nothing. I think this would be an ideal place to use a combined bubble/link to helper page, if Abram can find the code for that.</font><br />
<br />
<font color=dodgerblue><br />
*Should there be something in this section other than just all of these equations? I think I'd really like it if there were more text… </font><font color=Mediumblue>I think so, too. Any Suggestions?</font><br />
:<font color=dodgerblue>All I know about cross-caps is what you taught me on this page, so no, sorry. -[[User:Kderosier|Kate]] 18:32, 9 June 2011 (UTC)</font><font color=Mediumblue>I'm on it.</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Cross-cap&diff=26628Talk:Cross-cap2011-07-21T02:08:35Z<p>Rebecca: /* Good writing */</p>
<hr />
<div>==Final Review==<br />
<br />
<br />
=== Messages to the Future ===<br />
<br />
* No comments seemed necessary.<br />
<br />
=== References and footnotes ===<br />
<br />
* All images are properly attributed in the page you see when you click on the image. Attributions include original source and remarks if you've modified.<br />
* No direct quotes are used.<br />
* References for text are at the end of the page, with option links to the footnotes within the text.<br />
<br />
=== Good writing ===<br />
<br />
The following items are just meant to be reminders. If one of these items needs clarification, or seems like a great idea that you don't know how to implement, see [[What_Makes_a_Good_Math_Images_Page%3F| What Makes a Good Math Images Page?]].<br />
<br />
'''Context (aka Generating interest aka Who cares?)'''<br />
<br />
* I explain the one-sidedness and non-orientability. The Why It's Interesting section mostly points out that the Cross-cap is interesting as it is a model of the Real Projective Plane.<br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:08, 21 July 2011 (UTC) If you have time, I'd like to see more about how it's used to model human vision. You could even just add it to future directions for the page. </font color><br />
<br />
'''Quality of prose and page structuring'''<br />
<br />
* The beginning paragraph(s) of the page introduce the cross-capped disk. I realize that they are a bit technical, however I have done my best to explain the terminology I use and provide links.<br />
* Although it is a bit conceptual, I included a discussion of dimensions in the Basic Description as I believe it is crucial to understanding the self intersection of the Cross-cap that often frustrates people.<br />
* I placed the equations that parametrize the Cross-capped disk toward the end of the More Mathematical Explanation, and had the explanation and construction of the Cross-cap at the beginning. The<br />
<br />
'''Integration of Images and Text'''<br />
<br />
* Wherever an image or animation is used to help with an explanation, the reader is explicitly instructed to refer to the image.<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:07, 21 July 2011 (UTC) The applets are so cool and it's nice that they're hidden because they slow the page down a bit. You might want to add a disclaimer "This applet may take up to a minute to load" or something along those lines so people don't give up on it. It just took a while (20 seconds?) on my computer. </font color><br />
<br />
'''Connections to other mathematical topics'''<br />
<br />
* This page is heavily tied to the Mobius strip and Real Projective Plane. <br />
* Fluidly links to such topics as [[Dimensions]], [[Mobius Strip]], [Real Projective Plane]], [[Parametric Equations]], and [[Topology Glossary]].<br />
<br />
'''Examples, Calculations, Applications, Proofs'''<br />
<br />
* I introduce new ideas with explanations and analogies.<br />
* Most of the proofs on this page are visual of conceptual, and are explained step by step.<br />
<br />
<br />
'''Mathematical Accuracy and precision of language'''<br />
<br />
* In terms of the mathematical and technical accuracy of the page: I sent it to Don Shimmomoto for review, and he approved it with a few comments, which I have since addressed.<br />
* I try to make my statements as precise as they can be without overwhelming the reader with too many words or dense symbols. I realize that some parts of the page are slightly denser than others, and did my best to thin technical heavy parts into slightly longer, less dense sections. <br />
* I have many explanations, analogies, mouse-overs, and links to aid readers with new terms and concepts .<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:05, 21 July 2011 (UTC) "Surface that is non-orientable, and has only one side." - no comma<br />
* Consider bolding "4 embeddable"<br />
</font color><br />
<br />
'''Layout'''<br />
<br />
* Text is in short paragraphs, and broken up by relevant images throughout.<br />
* Hide and mouse-over features are used as appropriate to reduce clutter and scariness. <br />
** I did hide a second method of constructing of the Cross-cap. The interactive applets are also hidden, as they take up a lot of page space.<br />
** I did not hide the parametrization section. I figured that it was unnecessary as the ME section is already hidden at the start.<br />
* To whatever extent possible, pages do not have large, awkward chunks of white space.<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:06, 21 July 2011 (UTC) The layout of your pictures is pretty spaced out in my window. Did you consider making image 8 and 10 smaller? </font color><br />
<br />
==Harrison's Notes to Self==<br />
<br />
[[User:Htasoff|Htasoff]] 14:15, 8 June 2011 (UTC)<br />
<br />
Accuracy of the article<br />
<br />
*There is virtually nothing in the article (other than the lovely graphics) that is not false. Starting with the misguided attempt to roughly define a cross-cap in the first sentence.<br />
<br />
* First of all, a cross-cap is never topologically equivalent to a Moebius strip. It is a continuous image by a certain type of map of the (closed) Moebius strip into 3-space, a map that has an open interval's worth of double-points.<br />
<br />
* As a topological subspace of 3-space, it is the space obtained by starting with a closed disk D2, choosing an interval in the disk's interior -- say the image of [-1,1] via an embedding h: [-1,1] → int(D2) -- and then identifying the points h(x) and h(-x) with each other for all x in (0,1].<br />
<br />
* A cross-cap may have a boundary that is a round (perfect) circle, but is required only to have a boundary that is an unknotted simple closed curve.<br />
<br />
* Further, there are continuous deformations of the usual picture of a Moebius band to a picture that is still topologically a Moebius band embedded in 3-space (i.e., with no self-intersections), such that its boundary is a perfect circle. So this perfect-circle-boundary property in no way characterizes a cross-cap.<br />
<br />
* The word cross-cap has been erroneously used to mean a cross-cap with a disk glued on to its boundary (making a continuous image of a projective plane). But this is an error, and it should not be perpetuated in this article. Rather, the article should warn people to avoid this misuse of the word.Daqu 00:53, 4 December 2006 (UTC)Daqu 01:18, 4 December 2006 (UTC)<br />
<br />
http://en.wikipedia.org/wiki/Talk:Cross-cap<br />
<br />
Text in MME is getting truncated when viewed through edit with form, but still appears on the page.<br />
<br />
Note to self: f: X --> Y means X is a subspace of the original Y.<br />
<br />
[[User:Htasoff|Htasoff]] 20:09, 2 June 2011 (UTC)<br />
Need the mathematical accuracy of this simplification to be checked: <balloon title="Finite and without edges.">closed surface</balloon><br />
<br />
http://vmm.math.uci.edu/3D-XplorMath/j/applets/en/tree/FullTree.html<br />
Useful?<br />
<br />
=General Comments=<br />
'''Jenn Chan (chanj)'''<br><br />
Hey, I noticed that you have a request for an applet for the cross-cap page, and I found this web site that has what you're looking for.<br><br />
http://3d-xplormath.org/j/applets/en/index.html <br>Cross-cap is on the list.<br><br><font color=Mediumblue>Thank you. I have seen that one and it is really nice. Reza at Drexel made some applets for me that display the exact figures defined by the parametrization on the page, which I made in Mathematica. So all is well.</font><br />
<font color=orangered> Your capital letters seem funky to me. Should "Cross-cap" be capitalized? What about "Real Projective Plane"? -Richard 6/9</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:27, 9 June 2011 (UTC): Agreed.</font><br />
<br />
=Section-specific comments=<br />
==Intro==<br />
<font color=orangered> I don't exactly know our policy on this, but do we want links to other pages in our opening sentence/paragraph? I almost think it's better to wait to link til you introduce the word in the basic description. -Richard 6/9</font><br />
<br />
<br />
==Basic Description==<br />
<font color=orangered> <br />
*The closed-surface mouseover seems incomplete to me. It's just adjectives, not a definition?<font color=Mediumblue>CHECK</font><br />
<br />
*Second paragraph: would it be better to talk about the main image first? I'm getting confused here with all of "the upper surface of the outside of the Cross-cap" It's hard to keep track.<br />
:* what if you start out by saying I'll refer to this part as ceiling, this part as floor, this part as roof/top and this part as the bottom. Maybe with a diagram?<font color=Mediumblue>CHECK, added Labels to image.</font><br />
<br />
*Repeated "the". </font>"So '''the the''' top of the Cross-cap..."<br />
<font color=orangered><font color=Mediumblue>CHECK</font><br />
<br />
*You sound very informal.<font color=Mediumblue>Rectified</font><br />
:*"Here is why."<br />
:*Now to explain..."<br />
<br />
* When you talk about seeing the cross-cap in the fourth dimension, I really like your description. Might it also be helpful if you used an example with time at the fourth dimension?<br />
:* At time t = 1, you could be at (8,7,6) for one parametrization and at the same point when t=5 for another parametrization. These intersect in 3 dimensions, but not 4.<font color=Mediumblue>I had been thinking about that, and have yet to figure out the best way to convey this. The proper animation would be great, but is beyond my knowledge of how to put together. If someone could hunt down how to do this, it would be great.</font><br />
<br />
*What's "4 embeddable"?????? Maybe a mouseover here if the definition is already on another page.<font color=Mediumblue>Switched the order of the sentence to, hopefully, improve clarity.</font><br />
<br />
-Richard 6/9<br />
</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Most of this section does a good job of being as basic as possible, but your first paragraph is really intimidating, mostly because it sort of starts off with all this terminology that a reader might never have seen before.</font><br />
<br />
<font color=dodgerblue><br />
*''Unlike another, more well-known, one-sided object, the Mobius strip, the Cross-cap is a closed surface, and, as a result, 3 dimensional models of it intersect, or pass through, themselves.''<font color=Mediumblue>CHECK</font><br />
:*This sentence has way too many commas in it. Most of them aren't incorrect, but it took me several read-throughs to figure that out. I'd try and rephrase it so it's simpler, even if that takes two sentences.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*The discussion of why it self-intersects made sense, but I think it'd be even clearer if you had a picture illustrating the ball example. </font><font color=Mediumblue>CHECK</font><br />
:<font color=dodgerblue>Yup, picture helps a lot.</font><br />
<br />
<font color=dodgerblue><br />
*This section has a lot of text at once. I think it'd be good if you broke it up with sub-sections, and maybe added more images. (Perhaps an image showing what you mean by floor and ceiling would be helpful.)</font><font color=Mediumblue>CHECK</font><br />
<br />
==A More Mathematical Explanation==<br />
<br />
<font color=orangered> <br />
Maybe make "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" and "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" be in math writing.<font color=Mediumblue>CHECK</font><br />
-Richard 6/9</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Putting the domain for your parametrizations as bullet points under the equations doesn't make sense to me.<br />
</font><font color=Mediumblue>I did away with the bullet point. Hopefully this will avoid confusion.</font><br />
:<font color=dodgerblue>Yes, I find it much less confusing now.<br />
<br />
<font color=dodgerblue><br />
*Both generate the same shape, they merely construct it in a different orientation. The following parametrization''',''' generates '''a the''' Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<br />
:*I would suggest changing this to:<br />
::Both '''sets of equations''' generate the same shape, they merely construct it in a different orientation. The following parametrization generates a Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*Can you put in images for the different parametrizations, so I can see how they differ from each other? <br />
</font><font color=Mediumblue>I left a note to the Rensselaer people asking if they could help me upload 3D graphics.</font><br />
<br />
<font color=dodgerblue><br />
*Typo: ''Sitching the cos(u)…'' - should be "Switching"<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*I think it would be much more helpful to have a bubble on homeomorphic than a red link.<font color=Mediumblue>CHECK</font><br />
</font><font color=Mediumblue><s>It's a big idea that I don't think can be summarized in a bubble.</s></font><br />
:<font color=dodgerblue>Even just saying "Two forms/shapes/things are homeomorphic if they are considered topologically the same" would be more helpful than nothing. I think this would be an ideal place to use a combined bubble/link to helper page, if Abram can find the code for that.</font><br />
<br />
<font color=dodgerblue><br />
*Should there be something in this section other than just all of these equations? I think I'd really like it if there were more text… </font><font color=Mediumblue>I think so, too. Any Suggestions?</font><br />
:<font color=dodgerblue>All I know about cross-caps is what you taught me on this page, so no, sorry. -[[User:Kderosier|Kate]] 18:32, 9 June 2011 (UTC)</font><font color=Mediumblue>I'm on it.</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Cross-cap&diff=26627Talk:Cross-cap2011-07-21T02:07:21Z<p>Rebecca: /* Good writing */</p>
<hr />
<div>==Final Review==<br />
<br />
<br />
=== Messages to the Future ===<br />
<br />
* No comments seemed necessary.<br />
<br />
=== References and footnotes ===<br />
<br />
* All images are properly attributed in the page you see when you click on the image. Attributions include original source and remarks if you've modified.<br />
* No direct quotes are used.<br />
* References for text are at the end of the page, with option links to the footnotes within the text.<br />
<br />
=== Good writing ===<br />
<br />
The following items are just meant to be reminders. If one of these items needs clarification, or seems like a great idea that you don't know how to implement, see [[What_Makes_a_Good_Math_Images_Page%3F| What Makes a Good Math Images Page?]].<br />
<br />
'''Context (aka Generating interest aka Who cares?)'''<br />
<br />
* I explain the one-sidedness and non-orientability. The Why It's Interesting section mostly points out that the Cross-cap is interesting as it is a model of the Real Projective Plane.<br />
<br />
'''Quality of prose and page structuring'''<br />
<br />
* The beginning paragraph(s) of the page introduce the cross-capped disk. I realize that they are a bit technical, however I have done my best to explain the terminology I use and provide links.<br />
* Although it is a bit conceptual, I included a discussion of dimensions in the Basic Description as I believe it is crucial to understanding the self intersection of the Cross-cap that often frustrates people.<br />
* I placed the equations that parametrize the Cross-capped disk toward the end of the More Mathematical Explanation, and had the explanation and construction of the Cross-cap at the beginning. The<br />
<br />
'''Integration of Images and Text'''<br />
<br />
* Wherever an image or animation is used to help with an explanation, the reader is explicitly instructed to refer to the image.<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:07, 21 July 2011 (UTC) The applets are so cool and it's nice that they're hidden because they slow the page down a bit. You might want to add a disclaimer "This applet may take up to a minute to load" or something along those lines so people don't give up on it. It just took a while (20 seconds?) on my computer. </font color><br />
<br />
'''Connections to other mathematical topics'''<br />
<br />
* This page is heavily tied to the Mobius strip and Real Projective Plane. <br />
* Fluidly links to such topics as [[Dimensions]], [[Mobius Strip]], [Real Projective Plane]], [[Parametric Equations]], and [[Topology Glossary]].<br />
<br />
'''Examples, Calculations, Applications, Proofs'''<br />
<br />
* I introduce new ideas with explanations and analogies.<br />
* Most of the proofs on this page are visual of conceptual, and are explained step by step.<br />
<br />
<br />
'''Mathematical Accuracy and precision of language'''<br />
<br />
* In terms of the mathematical and technical accuracy of the page: I sent it to Don Shimmomoto for review, and he approved it with a few comments, which I have since addressed.<br />
* I try to make my statements as precise as they can be without overwhelming the reader with too many words or dense symbols. I realize that some parts of the page are slightly denser than others, and did my best to thin technical heavy parts into slightly longer, less dense sections. <br />
* I have many explanations, analogies, mouse-overs, and links to aid readers with new terms and concepts .<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:05, 21 July 2011 (UTC) "Surface that is non-orientable, and has only one side." - no comma<br />
* Consider bolding "4 embeddable"<br />
</font color><br />
<br />
'''Layout'''<br />
<br />
* Text is in short paragraphs, and broken up by relevant images throughout.<br />
* Hide and mouse-over features are used as appropriate to reduce clutter and scariness. <br />
** I did hide a second method of constructing of the Cross-cap. The interactive applets are also hidden, as they take up a lot of page space.<br />
** I did not hide the parametrization section. I figured that it was unnecessary as the ME section is already hidden at the start.<br />
* To whatever extent possible, pages do not have large, awkward chunks of white space.<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:06, 21 July 2011 (UTC) The layout of your pictures is pretty spaced out in my window. Did you consider making image 8 and 10 smaller? </font color><br />
<br />
==Harrison's Notes to Self==<br />
<br />
[[User:Htasoff|Htasoff]] 14:15, 8 June 2011 (UTC)<br />
<br />
Accuracy of the article<br />
<br />
*There is virtually nothing in the article (other than the lovely graphics) that is not false. Starting with the misguided attempt to roughly define a cross-cap in the first sentence.<br />
<br />
* First of all, a cross-cap is never topologically equivalent to a Moebius strip. It is a continuous image by a certain type of map of the (closed) Moebius strip into 3-space, a map that has an open interval's worth of double-points.<br />
<br />
* As a topological subspace of 3-space, it is the space obtained by starting with a closed disk D2, choosing an interval in the disk's interior -- say the image of [-1,1] via an embedding h: [-1,1] → int(D2) -- and then identifying the points h(x) and h(-x) with each other for all x in (0,1].<br />
<br />
* A cross-cap may have a boundary that is a round (perfect) circle, but is required only to have a boundary that is an unknotted simple closed curve.<br />
<br />
* Further, there are continuous deformations of the usual picture of a Moebius band to a picture that is still topologically a Moebius band embedded in 3-space (i.e., with no self-intersections), such that its boundary is a perfect circle. So this perfect-circle-boundary property in no way characterizes a cross-cap.<br />
<br />
* The word cross-cap has been erroneously used to mean a cross-cap with a disk glued on to its boundary (making a continuous image of a projective plane). But this is an error, and it should not be perpetuated in this article. Rather, the article should warn people to avoid this misuse of the word.Daqu 00:53, 4 December 2006 (UTC)Daqu 01:18, 4 December 2006 (UTC)<br />
<br />
http://en.wikipedia.org/wiki/Talk:Cross-cap<br />
<br />
Text in MME is getting truncated when viewed through edit with form, but still appears on the page.<br />
<br />
Note to self: f: X --> Y means X is a subspace of the original Y.<br />
<br />
[[User:Htasoff|Htasoff]] 20:09, 2 June 2011 (UTC)<br />
Need the mathematical accuracy of this simplification to be checked: <balloon title="Finite and without edges.">closed surface</balloon><br />
<br />
http://vmm.math.uci.edu/3D-XplorMath/j/applets/en/tree/FullTree.html<br />
Useful?<br />
<br />
=General Comments=<br />
'''Jenn Chan (chanj)'''<br><br />
Hey, I noticed that you have a request for an applet for the cross-cap page, and I found this web site that has what you're looking for.<br><br />
http://3d-xplormath.org/j/applets/en/index.html <br>Cross-cap is on the list.<br><br><font color=Mediumblue>Thank you. I have seen that one and it is really nice. Reza at Drexel made some applets for me that display the exact figures defined by the parametrization on the page, which I made in Mathematica. So all is well.</font><br />
<font color=orangered> Your capital letters seem funky to me. Should "Cross-cap" be capitalized? What about "Real Projective Plane"? -Richard 6/9</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:27, 9 June 2011 (UTC): Agreed.</font><br />
<br />
=Section-specific comments=<br />
==Intro==<br />
<font color=orangered> I don't exactly know our policy on this, but do we want links to other pages in our opening sentence/paragraph? I almost think it's better to wait to link til you introduce the word in the basic description. -Richard 6/9</font><br />
<br />
<br />
==Basic Description==<br />
<font color=orangered> <br />
*The closed-surface mouseover seems incomplete to me. It's just adjectives, not a definition?<font color=Mediumblue>CHECK</font><br />
<br />
*Second paragraph: would it be better to talk about the main image first? I'm getting confused here with all of "the upper surface of the outside of the Cross-cap" It's hard to keep track.<br />
:* what if you start out by saying I'll refer to this part as ceiling, this part as floor, this part as roof/top and this part as the bottom. Maybe with a diagram?<font color=Mediumblue>CHECK, added Labels to image.</font><br />
<br />
*Repeated "the". </font>"So '''the the''' top of the Cross-cap..."<br />
<font color=orangered><font color=Mediumblue>CHECK</font><br />
<br />
*You sound very informal.<font color=Mediumblue>Rectified</font><br />
:*"Here is why."<br />
:*Now to explain..."<br />
<br />
* When you talk about seeing the cross-cap in the fourth dimension, I really like your description. Might it also be helpful if you used an example with time at the fourth dimension?<br />
:* At time t = 1, you could be at (8,7,6) for one parametrization and at the same point when t=5 for another parametrization. These intersect in 3 dimensions, but not 4.<font color=Mediumblue>I had been thinking about that, and have yet to figure out the best way to convey this. The proper animation would be great, but is beyond my knowledge of how to put together. If someone could hunt down how to do this, it would be great.</font><br />
<br />
*What's "4 embeddable"?????? Maybe a mouseover here if the definition is already on another page.<font color=Mediumblue>Switched the order of the sentence to, hopefully, improve clarity.</font><br />
<br />
-Richard 6/9<br />
</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Most of this section does a good job of being as basic as possible, but your first paragraph is really intimidating, mostly because it sort of starts off with all this terminology that a reader might never have seen before.</font><br />
<br />
<font color=dodgerblue><br />
*''Unlike another, more well-known, one-sided object, the Mobius strip, the Cross-cap is a closed surface, and, as a result, 3 dimensional models of it intersect, or pass through, themselves.''<font color=Mediumblue>CHECK</font><br />
:*This sentence has way too many commas in it. Most of them aren't incorrect, but it took me several read-throughs to figure that out. I'd try and rephrase it so it's simpler, even if that takes two sentences.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*The discussion of why it self-intersects made sense, but I think it'd be even clearer if you had a picture illustrating the ball example. </font><font color=Mediumblue>CHECK</font><br />
:<font color=dodgerblue>Yup, picture helps a lot.</font><br />
<br />
<font color=dodgerblue><br />
*This section has a lot of text at once. I think it'd be good if you broke it up with sub-sections, and maybe added more images. (Perhaps an image showing what you mean by floor and ceiling would be helpful.)</font><font color=Mediumblue>CHECK</font><br />
<br />
==A More Mathematical Explanation==<br />
<br />
<font color=orangered> <br />
Maybe make "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" and "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" be in math writing.<font color=Mediumblue>CHECK</font><br />
-Richard 6/9</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Putting the domain for your parametrizations as bullet points under the equations doesn't make sense to me.<br />
</font><font color=Mediumblue>I did away with the bullet point. Hopefully this will avoid confusion.</font><br />
:<font color=dodgerblue>Yes, I find it much less confusing now.<br />
<br />
<font color=dodgerblue><br />
*Both generate the same shape, they merely construct it in a different orientation. The following parametrization''',''' generates '''a the''' Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<br />
:*I would suggest changing this to:<br />
::Both '''sets of equations''' generate the same shape, they merely construct it in a different orientation. The following parametrization generates a Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*Can you put in images for the different parametrizations, so I can see how they differ from each other? <br />
</font><font color=Mediumblue>I left a note to the Rensselaer people asking if they could help me upload 3D graphics.</font><br />
<br />
<font color=dodgerblue><br />
*Typo: ''Sitching the cos(u)…'' - should be "Switching"<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*I think it would be much more helpful to have a bubble on homeomorphic than a red link.<font color=Mediumblue>CHECK</font><br />
</font><font color=Mediumblue><s>It's a big idea that I don't think can be summarized in a bubble.</s></font><br />
:<font color=dodgerblue>Even just saying "Two forms/shapes/things are homeomorphic if they are considered topologically the same" would be more helpful than nothing. I think this would be an ideal place to use a combined bubble/link to helper page, if Abram can find the code for that.</font><br />
<br />
<font color=dodgerblue><br />
*Should there be something in this section other than just all of these equations? I think I'd really like it if there were more text… </font><font color=Mediumblue>I think so, too. Any Suggestions?</font><br />
:<font color=dodgerblue>All I know about cross-caps is what you taught me on this page, so no, sorry. -[[User:Kderosier|Kate]] 18:32, 9 June 2011 (UTC)</font><font color=Mediumblue>I'm on it.</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Cross-cap&diff=26626Talk:Cross-cap2011-07-21T02:06:30Z<p>Rebecca: /* Good writing */</p>
<hr />
<div>==Final Review==<br />
<br />
<br />
=== Messages to the Future ===<br />
<br />
* No comments seemed necessary.<br />
<br />
=== References and footnotes ===<br />
<br />
* All images are properly attributed in the page you see when you click on the image. Attributions include original source and remarks if you've modified.<br />
* No direct quotes are used.<br />
* References for text are at the end of the page, with option links to the footnotes within the text.<br />
<br />
=== Good writing ===<br />
<br />
The following items are just meant to be reminders. If one of these items needs clarification, or seems like a great idea that you don't know how to implement, see [[What_Makes_a_Good_Math_Images_Page%3F| What Makes a Good Math Images Page?]].<br />
<br />
'''Context (aka Generating interest aka Who cares?)'''<br />
<br />
* I explain the one-sidedness and non-orientability. The Why It's Interesting section mostly points out that the Cross-cap is interesting as it is a model of the Real Projective Plane.<br />
<br />
'''Quality of prose and page structuring'''<br />
<br />
* The beginning paragraph(s) of the page introduce the cross-capped disk. I realize that they are a bit technical, however I have done my best to explain the terminology I use and provide links.<br />
* Although it is a bit conceptual, I included a discussion of dimensions in the Basic Description as I believe it is crucial to understanding the self intersection of the Cross-cap that often frustrates people.<br />
* I placed the equations that parametrize the Cross-capped disk toward the end of the More Mathematical Explanation, and had the explanation and construction of the Cross-cap at the beginning. The<br />
<br />
'''Integration of Images and Text'''<br />
<br />
* Wherever an image or animation is used to help with an explanation, the reader is explicitly instructed to refer to the image.<br />
<br />
<br />
'''Connections to other mathematical topics'''<br />
<br />
* This page is heavily tied to the Mobius strip and Real Projective Plane. <br />
* Fluidly links to such topics as [[Dimensions]], [[Mobius Strip]], [Real Projective Plane]], [[Parametric Equations]], and [[Topology Glossary]].<br />
<br />
'''Examples, Calculations, Applications, Proofs'''<br />
<br />
* I introduce new ideas with explanations and analogies.<br />
* Most of the proofs on this page are visual of conceptual, and are explained step by step.<br />
<br />
<br />
'''Mathematical Accuracy and precision of language'''<br />
<br />
* In terms of the mathematical and technical accuracy of the page: I sent it to Don Shimmomoto for review, and he approved it with a few comments, which I have since addressed.<br />
* I try to make my statements as precise as they can be without overwhelming the reader with too many words or dense symbols. I realize that some parts of the page are slightly denser than others, and did my best to thin technical heavy parts into slightly longer, less dense sections. <br />
* I have many explanations, analogies, mouse-overs, and links to aid readers with new terms and concepts .<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:05, 21 July 2011 (UTC) "Surface that is non-orientable, and has only one side." - no comma<br />
* Consider bolding "4 embeddable"<br />
</font color><br />
<br />
'''Layout'''<br />
<br />
* Text is in short paragraphs, and broken up by relevant images throughout.<br />
* Hide and mouse-over features are used as appropriate to reduce clutter and scariness. <br />
** I did hide a second method of constructing of the Cross-cap. The interactive applets are also hidden, as they take up a lot of page space.<br />
** I did not hide the parametrization section. I figured that it was unnecessary as the ME section is already hidden at the start.<br />
* To whatever extent possible, pages do not have large, awkward chunks of white space.<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:06, 21 July 2011 (UTC) The layout of your pictures is pretty spaced out in my window. Did you consider making image 8 and 10 smaller? </font color><br />
<br />
==Harrison's Notes to Self==<br />
<br />
[[User:Htasoff|Htasoff]] 14:15, 8 June 2011 (UTC)<br />
<br />
Accuracy of the article<br />
<br />
*There is virtually nothing in the article (other than the lovely graphics) that is not false. Starting with the misguided attempt to roughly define a cross-cap in the first sentence.<br />
<br />
* First of all, a cross-cap is never topologically equivalent to a Moebius strip. It is a continuous image by a certain type of map of the (closed) Moebius strip into 3-space, a map that has an open interval's worth of double-points.<br />
<br />
* As a topological subspace of 3-space, it is the space obtained by starting with a closed disk D2, choosing an interval in the disk's interior -- say the image of [-1,1] via an embedding h: [-1,1] → int(D2) -- and then identifying the points h(x) and h(-x) with each other for all x in (0,1].<br />
<br />
* A cross-cap may have a boundary that is a round (perfect) circle, but is required only to have a boundary that is an unknotted simple closed curve.<br />
<br />
* Further, there are continuous deformations of the usual picture of a Moebius band to a picture that is still topologically a Moebius band embedded in 3-space (i.e., with no self-intersections), such that its boundary is a perfect circle. So this perfect-circle-boundary property in no way characterizes a cross-cap.<br />
<br />
* The word cross-cap has been erroneously used to mean a cross-cap with a disk glued on to its boundary (making a continuous image of a projective plane). But this is an error, and it should not be perpetuated in this article. Rather, the article should warn people to avoid this misuse of the word.Daqu 00:53, 4 December 2006 (UTC)Daqu 01:18, 4 December 2006 (UTC)<br />
<br />
http://en.wikipedia.org/wiki/Talk:Cross-cap<br />
<br />
Text in MME is getting truncated when viewed through edit with form, but still appears on the page.<br />
<br />
Note to self: f: X --> Y means X is a subspace of the original Y.<br />
<br />
[[User:Htasoff|Htasoff]] 20:09, 2 June 2011 (UTC)<br />
Need the mathematical accuracy of this simplification to be checked: <balloon title="Finite and without edges.">closed surface</balloon><br />
<br />
http://vmm.math.uci.edu/3D-XplorMath/j/applets/en/tree/FullTree.html<br />
Useful?<br />
<br />
=General Comments=<br />
'''Jenn Chan (chanj)'''<br><br />
Hey, I noticed that you have a request for an applet for the cross-cap page, and I found this web site that has what you're looking for.<br><br />
http://3d-xplormath.org/j/applets/en/index.html <br>Cross-cap is on the list.<br><br><font color=Mediumblue>Thank you. I have seen that one and it is really nice. Reza at Drexel made some applets for me that display the exact figures defined by the parametrization on the page, which I made in Mathematica. So all is well.</font><br />
<font color=orangered> Your capital letters seem funky to me. Should "Cross-cap" be capitalized? What about "Real Projective Plane"? -Richard 6/9</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:27, 9 June 2011 (UTC): Agreed.</font><br />
<br />
=Section-specific comments=<br />
==Intro==<br />
<font color=orangered> I don't exactly know our policy on this, but do we want links to other pages in our opening sentence/paragraph? I almost think it's better to wait to link til you introduce the word in the basic description. -Richard 6/9</font><br />
<br />
<br />
==Basic Description==<br />
<font color=orangered> <br />
*The closed-surface mouseover seems incomplete to me. It's just adjectives, not a definition?<font color=Mediumblue>CHECK</font><br />
<br />
*Second paragraph: would it be better to talk about the main image first? I'm getting confused here with all of "the upper surface of the outside of the Cross-cap" It's hard to keep track.<br />
:* what if you start out by saying I'll refer to this part as ceiling, this part as floor, this part as roof/top and this part as the bottom. Maybe with a diagram?<font color=Mediumblue>CHECK, added Labels to image.</font><br />
<br />
*Repeated "the". </font>"So '''the the''' top of the Cross-cap..."<br />
<font color=orangered><font color=Mediumblue>CHECK</font><br />
<br />
*You sound very informal.<font color=Mediumblue>Rectified</font><br />
:*"Here is why."<br />
:*Now to explain..."<br />
<br />
* When you talk about seeing the cross-cap in the fourth dimension, I really like your description. Might it also be helpful if you used an example with time at the fourth dimension?<br />
:* At time t = 1, you could be at (8,7,6) for one parametrization and at the same point when t=5 for another parametrization. These intersect in 3 dimensions, but not 4.<font color=Mediumblue>I had been thinking about that, and have yet to figure out the best way to convey this. The proper animation would be great, but is beyond my knowledge of how to put together. If someone could hunt down how to do this, it would be great.</font><br />
<br />
*What's "4 embeddable"?????? Maybe a mouseover here if the definition is already on another page.<font color=Mediumblue>Switched the order of the sentence to, hopefully, improve clarity.</font><br />
<br />
-Richard 6/9<br />
</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Most of this section does a good job of being as basic as possible, but your first paragraph is really intimidating, mostly because it sort of starts off with all this terminology that a reader might never have seen before.</font><br />
<br />
<font color=dodgerblue><br />
*''Unlike another, more well-known, one-sided object, the Mobius strip, the Cross-cap is a closed surface, and, as a result, 3 dimensional models of it intersect, or pass through, themselves.''<font color=Mediumblue>CHECK</font><br />
:*This sentence has way too many commas in it. Most of them aren't incorrect, but it took me several read-throughs to figure that out. I'd try and rephrase it so it's simpler, even if that takes two sentences.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*The discussion of why it self-intersects made sense, but I think it'd be even clearer if you had a picture illustrating the ball example. </font><font color=Mediumblue>CHECK</font><br />
:<font color=dodgerblue>Yup, picture helps a lot.</font><br />
<br />
<font color=dodgerblue><br />
*This section has a lot of text at once. I think it'd be good if you broke it up with sub-sections, and maybe added more images. (Perhaps an image showing what you mean by floor and ceiling would be helpful.)</font><font color=Mediumblue>CHECK</font><br />
<br />
==A More Mathematical Explanation==<br />
<br />
<font color=orangered> <br />
Maybe make "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" and "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" be in math writing.<font color=Mediumblue>CHECK</font><br />
-Richard 6/9</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Putting the domain for your parametrizations as bullet points under the equations doesn't make sense to me.<br />
</font><font color=Mediumblue>I did away with the bullet point. Hopefully this will avoid confusion.</font><br />
:<font color=dodgerblue>Yes, I find it much less confusing now.<br />
<br />
<font color=dodgerblue><br />
*Both generate the same shape, they merely construct it in a different orientation. The following parametrization''',''' generates '''a the''' Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<br />
:*I would suggest changing this to:<br />
::Both '''sets of equations''' generate the same shape, they merely construct it in a different orientation. The following parametrization generates a Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*Can you put in images for the different parametrizations, so I can see how they differ from each other? <br />
</font><font color=Mediumblue>I left a note to the Rensselaer people asking if they could help me upload 3D graphics.</font><br />
<br />
<font color=dodgerblue><br />
*Typo: ''Sitching the cos(u)…'' - should be "Switching"<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*I think it would be much more helpful to have a bubble on homeomorphic than a red link.<font color=Mediumblue>CHECK</font><br />
</font><font color=Mediumblue><s>It's a big idea that I don't think can be summarized in a bubble.</s></font><br />
:<font color=dodgerblue>Even just saying "Two forms/shapes/things are homeomorphic if they are considered topologically the same" would be more helpful than nothing. I think this would be an ideal place to use a combined bubble/link to helper page, if Abram can find the code for that.</font><br />
<br />
<font color=dodgerblue><br />
*Should there be something in this section other than just all of these equations? I think I'd really like it if there were more text… </font><font color=Mediumblue>I think so, too. Any Suggestions?</font><br />
:<font color=dodgerblue>All I know about cross-caps is what you taught me on this page, so no, sorry. -[[User:Kderosier|Kate]] 18:32, 9 June 2011 (UTC)</font><font color=Mediumblue>I'm on it.</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Cross-cap&diff=26625Talk:Cross-cap2011-07-21T02:05:08Z<p>Rebecca: /* Final Review */</p>
<hr />
<div>==Final Review==<br />
<br />
<br />
=== Messages to the Future ===<br />
<br />
* No comments seemed necessary.<br />
<br />
=== References and footnotes ===<br />
<br />
* All images are properly attributed in the page you see when you click on the image. Attributions include original source and remarks if you've modified.<br />
* No direct quotes are used.<br />
* References for text are at the end of the page, with option links to the footnotes within the text.<br />
<br />
=== Good writing ===<br />
<br />
The following items are just meant to be reminders. If one of these items needs clarification, or seems like a great idea that you don't know how to implement, see [[What_Makes_a_Good_Math_Images_Page%3F| What Makes a Good Math Images Page?]].<br />
<br />
'''Context (aka Generating interest aka Who cares?)'''<br />
<br />
* I explain the one-sidedness and non-orientability. The Why It's Interesting section mostly points out that the Cross-cap is interesting as it is a model of the Real Projective Plane.<br />
<br />
'''Quality of prose and page structuring'''<br />
<br />
* The beginning paragraph(s) of the page introduce the cross-capped disk. I realize that they are a bit technical, however I have done my best to explain the terminology I use and provide links.<br />
* Although it is a bit conceptual, I included a discussion of dimensions in the Basic Description as I believe it is crucial to understanding the self intersection of the Cross-cap that often frustrates people.<br />
* I placed the equations that parametrize the Cross-capped disk toward the end of the More Mathematical Explanation, and had the explanation and construction of the Cross-cap at the beginning. The<br />
<br />
'''Integration of Images and Text'''<br />
<br />
* Wherever an image or animation is used to help with an explanation, the reader is explicitly instructed to refer to the image.<br />
<br />
<br />
'''Connections to other mathematical topics'''<br />
<br />
* This page is heavily tied to the Mobius strip and Real Projective Plane. <br />
* Fluidly links to such topics as [[Dimensions]], [[Mobius Strip]], [Real Projective Plane]], [[Parametric Equations]], and [[Topology Glossary]].<br />
<br />
'''Examples, Calculations, Applications, Proofs'''<br />
<br />
* I introduce new ideas with explanations and analogies.<br />
* Most of the proofs on this page are visual of conceptual, and are explained step by step.<br />
<br />
<br />
'''Mathematical Accuracy and precision of language'''<br />
<br />
* In terms of the mathematical and technical accuracy of the page: I sent it to Don Shimmomoto for review, and he approved it with a few comments, which I have since addressed.<br />
* I try to make my statements as precise as they can be without overwhelming the reader with too many words or dense symbols. I realize that some parts of the page are slightly denser than others, and did my best to thin technical heavy parts into slightly longer, less dense sections. <br />
* I have many explanations, analogies, mouse-overs, and links to aid readers with new terms and concepts .<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 02:05, 21 July 2011 (UTC) "Surface that is non-orientable, and has only one side." - no comma<br />
* Consider bolding "4 embeddable"<br />
</font color><br />
<br />
'''Layout'''<br />
<br />
* Text is in short paragraphs, and broken up by relevant images throughout.<br />
* Hide and mouse-over features are used as appropriate to reduce clutter and scariness. <br />
** I did hide a second method of constructing of the Cross-cap. The interactive applets are also hidden, as they take up a lot of page space.<br />
** I did not hide the parametrization section. I figured that it was unnecessary as the ME section is already hidden at the start.<br />
* To whatever extent possible, pages do not have large, awkward chunks of white space.<br />
<br />
==Harrison's Notes to Self==<br />
<br />
[[User:Htasoff|Htasoff]] 14:15, 8 June 2011 (UTC)<br />
<br />
Accuracy of the article<br />
<br />
*There is virtually nothing in the article (other than the lovely graphics) that is not false. Starting with the misguided attempt to roughly define a cross-cap in the first sentence.<br />
<br />
* First of all, a cross-cap is never topologically equivalent to a Moebius strip. It is a continuous image by a certain type of map of the (closed) Moebius strip into 3-space, a map that has an open interval's worth of double-points.<br />
<br />
* As a topological subspace of 3-space, it is the space obtained by starting with a closed disk D2, choosing an interval in the disk's interior -- say the image of [-1,1] via an embedding h: [-1,1] → int(D2) -- and then identifying the points h(x) and h(-x) with each other for all x in (0,1].<br />
<br />
* A cross-cap may have a boundary that is a round (perfect) circle, but is required only to have a boundary that is an unknotted simple closed curve.<br />
<br />
* Further, there are continuous deformations of the usual picture of a Moebius band to a picture that is still topologically a Moebius band embedded in 3-space (i.e., with no self-intersections), such that its boundary is a perfect circle. So this perfect-circle-boundary property in no way characterizes a cross-cap.<br />
<br />
* The word cross-cap has been erroneously used to mean a cross-cap with a disk glued on to its boundary (making a continuous image of a projective plane). But this is an error, and it should not be perpetuated in this article. Rather, the article should warn people to avoid this misuse of the word.Daqu 00:53, 4 December 2006 (UTC)Daqu 01:18, 4 December 2006 (UTC)<br />
<br />
http://en.wikipedia.org/wiki/Talk:Cross-cap<br />
<br />
Text in MME is getting truncated when viewed through edit with form, but still appears on the page.<br />
<br />
Note to self: f: X --> Y means X is a subspace of the original Y.<br />
<br />
[[User:Htasoff|Htasoff]] 20:09, 2 June 2011 (UTC)<br />
Need the mathematical accuracy of this simplification to be checked: <balloon title="Finite and without edges.">closed surface</balloon><br />
<br />
http://vmm.math.uci.edu/3D-XplorMath/j/applets/en/tree/FullTree.html<br />
Useful?<br />
<br />
=General Comments=<br />
'''Jenn Chan (chanj)'''<br><br />
Hey, I noticed that you have a request for an applet for the cross-cap page, and I found this web site that has what you're looking for.<br><br />
http://3d-xplormath.org/j/applets/en/index.html <br>Cross-cap is on the list.<br><br><font color=Mediumblue>Thank you. I have seen that one and it is really nice. Reza at Drexel made some applets for me that display the exact figures defined by the parametrization on the page, which I made in Mathematica. So all is well.</font><br />
<font color=orangered> Your capital letters seem funky to me. Should "Cross-cap" be capitalized? What about "Real Projective Plane"? -Richard 6/9</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:27, 9 June 2011 (UTC): Agreed.</font><br />
<br />
=Section-specific comments=<br />
==Intro==<br />
<font color=orangered> I don't exactly know our policy on this, but do we want links to other pages in our opening sentence/paragraph? I almost think it's better to wait to link til you introduce the word in the basic description. -Richard 6/9</font><br />
<br />
<br />
==Basic Description==<br />
<font color=orangered> <br />
*The closed-surface mouseover seems incomplete to me. It's just adjectives, not a definition?<font color=Mediumblue>CHECK</font><br />
<br />
*Second paragraph: would it be better to talk about the main image first? I'm getting confused here with all of "the upper surface of the outside of the Cross-cap" It's hard to keep track.<br />
:* what if you start out by saying I'll refer to this part as ceiling, this part as floor, this part as roof/top and this part as the bottom. Maybe with a diagram?<font color=Mediumblue>CHECK, added Labels to image.</font><br />
<br />
*Repeated "the". </font>"So '''the the''' top of the Cross-cap..."<br />
<font color=orangered><font color=Mediumblue>CHECK</font><br />
<br />
*You sound very informal.<font color=Mediumblue>Rectified</font><br />
:*"Here is why."<br />
:*Now to explain..."<br />
<br />
* When you talk about seeing the cross-cap in the fourth dimension, I really like your description. Might it also be helpful if you used an example with time at the fourth dimension?<br />
:* At time t = 1, you could be at (8,7,6) for one parametrization and at the same point when t=5 for another parametrization. These intersect in 3 dimensions, but not 4.<font color=Mediumblue>I had been thinking about that, and have yet to figure out the best way to convey this. The proper animation would be great, but is beyond my knowledge of how to put together. If someone could hunt down how to do this, it would be great.</font><br />
<br />
*What's "4 embeddable"?????? Maybe a mouseover here if the definition is already on another page.<font color=Mediumblue>Switched the order of the sentence to, hopefully, improve clarity.</font><br />
<br />
-Richard 6/9<br />
</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Most of this section does a good job of being as basic as possible, but your first paragraph is really intimidating, mostly because it sort of starts off with all this terminology that a reader might never have seen before.</font><br />
<br />
<font color=dodgerblue><br />
*''Unlike another, more well-known, one-sided object, the Mobius strip, the Cross-cap is a closed surface, and, as a result, 3 dimensional models of it intersect, or pass through, themselves.''<font color=Mediumblue>CHECK</font><br />
:*This sentence has way too many commas in it. Most of them aren't incorrect, but it took me several read-throughs to figure that out. I'd try and rephrase it so it's simpler, even if that takes two sentences.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*The discussion of why it self-intersects made sense, but I think it'd be even clearer if you had a picture illustrating the ball example. </font><font color=Mediumblue>CHECK</font><br />
:<font color=dodgerblue>Yup, picture helps a lot.</font><br />
<br />
<font color=dodgerblue><br />
*This section has a lot of text at once. I think it'd be good if you broke it up with sub-sections, and maybe added more images. (Perhaps an image showing what you mean by floor and ceiling would be helpful.)</font><font color=Mediumblue>CHECK</font><br />
<br />
==A More Mathematical Explanation==<br />
<br />
<font color=orangered> <br />
Maybe make "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" and "u = [0, 2π) and v = [0, \tfrac{\pi}{2}]" be in math writing.<font color=Mediumblue>CHECK</font><br />
-Richard 6/9</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:22, 9 June 2011 (UTC):<br />
<br />
*Putting the domain for your parametrizations as bullet points under the equations doesn't make sense to me.<br />
</font><font color=Mediumblue>I did away with the bullet point. Hopefully this will avoid confusion.</font><br />
:<font color=dodgerblue>Yes, I find it much less confusing now.<br />
<br />
<font color=dodgerblue><br />
*Both generate the same shape, they merely construct it in a different orientation. The following parametrization''',''' generates '''a the''' Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<br />
:*I would suggest changing this to:<br />
::Both '''sets of equations''' generate the same shape, they merely construct it in a different orientation. The following parametrization generates a Cross-cap in a different way from the first two, producing a model slightly more similar to the one at the top of the page.<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*Can you put in images for the different parametrizations, so I can see how they differ from each other? <br />
</font><font color=Mediumblue>I left a note to the Rensselaer people asking if they could help me upload 3D graphics.</font><br />
<br />
<font color=dodgerblue><br />
*Typo: ''Sitching the cos(u)…'' - should be "Switching"<font color=Mediumblue>CHECK</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*I think it would be much more helpful to have a bubble on homeomorphic than a red link.<font color=Mediumblue>CHECK</font><br />
</font><font color=Mediumblue><s>It's a big idea that I don't think can be summarized in a bubble.</s></font><br />
:<font color=dodgerblue>Even just saying "Two forms/shapes/things are homeomorphic if they are considered topologically the same" would be more helpful than nothing. I think this would be an ideal place to use a combined bubble/link to helper page, if Abram can find the code for that.</font><br />
<br />
<font color=dodgerblue><br />
*Should there be something in this section other than just all of these equations? I think I'd really like it if there were more text… </font><font color=Mediumblue>I think so, too. Any Suggestions?</font><br />
:<font color=dodgerblue>All I know about cross-caps is what you taught me on this page, so no, sorry. -[[User:Kderosier|Kate]] 18:32, 9 June 2011 (UTC)</font><font color=Mediumblue>I'm on it.</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Dandelin_Spheres_Theory&diff=25648Talk:Dandelin Spheres Theory2011-07-16T03:01:44Z<p>Rebecca: /* Layout */</p>
<hr />
<div>=Response to Checklist=<br />
==Messages to the Future==<br />
* Have left message for future directions.<br />
<br />
==References and footnotes==<br />
* All images are properly attributed in the page you see when you click on the image. Attributions include original source and remarks if you've modified.<br />
* Direct quotes from textual sources are cited.<br />
** References for text are at the end of the page, with option links to the footnotes within the text.<br />
<br />
==Good writing==<br />
<br />
===Context (aka Generating interest aka Who cares?)===<br />
<br />
* This page is specifically for college students who have interest of math, since it contains bunch of proof and not a lot fun.<br />
* I don't know if I need to move my application section to '''why interesting'''<br />
<br />
===Quality of prose and page structuring===<br />
* The beginning paragraph(s) of the page clearly define the topic or purpose of the page as a whole, and may outline the page or preview conclusions that will be reached later in the page.<br />
* The purpose of each section is clearly relevant to the purpose of the page as a whole.<br />
* Still, I don't have a thesis but I follow the section titles as thesis.<br />
* Do not need a helper page.<br />
* My order is definition > 1 proof > 2 proof > application.<br />
<br />
===Integration of Images and Text===<br />
<br />
* Because my images are used be facilitate proofs, I use a lot of words to explain. Since the images I found are from an applet, they are not clear enough, I'm still looking for better ones.<br />
* The text explicitly points out what the reader should observe in a picture. <br />
<br />
Connections to other mathematical topics<br />
<br />
* Wherever possible, relationships between the content of this page and of other topics/ideas in mathematics are identified and explicitly described.<br />
* I made a '''see also''' section to leave links to related topics.<br />
<br />
===Examples, Calculations, Applications, Proofs===<br />
<br />
* Do not have difficult concepts. And always introduce first.<br />
* Proofs are included wherever they would be of interest (this probably means anytime you have a statement whose truth is not totally self-evident and which is important to the page as a whole), but ONLY if writer feels comfortable with the proof (otherwise, it is perfectly acceptable to leave a proof for others).<br />
* Applications of equations, theorems, etc, either to other branches of math or to the world outside of math, whenever these applications seem interesting and/or are needed to set a context (see context section, above). <br />
<br />
===Mathematical Accuracy and precision of language===<br />
<br />
* No error for equations.<br />
* My page has a lot of proof and symbols, I hope they are not overwhelming.<br />
* Any mathematical term that the reader can't be expected to know is defined (err on the side of defining too many terms), either in the body text or via a mouse-over or link to another web resource or a helper page. <br />
<br />
==Layout==<br />
<br />
* Text is in short paragraphs, and broken up by relevant images throughout.<br />
* Hide and mouse-over features are used as appropriate to reduce clutter and scariness. Proofs and large masses of equations in particular should be hidden, and terms should often be defined by mouse-over, rather than in text, if the definitions are short and readers may already know them. But if people cannot be expected to know them, then they should be defined in proper mathematical style, that is, the word being defined should be boldfaced to announce that what follows is a definition, not a rough description.<br />
* To whatever extent possible, pages do not have large, awkward chunks of white space.<br />
* No image in one section of a page vertically aligns with the text or a heading of a different section.<br />
* In hidden text, none of the preview text appears as weird computer code (see Wiki Tricks for help on this).<br />
* The page has been viewed at a few different window sizes to make sure funky things don't happen.<br />
* <font color=slateblue> Much better with less hidden text </font color><br />
<br />
=Discussion=<br />
<br />
<font color=plum>Flora 23:41, 24 June 2011 (UTC) Finish most of the page, still need to work on the application of dandelin spheres, and partial work of the spheres tangent to a circle.</font><br />
<br />
<font color=slateblue>* [[User:Rebecca|Rebecca]] 04:26, 6 July 2011 (UTC)Hi, my name is Becky and I'm one of the people responsible for giving feedback on the project. I've been working primarily with Swarthmore, but I'll be reading a few of your pages as well. <br />
* This is a great idea for a page. Very visual and well presented!</font color><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:42, 6 July 2011 (UTC): Hey Flora, I was just coming back to see how this page was going and it looks like you've made a lot of changes! The things you've fixed definitely help - those sections are a lot easier to read. Like Becky pointed out, there's a little more re-organization left to do, but the content is great, and by the time you're done, this is gonna be a kickass page!</font><br />
<br />
=General Comments=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:46, 29 June 2011 (UTC):<br />
*First off- your table of contents is frighteningly large. There are so many sections, and your section titles are really long, and just ''looking'' at the table of contents makes me feel exhausted. See if you can shorten the section titles, or if you can merge any sections. Maybe some of the proofs can be introduced without having a section title?</font><br />
::<font color=plum>I changed it. Is it much better?</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:22, 29 June 2011 (UTC): THIS IS SO MUCH BETTER!!! :D </font><br />
<br />
*<font color=dodgerblue>Second, as I mentioned on Anna's & Phoebe's pages, a lot of people will miss the content that you have before the table of contents. What they've told us here is that it's better to give just like a one-sentence caption for your picture there, and to move the rest of the information into the Basic Description section, because that's where most people start reading.</font><br />
::Flora 00:29, 30 June 2011 (UTC)<font color=plum>I left 3sentences for this part, I hope this works.</font><br />
<br />
*<font color=dodgerblue>In general, you need to provide a lot more context for what you're doing. Nearly every section could use a bit more explanation for what you're going to do in that section and why. Try and make sure each section has a "topic sentence" or thesis.</font><br />
<br />
<br />
*<font color=dodgerblue>This page is very hard to read. There are a lot of proof-reading type mistakes, but there's also a lack of interest. I had no real sense of what you were doing or why I should care. The organization of this page where you just have to click and click and click to expand more and more dense and confusing proofs was very discouraging. See if you can streamline your organization and find ways to make it clear why I should care about each of your proofs.</font><br />
<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 04:35, 6 July 2011 (UTC) I think overall you have too many "hide/shows" on your page. I understand why you would use them because you have so much information, but it seems like I'm getting lost as I'm reading the page. I would suggest cutting out at the very least half of them. <br />
* I also think you need less sections in the page. It's generally a good idea to divide the text up using section headings, but I think you've got too many on this page. <br />
* I also have to agree with Kate. A lot of the content on this page is GREAT- really informative and interesting, but it's hard to stay interested because I keep losing track of why I'm reading about these things. Would you consider cutting out some of the information and providing more context for the sections you keep? You could discuss this with your prof. at Sweet Briar and see what she thinks as well. </font color><br />
<br />
=Section-specific comments=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:46, 29 June 2011 (UTC): About the image caption before the table of contents - <br />
*''a ball floats in the cone with a touch of the ocean surface.''<br />
::First, you forgot to capitalize this sentence! Second, the ball is the guy's head, right? I think it might be clearer what you're talking about if you say that it's his head. Third, I'm not really sure what you mean by "with a touch of the ocean surface".</font><br />
<br />
*<font color=dodgerblue>''This image can be described as using a plane to cut a cone to create an ellipse, and two different balls tangent to the cone and the ellipse.''<br />
::Awkward wording. I'd try "We can view the water level inside the cone as being an ellipse created by the intersection of a cone and a plane, and the fish and the man's head as being spheres that are tangent to the cone and the ellipse."</font><br />
Flora 00:32, 30 June 2011 (UTC)<font color=plum>Fixed this part</font><br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:46, 29 June 2011 (UTC):<br />
*''As Figure 1 shows. ''<br />
::Awkward wording, try "See Figure 1". Also, this link didn't work for me - is there a picture that goes with it anywhere?</font><br />
*<font color=dodgerblue>The sentence beginning with "In addition" shouldn't be indented.</font><br />
*<font color=dodgerblue>''Since the Dandelin Spheres are created by Conic Sections'' - don't capitalize "conic sections".</font><br />
*<font color=dodgerblue>''(However, parabola can only create one sphere, instead of two.) The inner and outer spheres tangent internally to a cone and also to a plane intersecting the cone are called Dandelin spheres. ''<br />
::I think the part in parentheses should go next to "Parabola" in your bulleted list, not after it. The other sentence is redundant with the definition you gave above - you can probably just delete it.</font><br />
<br />
Flora 00:09, 30 June 2011 (UTC)<font color=plum>Have fixed this part. very appreciate your comments</font><br />
<br />
<font color=slateblue><br />
* I would consider removing the third paragraph of this section. The third paragraph introduces new definitions like "foci and focal constants" that might be overwhelming, and it seems like you might not need to discuss these topics yet. <br />
* I would also recommend adding more images to this basic description. You're writing is very clear, but especially for someone who hasn't encountered these ideas before, it might be difficult to pick out which parts of the main image relate to your explanations. For example, you could make another image of a cone sitting in water with an arrow pointing to the sphere and a label that says "an example of a Dandelin sphere". <br />
* Another image might help in the area where you list the types of conic sections. You could make an image that shows a cone standing upright with a circular conic section as well as a cone tilted sideways with an ellipse for a conic section. <br />
</font color><br />
<br />
===History of Dandelin Spheres===<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:46, 29 June 2011 (UTC): ''He also gave a elegant proof that the spheres intersect the conic section at its foci. '' - I think you should say that the spheres "are tangent to" the conic section, not that they intersect.</font><br />
:<font color=dodgerblue>''(Also, it's "an elegant", not "a elegant"!)''</font><br />
Flora 00:09, 30 June 2011 (UTC)<font color=plum>Fixed. But not update yet. XD</font><br />
<br />
<font color=slate blue> <br />
*[[User:Rebecca|Rebecca]] 04:29, 6 July 2011 (UTC) Good history. You hit the key points, and keep it short. </font color><br />
<br />
==A More Mathematical Explanation==<br />
===Two Theorems Proved by the Dandelin Spheres Theory===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:46, 29 June 2011 (UTC):<br />
*I don't think you need to use bullet points in this section - you can just have two paragraphs.</font><br />
:<font color=plum>Fixed</font><br />
*<font color=dodgerblue>'''''Focus-Directrix Property''', The first theorem is that a closed conic section (i.e. an ellipse) is the locus of points such that the sum of the distances to two fixed points (the foci) is constant.''<br />
::Some grammar mistakes, and I think just "the first theorem" is a little unclear. Try either<br />
:::'''Focus-Directrix Property:''' The first theorem proven by Dandelin Spheres is that a closed conic section…<br />
::or<br />
:::The '''Focus-Directrix Property''' is the first theorem proven by Dandelin Spheres. It states that a closed conic section…<br />
::or<br />
:::The '''Focus-Directrix Property, the first theorem proven by Dandelin Spheres, is that a closed conic section…<br />
</font><br />
:<font color=plum>Fixed</font><br />
*<font color=dodgerblue>"locus" might be an unfamiliar word for some people - you might want to use a green definition balloon here.</font><br />
:<font color=plum>I have added a balloon~</font><br />
*<font color=dodgerblue>''That the intersection of the plane with the cone is symmetric about the perpendicular bisector of the line through F_1 and F_2 may be counterintuitive, but this argument makes it clear.''<br />
::This sentence is confusing - it's connection with what went before isn't obvious.</font><br />
:<font color=plum>I deleted this sentence</font><br />
*<font color=dodgerblue>''Sum of Distances to Foci Property, the second theorem…''<br />
::Same issues as the sentence about the first theorem, same suggestions for fixing it.</font><br />
:<font color=plum>Fixed</font><br />
*<font color=dodgerblue>The paragraph that starts "The directrix of a conic section can be found…" is hard to understand without a picture.</font><br />
:<font color=plum>I will try to find a image for it, but it kinda hard</font><br />
*<font color=dodgerblue>I don't think the hidden part here should be hidden. Also, be careful with your spacing near the end of this section.</font><br />
:<font color=plum>Fixed</font><br />
*<font color=dodgerblue>''This will be shown in the part of Applied Dandelin Spheres.'' and ''These two Theorems will be proved in the part of Explore different Dandelin Spheres. ''<br />
::You don't need the "of"s - you should just say "This will be shown in the section Section Title" or "See Section Title". Also, don't capitalize "theorems".</font><br />
:<font color=plum>Fixed</font><br />
<br />
*<font color=dodgerblue>I found it confusing that in this section you introduce the two theorems and seem to give a brief outline of the proofs, but then leave the proof to a later section. Is there a reason you decided not to do the proofs here?</font><br />
:<font color=plum>I just state the two theorems in this part, but did not prove them. Because I need to prove these two theorems for each conic section, so I put the proof in explore section</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 13:26, 30 June 2011 (UTC): Ok, that makes sense. It wasn't clear to me as I was reading though, so you might want to say just that: "The proofs of these two theorems are different for each conic section, and will be given below" or something.</font><br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 04:31, 6 July 2011 (UTC) I have a few formatting suggestions... <br />
* I would use a colon not a comma after "sum of distances to foci property" and the other small headings in this section.<br />
* I think we've been trying to use bold to indicate words that we are about to define, so I wouldn't use it for "Pappus of Alexandria" and things like that.<br />
* I think mouseover would work well for "the focus," "the directrix," and "eccentricity." That way you can use the word normally in your sentences and put the definition in the bubble, and you can avoid parentheses. <br />
* Nice use of the mouseover for "locus"<br />
</font color><br />
<br />
===Mathematical Description of Two Theorems and Notation===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:13, 29 June 2011 (UTC):<br />
*I don't understand the purpose of this section. As far as I can tell, you're making believable but unjustified claims about a picture involving Dandelin Spheres for no apparent reason. Is this part of a proof for one of the two theorems? Can this section be integrated into either the previous or the following sections?</font><br />
*<font color=dodgerblue>The picture in this section is kind of hard to see - can you find one that's bigger and less blurry?</font><br />
*<font color=dodgerblue>''Germinal Pierre Dandelin emloys spheres inscribed to a cone which touch the intersecting plane in two points which are foci of the conic section. In what follows all the three Dandelin's proofs are presented.''<br />
::Why is this sentence hidden? It's very short and not too mathematical. It's not obvious why the sentence is ''relevant'', but you should fix that by giving it context, not by hiding it. Also, what are these three proofs? We were just talking about using Dandelin Spheres to prove two theorems, not three theorems. Are these three proofs the proofs published by Dandelin to show that the spheres do in fact touch the conic section at its foci?</font><br />
<br />
::<font color=dodgerblue>Also, "all the three Dandelin's proofs" is bad English - say "all three of Dandelin's proofs"</font><br />
<br />
<font color=plum>I deleted this section, and I'll try to find a better image.</font><br />
<br />
==Explore Different Dandelin Spheres==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:29, 29 June 2011 (UTC):<br />
*Don't capitalize "conic section"</font><br />
*<font color=dodgerblue>''And it can also help to prove that the intersection(s) are focus(foci), after we could prove the shape of the plane. ''<br />
::Try to reword this so that it either doesn't start with "And" or is connected to the preceding sentence.</font><br />
::<font color=dodgerblue>I know you're having a difficult time with whether or not to make things plural because not all conic sections have two foci, but I think you can just go with plural all the time - even if one specific parabola has only one intersection and one focus, you're making statements about ''all'' the tangencies between Dandelin spheres and conic sections. Your sentences will be much easier to read that way.</font><br />
::<font color=dodgerblue>I have no idea what "after we could prove the shape of the plane" is supposed to mean.</font><br />
<br />
*<font color=dodgerblue>''All we need to do is to show, that a conic section under consideration, satisfies the definition of circle, ellipse, hyperbola, or parabola. ''<br />
::Unnecessary commas and missing or wrong determiners - should be "All we need to do is to show that the conic section under consideration satisfies the definition of a circle, an ellipse, a hyperbola, or a parabola."<br />
::Or, if you don't like listing all the conic sections out, you can say "the definition of some conic section."<br />
</font><br />
<br />
*<font color=dodgerblue>Linking to an applet like that is fine, but ''Using the '''Applet''' to play with Dandelin Spheres'' isn't a complete sentence. Try "Use this '''applet''' to play with Dandelin Spheres" or "This '''applet''' lets you play with Dandelin Spheres."</font><br />
<font color=plum>Fixed these problems</font><br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 04:37, 6 July 2011 (UTC) Nice inclusion of an applet, and Kate's suggestion for the way to introduce it works well! </font color><br />
<br />
===Spheres Tangent To A Circle===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:46, 29 June 2011 (UTC):<br />
*''Here we will show some detail about Dandelin Spheres Tangent To A Circle.''<br />
::This sentence is awkward. Try "More information about Dandelin Spheres that are tangent to a circle" or use a Hide/Show template without a preview or don't hide this section at all.</font><br />
*<font color=dodgerblue>''In <s>the image</s> Figure 2, when the plane \pi intersects all generators of the cone, <s>as in down figure,</s> it is possible to inscribe two spheres which will touch the conical surface and the plane. ''</font><br />
::<font color=dodgerblue>The labels in the picture are really hard to see - I can't find the label &pi; for the plane.</font><br />
<br />
*<font color=dodgerblue>Make sure the labels you use in the picture and the text match up - the picture seems to have k and k' , not k<sub>1</sub> and k<sub>2</sub>. Actually, I don't see most of the labels you're using in the picture. This is a problem.</font><br />
<br />
*<font color=dodgerblue>You should say "The upper sphere, G<sub>1</sub>,…" and "The lower sphere, G<sub>2</sub>,…" and "The arbitrarily chosen…"</font><br />
<br />
*<font color=dodgerblue>''We see that points, P_1 and F are the tangency points of the upper sphere and points, P_2 and F the tangency points of the lower sphere of the tangents drawn from the point P exterior to the spheres. ''<br />
::The first part should be:<br />
:::We see that points P_1 and F are the tangency points of the upper sphere, and points P_2 and F are the tangency points of the lower sphere<br />
::and I have no idea what the second part of this sentence is supposed to mean.</font><br />
<font color=plum>I fixed this part</font><br />
<br />
'''Distances From P To Tangent Points Of The Spheres Are Equal'''<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 19:14, 29 June 2011 (UTC):<br />
*This section was really hard to follow, mostly because I can't see what's going on in the picture. Can you get a bigger, clearer picture.</font><br />
*<font color=dodgerblue>''Showing in the image Proof of the Sphere a sphere centered at point O.''<br />
::"Proof of the Sphere" isn't really a good title for this image. Why not just call it by a number? Also, this isn't a complete sentence. Try:<br />
:::"Shown in the image Image Title is a sphere centered at point O."<br />
::or<br />
:::"Image Title shows a sphere centered at point O."<br />
</font><br />
*<font color=dodgerblue>''<s>Besides, s</s> '''S'''ide'''s''' OA and OB are the radi'''i''' of the sphere, so OA=OB.''</font><br />
*<font color=dodgerblue>I don't think this hidden section should be hidden.</font><br />
*<font color=dodgerblue>I don't think the last couple sentences here should be italicized.</font><br />
*<font color=dodgerblue>What is N? I don't see an N in either picture.</font><br />
<font color=plum>Fixed</font><br />
<br />
'''Proof of Conic Section Focal Properties'''<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 19:26, 29 June 2011 (UTC):<br />
*''By intersecting either of the two right circular conical surfaces (nappes) with the plane perpendicular to the axis of the cone the resulting intersection is a circle. ''<br />
::This sentence doesn't make sense. What is a "nappe"? "By intersecting… the resulting intersection is…" isn't a valid grammatical construction. I think maybe you're trying to say "When either of the two right circular conical surfaces are intersected with the plane perpendicular to the axis of the cone, the resulting intersection is a circle," but I still don't really know what that sentence means.</font><br />
*<font color=dodgerblue>Don't italicize the sentence beginning with "Also, we can assume…"</font><br />
*<font color=dodgerblue>''We can say that PF is the radius of the circle. The conic section is a circle. ''<br />
::I would say "Since PF is the distance from a point to the edge of the conic section, we know that the conic section has a constant radius, and is therefore a circle."</font><br />
<font color=plum>Fixed</font><br />
<br />
'''Proof of The Tangent Point Is The Center'''<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 19:26, 29 June 2011 (UTC): What you've said here doesn't seem to be long enough to be worth being it's own section, nor does it seem like an adequate proof of anything. Can't you just use that the spheres are tangent at the point that's the endpoint of the constant radius to show that it's the center?</font><br />
<font color=plum>Fixed</font><br />
<br />
===Spheres Tangent To An Ellipse===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 19:57, 29 June 2011 (UTC):<br />
*''In <s>the image</s> Figure 3, when the plane \pi intersects all generators of the cone, <s>as in down figure,</s> …''</font><br />
*<font color=dodgerblue>Again, you've gotta say "The [adjectives] sphere" and "The [adjectives] line". If there's no adjectives, then it's okay to say "sphere G" or "line SP", but when you add adjectives like "upper", "lower", or "arbitrarily chosen generating", you've gotta put a "the" in front. And no comma in "points P and F".</font><br />
<font color=plum>Fixed</font><br />
'''Distances From P To Tangent Points Of The Spheres Are Equal'''<br />
*<font color=dodgerblue>''Since sphere A is tangent to the cone and the tangent line k_1 is a circle, and point P_1 '''is''' on tangent line k_1, line P_1 P is tangent to sphere A. '''T'''he sphere is also tangent to the ellipse at point F_1, so the line F_1 P on the ellipse is '''also''' tangent to the sphere.''<br />
::Also, I don't see anything labeled A in the picture.</font><br />
<br />
*<font color=dodgerblue>''Using the same method.''<br />
:::First, this isn't a complete sentence. You should use it like this:<br />
:::"Using the same method, statement X is true" or "Using the same method, X=Y."</font><br />
::<font color=dodgerblue>Second, it doesn't read well to say "Using the same method" and then give the whole argument again. Either cut the argument and just present Eq. 2, or cut the "Using the same method" sentence.</font><br />
<font color=plum>Fixed</font><br />
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'''Proof of Conic Section Focal Properties'''<br />
*<font color=dodgerblue>''When the cutting plane is inclined to the axis of the cone at a greater angle than that made by the generating segment or generator (the slanting edge of the cone), i.e., when the plane cuts all generators of a single cone, the resulting curve is the ellipse. ''<br />
::This sentence doesn't make sense.</font><br />
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*<font color=dodgerblue>That "thus" is unnecessary, because of the "since". Say either "Since X is true, Y is true." or "X is true. Thus, Y is true."</font><br />
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*<font color=dodgerblue>You need more of an explanation as to how the picture and the numbered points below it connect to what was going on before.</font><br />
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*<font color=dodgerblue>Calling it the "fish's belt" was very confusing - what fish? what belt? "Hat band" was less so, because a hat band is a thing, and I could go look for something in the picture that looked like a hat band, but a fish's belt isn't a thing.</font><br />
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*<font color=dodgerblue>''Thus, the intersection curve is the locus of points in the plane for which sum of distances from the two fixed points F_1 and F_2, is constant, the curve E is an ellipse. ''<br />
::Should be "Since the intersection curve is the locus of points in the plane for which the sum of the distances from the fixed points F_1 and F_2 is constant, the intersection curve is an ellipse."</font><br />
<font color=plum>Fixed</font><br />
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'''Proof of The Tangent Points Are The Foci'''<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 19:57, 29 June 2011 (UTC):<br />
*This subject heading is incorrect, it should be "Proof that the Tangent Points Are the Foci"</font><br />
*<font color=dodgerblue>There should be a comma after "major diameter"</font><br />
*<font color=dodgerblue>''By using the definition of ellipses, point P can be any point on the ellipse, and the only points F_1 and F_2, satisfied that P_1 P_2 = P F_1 + P F_2 is constant, are the foci of the ellipse. ''<br />
::Try "By definition, any two points F_1 and F_2 that make P F_1 + P F_2 constant for all points P on the ellipse are the foci of that ellipse.</font>"<br />
<font color=plum>Fixed</font><br />
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===Spheres Tangent To A Hyperbola===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 20:23, 29 June 2011 (UTC):<br />
*''When the intersecting plane is inclined to the vertical axis at a smaller angle than '''is''' the generator of the cone,''</font><br />
*<font color=dodgerblue>Again, the labels in the picture are hard to read, and not all of the letters you use in the text seem to be there.</font><br />
<font color=plum>Fixed</font><br />
'''Distances From P To Tangent Points Of The Spheres Are Equal'''<br />
'''Proof of Conic Section Focal Properties'''<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 20:23, 29 June 2011 (UTC):<br />
*No commas around "are parallel"</font><br />
*<font color=dodgerblue>that sentence should end with a period: "…of equal length."</font><br />
*<font color=dodgerblue>Since/thus issues again.</font><br />
*<font color=dodgerblue>'' '''Since''' the intersection curve is the locus of points in the plane for which '''the''' difference of '''the''' distances from the two fixed points F' and F [no comma here] is constant, the conic section curve is a hyperbola. ''</font><br />
<font color=plum>Fixed</font><br />
'''Proof of The Tangent Points Are The Foci'''<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 20:23, 29 June 2011 (UTC): Section title should be "Proof that the Tangent Points Are the Foci"</font><br />
<font color=plum>Fixed</font><br />
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===Sphere Tangent To A Parabola===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 21:02, 29 June 2011 (UTC):<br />
*Your first paragraph is really hard to follow without a picture. Please please please add a picture!</font><br />
*<font color=dodgerblue>Don't capitalize "parabola"</font><br />
*<font color=dodgerblue>Again, you're using letters that aren't in your picture.</font><br />
*<font color=dodgerblue>''Inscribed sphere<s>s</s> A, centered at C, touch'''es''' the plane <s>on the same side</s> at point F and the cone surface at circle k. ''</font><br />
*<font color=dodgerblue>There shouldn't be a comma between "k" and "at point T" in the sentence that begins "The generator intersects…"</font><br />
*<font color=dodgerblue>You should probably write "V" (for the vertex) in math font, to be consistent with all your other letters. I think you need to fix it in the hyperbola section too.</font><br />
<font color=plum>Fixed</font><br />
'''The Distances From P To The Tangent Points Of The Spheres Are Equal'''<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 21:02, 29 June 2011 (UTC):<br />
*Incomplete sentence: ''The sphere A centered at point C situated below the cone vertex V.'' (Should say "is centered")</font><br />
*<font color=dodgerblue>Having two things called p is confusing to me.</font><br />
*<font color=dodgerblue>Typo! ''This creates two tiangles'' (Should be "triangles")</font><br />
*<font color=dodgerblue>''As we shown the proof in Proof of the circle. Since point F and point T are on the sphere, Similarly as in the case of circle it holds true that: ''<br />
::Should be: "As we showed in the proof Proof Title, because points F and T are on the sphere, we know that: " <br />
</font><br />
<font color=plum>Fixed</font><br />
'''Proof of Conic Section Focal Properties'''<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 21:02, 29 June 2011 (UTC):</font><br />
*<font color=dodgerblue>''In this case, it is a little different that we can not use''<br />
::Should be "This is different from the previous cases, in that we cannot use…"</font><br />
*<font color=dodgerblue>I don'tt think this last bit about the angles should be hidden. Also, don't start those lines with a space, the text shouldn't be in a box.</font><br />
<font color=plum>Fixed</font><br />
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'''The Distances From P To The Tangent Points Of The Spheres Are Equal'''<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 21:02, 29 June 2011 (UTC):<br />
*The hidden paragraphs just before this section seems to be redundant with the information at the top of the paragraph on parabolas. Also, it pains me to suggest making the table of contents longer, but I think if you're going to do the same thing over again a different way, which is what it sounds like, this whole hidden section needs to have another heading.</font><br />
*<font color=dodgerblue>Yet again, your labels don't seem to match your picture. Which plane is plane &pi;?</font><br />
*<font color=dodgerblue>''The segments, PF and PT belong to tangents drawn from P to the sphere, we can get: ''<br />
::Should be "Since the segments PF and PT belong to tangents drawn from P to the sphere, we can get:"</font><br />
*<font color=dodgerblue>''Since '''the''' planes of the circles[no comma here] k and k' are parallel to each other and perpendicular to the section through the cone axis, and '''since''' the plane \pi is parallel to the slanting edge VB, <s>then</s> the intersection d, of planes E and K, is also perpendicular to the section through the cone axis. '''PN is the'' perpendicular from P to the line d. '''Thus''', ''</font><br />
<font color=plum>Fixed</font><br />
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'''Proof of Conic Section Focal Properties'''<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 21:02, 29 June 2011 (UTC):</font><br />
*<font color=dodgerblue>''Since we get Eq. 2 and Eq. 3 from above proof, ''<br />
::Should be "We get Eq. 2 and Eq. 3 from the above proof. Therefore, for any point P on the intersection curve the distance from the fixed point F is the same as it is from the fixed line d, '''proving''' that the intersection curve is the parabola.''</font><br />
<font color=plum>Fixed</font><br />
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'''Proof of The Tangent Point Is The Focus'''<br />
*<font color=dodgerblue>Should be called "Proof that the Tangent Point Is the Focus"</font><br />
<font color=plum>Fixed</font><br />
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==Applied Dandelin Spheres==<br />
===Conic Section Eccentricity===<br />
'''Ellipse's Eccentricity'''<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 04:39, 6 July 2011 (UTC) When you talk about a "hinge line" in the Ellipse's Eccentriciy section, you should either bold "hinge line" and keep the definition the way you have it in the next sentence, or put the definition in a mouseover. <br />
* "Hinge line is a leg ofboth blue and red right triangles." TYPO. You need to add a space "of both" <br />
</font color><br />
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'''Hyperbola's Eccentricity'''<br />
'''Parabola's Eccentricity'''<br />
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===Newton's Astronomy Theory===<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 04:41, 6 July 2011 (UTC) When you talk about a "hinge line" in the Ellipse's Eccentriciy section, you should either bold "hinge line" and keep the definition the way you have it in the next sentence, or put the definition in a mouseover. <br />
* "Hinge line is a leg ofboth blue and red right triangles." TYPO. You need to add a space "of both" <br />
</font color><br />
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===Interesting Math problems===<br />
<font color=slateblue><br />
*[[User:Rebecca|Rebecca]] 04:41, 6 July 2011 (UTC) Again, I don't think "De Villiers" should be bold. </font color><br />
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==Why It's Interesting==<br />
<font color=slateblue><br />
* [[User:Rebecca|Rebecca]] 04:47, 6 July 2011 (UTC) I think this video could be moved much higher up in the page. It could even be in one of the first sections. <br />
* Also, I think it might be a good idea for you to work on the organization of this page before you add to the why it's interesting section. I'm sure you'll have great info for this section eventually, but for now you should focus on explaining why things are interesting as you give proofs/explain topics. This will keep readers interested as they go. Then you can use this section to elaborate on ideas you introduced earlier. Again, this is just a suggestion, but I think it will help give your page more direction and ultimately make it better. <br />
* Finally, I want to reiterate how impressive this is as a page. I think you've got your work cut out for you as far as organization, but it's evident that you've conquered a tough topic. You have a great start here, but I think the next step is to work on combining sections and removing some of the hide shows, adding more pictures (although you do a have a good number and the applets/movies help!), and providing context so that people have incentive to keep reading. Nice work Flora!<br />
</font color></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=SB11&diff=25647SB112011-07-16T02:59:57Z<p>Rebecca: /* Phoebe Jiang */</p>
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<div>=<center> Sweet Briar 2011 </center>=<br />
<br />
==Discussion==<br />
<font color=navy>Please feel free to discuss math pages or leave a message for the creators!</font><br />
<br />
Hey girls, the discussion bar on the very top of every page next to "page" is really helpful and necessary for peer review or faculty review. If you guys go through other people's page and want to comment on their work, please do. [[User:PhoebeJiang|Phoebe]] 15:09, 11 June 2011 (UTC)<br />
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==Summer 2011 Projects==<br />
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===Anna Donko===<br />
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*[[Steiner's Porism]]<br />
:<font color=peach> Need to work on explaining algebraic formulas.</font> <br />
PLEASE look at this!! I would really appreciate comments and suggestions!!<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 18:27, 28 June 2011 (UTC): Just left you a lot of comments on the discussion page.</font><br />
:<font color=peach> Working on reading and using all of the comments on the discussion page, thanks all who left me some feedback! </font><br />
*[[Boy's Surface]]<br />
:<font color=peach> Leah and I are trying to figure out how we want to lay out our page...Please hold back with the comments while we continue to reorganize as well as add to our page!</font><br />
:<font color=red> Need to work on explanation of parametrization...??</font><br />
:<font color=salmon> Left some comments~ [[User:PhoebeJiang|Phoebe]] 23:56, 13 July 2011 (UTC)</font><br />
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*[[Using the Rectangular Method to Determine Area]]<br />
:<font color=peach>Just started this new page!! I am going to ink this to the already existing page, [[Parabola]]</font><br />
::<font color=salmon>[[User:PhoebeJiang|Phoebe]] 21:51, 12 July 2011 (UTC) Great image! I like both pictures! The title is clear but I think you can make it shorter.</font><br />
:<font color=peach>Going to change my equations so they work out neater for the reader</font><br />
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:<font color=black> Planning to add much more to Rectangular Method (Explanations of why/how parabolas are used in the physical world, as well as differentiate between parabolas and catenaries, lastly I will find the area of an actual life sized piece of parabolic architecture) Now, I am going to work on applying suggestions to my Steiner page so I can send it in for final review!<br />
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===Phoebe Jiang===<br />
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*<big>[[Arbelos]]</big><br />
:{{hide|1=<br />
:<font color=salmon>Need to work on the two footnotes. And do a last revision, revise Pappus Chain and Bankoff Chain. <br />
:PLEASE look at this page. Comments are always welcome! </font>[[User:PhoebeJiang|Phoebe]] 19:49, 28 June 2011 (UTC)<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 13:21, 30 June 2011 (UTC): I've gone back through and responded to your comments or crossed things off where we both agree.</font><br />
:::<font color=salmon>[[User:PhoebeJiang|Phoebe]] 03:44, 8 July 2011 (UTC)Thank you Kate!!! <3 </font><br />
:<font color=salmon> Submitted for final review. </font><br />
::<font color=darkred> I've put up comments for you. See my thoughts about a spin-off page. [[User:AnnaP|AnnaP]] 7/12 </font> <br />
:::<font color=salmon>[[User:PhoebeJiang|Phoebe]] 21:35, 12 July 2011 (UTC) Thank you Anna and I've responded to your comments.</font>}}<br />
::::<font color=darkred> One more round of comments is up [[User:AnnaP|AnnaP]] 15:38, 15 July 2011 (UTC) </font> <br />
:::::<font color=salmon> Responded to Anna's second round of the comments. </font><br />
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*<big>[[Pappus Chain]]</big><br />
:{{hide|1=<br />
:<font color=salmon>This is used to be a subsection of [[Arbelos]]. Since arbelos is too long, I made Pappus chain a single page. I don't have time to finish it, so I think I'll leave the rest of the page for other people in the future. </font>}}<br />
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*<big>[[Euclidean Algorithm]] </big><br />
:{{hide|1=<br />
<font color=salmon><br />
:Need to work on Gabriel Lame and worst case of EA.<br />
:Done. Need revision~ [[User:PhoebeJiang|Phoebe]] 19:48, 28 June 2011 (UTC)<br />
::[[User:PhoebeJiang|Phoebe]] 03:44, 8 July 2011 (UTC)Please look at this page and leave some commenst!!! Thank you guys!! </font><br />
:<font color=salmon> Submitted for final review. </font>}}<br />
::<font color=darkred> I've put up comments [[User:AnnaP|AnnaP]] 17:39, 15 July 2011 (UTC) </font> <br />
:::<font color=salmon> Thank you! Responded to Anna's comments. </font><br />
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*<big>[[Application of the Euclidean Algorithm]]</big> <br />
:{{hide|1=<font color=salmon><br />
: Finish up with computer science section and knot theory.<br />
:Done. Need revision~ [[User:PhoebeJiang|Phoebe]] 19:48, 28 June 2011 (UTC)<br />
::[[User:PhoebeJiang|Phoebe]] 03:44, 8 July 2011 (UTC)Please look at this page also. PLEASE leave anything you think will make it better!!! Thank you guys!!</font>}}<br />
:I could really need comments on this page. Thanks in advance!<br />
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*<big>[[Pigeonhole Principle]]</big><br />
:{{hide|1=<font color=salmon><br />
:Just started it :P </font>[[User:PhoebeJiang|Phoebe]] 19:48, 28 June 2011 (UTC)<br />
:<font color=salmon>There is a problem I don't understand.</font> [[User:PhoebeJiang|Phoebe]] 02:06, 8 July 2011 (UTC)<br />
::<font color=orangered>Left some comments on the discussion page. Send us the problem you don't understand and we'll try it on our end of things (rscott3@swarthmore.edu). Let me know if you want me to read through the page again or anything. [[User:Rscott3|Richard]] 7/8</font><br />
:::<font color=salmon>[[User:PhoebeJiang|Phoebe]] 18:30, 8 July 2011 (UTC)Thank you Richard~ And I figured out the problem just now. :) </font><br />
::::<font color=orangered> Went back and looked over some of your changes. Left some responses to your comments. I'd be happy to read it again at some point if you'd like. [[User:Rscott3|Richard]] 7/12</font><br />
:::::<font color=salmon> [[User:PhoebeJiang|Phoebe]] 21:35, 12 July 2011 (UTC)Great! I'll check your responses. Thank you. </font><br />
:<font color=salmon>[[User:PhoebeJiang|Phoebe]] 21:32, 12 July 2011 (UTC)Finish writing the page. Will work on Richard's new comments. </font>}}<br />
:<font color=salmon> Responded to Richard's comments. Appreciate other suggestions.</font><br />
:<font color=slateblue> [[User:Rebecca|Rebecca]] 02:59, 16 July 2011 (UTC) I left a few comments. Overall, I think this page is great! </font color><br />
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===Flora Li===<br />
Please leave some comments for my pages, Thanks.<br />
*<big>[[Waves]]</big><br />
:{{HideThis|1=More|2=<br />
:Flora 15:20, 29 June 2011 (UTC)<font color=plum>Have done with the references.~</font><br />
:[[User:Flora1103|Flora]] 19:45, 10 June 2011 (UTC)<font color=plum> Need to work on '''Sine Wave Generration'''. Need to add more detail explaination to the graphs and the equetions.</font><br />
:<font color=plum>Flora 16:34, 28 June 2011 (UTC)I changed the title. And try to re-organize it to more "waves".</font><br />
::<font color=orangered>Left some feedback. [[User:Rscott3|Richard]] 6/29</font><br />
}}<br />
::Flora 20:14, 29 June 2011 (UTC)<font color=plum>Thanks very much~</font><br />
:Flora 20:35, 13 July 2011 (UTC)<font color=plum>Send to final review</font><br />
::<font color=darkred> Flora, can you go through the [[Checklist for writing pages]] on the discussion page before I go through the review process for this page? That makes my job much, much easier, and helps me give the most appropriate feedback. You can find examples by looking at the discussion pages of other pages on the final review page. Thanks [[User:AnnaP|AnnaP]] 7/14 </font><br />
::<font color=plum>Flora 21:25, 14 July 2011 (UTC)Have already went through the check list and leave them in discussion page. Sorry about that.</font><br />
:<font color=salmon> [[User:PhoebeJiang|Phoebe]] 21:58, 14 July 2011 (UTC) Comments are addressed. </font><br />
::<font color=plum>Flora 02:41, 15 July 2011 (UTC)Have responsed to your suggestions. Thanks very much.</font><br />
:::<font color=darkred> Take a look at my comments on the page [[User:AnnaP|AnnaP]] 16:08, 15 July 2011 (UTC) </font> <br />
:::<font color=plum>Flora 18:46, 15 July 2011 (UTC)Thanks very much for your comments. I responsed already, and I'm working on Fourier images now. I will post them later.</font><br />
*<big>[[Dandelin Spheres Theory]]</big><br />
:{{HideThis|1=More|2=<br />
:Flora 15:20, 29 June 2011 (UTC)<font color=plum>Have done with the references.~</font><br />
:Flora 22:20, 28 June 2011 (UTC)Have done most of it, still need to work on the references. I'm looking for any comments, plz~<br />
:<font color=plum>[[User:Flora1103|Flora]] 00:00, 11 June 2011 (UTC)I just start this topic. Working ont eh proofs</font><br />
:<font color=plum>Flora 20:50, 16 June 2011 (UTC) I find some useful information on a online school's webpage, but I couldn't open the page today. I don't know why. The url is [http://jwilson.coe.uga.edu/EMT668/EMAT6680.2002.Fall/Imler/EMAT%206690%20Instruc%20Unit-%20Conics/L4D1ii.html http://jwilson.coe.uga.edu/EMT668/EMAT6680.2002.Fall/Imler/EMAT%206690%20Instruc%20Unit-%20Conics/L4D1ii.html].</font><br />
:[[User:PhoebeJiang|Phoebe]] 00:43, 19 June 2011 (UTC) <font color=salmon>I have no problem viewing it. Try a different browser I think. </font><br />
:<font color=plum>Flora 15:39, 20 June 2011 (UTC) I fixed that problem, thx. I now editting "Prove of conic section curve", and I change one image that showed before, so I still need to edit "Explore hyperbola spheres" later.</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 21:12, 29 June 2011 (UTC): I left you a bunch of comments on this one, but I didn't get all the way through. It was slow reading and I ran out of time.</font><br />
:<font color=plum>Thanks very much.~</font><br />
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:Flora 02:20, 14 July 2011 (UTC)<font color=plum>Start to revise it</font><br />
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:Flora 21:55, 14 July 2011 (UTC)<font color=plum>Re-arranged the outlet, hope this is better.</font><br />
}}<br />
:<font color=plum>Flora 23:27, 15 July 2011 (UTC)Done with checklist. Will do one more revise before sending to final review.</font><br />
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*<big>[[Dihedral Groups]]</big><br />
:Welcome comments XD<br />
:{{HideThis|1=More|2=<br />
:<font color=plum>Flora 20:54, 27 June 2011 (UTC)I add the main image but not start this page yet. Will work on it from next week. XD</font><br />
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:<font color=plum>Flora 16:25, 13 July 2011 (UTC) Almost done with the page, still need to work on complex plane explanation, and subgroup part.</font><br />
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:<font color=plum>Flora 01:58, 15 July 2011 (UTC)Finish this page, need to revise.</font><br />
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}}<br />
:<font color=plum>Flora 23:26, 15 July 2011 (UTC)Done with checklist. Will do one more revise before sending to final review.</font><br />
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==Contact Us==<br />
<br />
===Faculty===<br />
'''Dr.Cammie Barnes''' <br />
<br />
*Email: cbarnes@sbc.edu<br />
<br />
*Skype: Cammie.Barnes<br />
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===Students===<br />
'''Anna Donko'''<br />
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*Email: donko14@sbc.edu<br />
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*Skype: anna.k.donko<br />
<br />
'''Phoebe Jiang'''<br />
<br />
*Email: jiang14@sbc.edu<br />
<br />
*Skype: blacki2014<br />
<br />
'''Flora Li'''<br />
<br />
*Email: li14@sbc.edu<br />
<br />
*Skype: Flora Li<br />
<br />
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[[User:PhoebeJiang|Phoebe]] 00:45, 19 June 2011 (UTC)<font color=salmon>Thanks for the info!</font><br />
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[http://en.wikipedia.org/wiki/Help:Displaying_a_formula#Forced_PNG_rendering Displaying a Formula]<br />
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[[PartnerHome]]</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Pigeonhole_Principle&diff=25646Talk:Pigeonhole Principle2011-07-16T02:58:55Z<p>Rebecca: /* Interesting Applications */</p>
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<div><font color=orangered> Pictures will be so cool for this one! [[User:Rscott3|Richard]] 6/29</font><br />
:<font color=salmon> [[User:PhoebeJiang|Phoebe]] 18:35, 8 July 2011 (UTC)Yeah, I realized that too. I'm not finished with this page yet, so I'll work on it! Thanks!<br />
::Ps: We have pretty much the same font color~ lol </font><br />
<br />
=General Comments=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*This page is really really cool. You've got a ton of opportunities for applications and pictures.<br />
<br />
*I'd make you Interesting Applications Section a "Why It's Interesting" section. I think this is more standard for math images. You can go to the edit with form tab to start that section.<br />
<br />
*You really only use examples to go into the topic. Is there some graphical proof or derivation that you could include?</font><br />
<br />
<br />
:[[User:PhoebeJiang|Phoebe]] 21:06, 8 July 2011 (UTC)<br />
<font color=purple><br />
<br />
:*First of all, thank you for leaving comments!! I use a different color to distinguish us. <br />
<br />
:*As you can see, I intend to use those 10 examples to lead in, giving readers a basic idea of what Pigeonhole principle is and how it works. The principle itself is pretty self-explanatary, so I didn't include the proof of this principle. Then, after you know how this simple principle helps in daily life, you will see the MME section with more examples and tricks about constructing pigeonholes. This is how I conceive this page, from easy to hard, from the description of pigeonhole principle, to applications (lead in), and eventually the hardest part, MME. So do you think I should put the applications under "Why interesting" after MME? If so, I'm afraid readers will feel overwhelmed by MME section. What do you think?<br />
::<font color=orangered> Okay, I see what you mean and I understand where you're coming from. To me, this page starts out with a very intuitive topic/description, and then gets more complicated in the current MME. What if there were some middle ground? I'm thinking like describing what average value is mathematically or something to put at the beginning of the MME to sort of segway into harder examples. There's a lot of examples on this page, and as the reader, I think it gets to be more difficult to pick out which examples are the most important ones. I don't know.... [[User:Rscott3|Richard]] 7/12</font><br />
:::<font color=purple> Richard! Check this out. I want some simple and interesting examples to lead in and I also want to put some hard applications under "why interesting" as you suggested. So, I'm thinking about splitting them into two sections, leaving the first 4-5 examples where they are now and put the rest of the examples after MME. Plus, those ten examples seem to be really long together. And people could apply those tricks mentioned in MME to see how the tricks work via the hard examples at the end of the page. What do you think about this idea? :) [[User:PhoebeJiang|Phoebe]] 20:38, 13 July 2011 (UTC) </font><br />
<br />
:*Pigeonhole principle is basically about combinatorics, about numbers. This principle itself doesn't have much to do with pictures. I agree with you about the pictures. I personally like graphs than simply words and numbers, so I'm thinking about adding more illustrative pictures on it. <br />
</font><br />
<br />
:*<font color=orangered> Phoebe, this page is looking great! I can read it through again if you want me to, just let me know when it's ready! [[User:Rscott3|Richard]] 7/12</font><br />
::*<font color=purple> [[User:PhoebeJiang|Phoebe]] 03:16, 14 July 2011 (UTC) Yeah actually could you read it through one more time, please? Tell me where I need to explain more precisely. Thanks a lot! </font><br />
<br />
=Intro=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*I'd reorganize this paragraph to something like this:<br />
::A pigeon is looking for a spot in the grid, but each box in the grid, or pigeonhole, is occupied. Where should the poor pigeon on the outside go? No matter which box he chooses, he must share with another pigeon. If all of the pigeons fit into the grid, here is definitely a pigeonhole contains more than one pigeon. This concept is known as the '''pigeonhole principle'''.<br />
*I think it's important to introduce the topic here in this section(I added a sentence at the end in my edit above).<br />
</font><br />
<br />
<br />
::[[User:PhoebeJiang|Phoebe]] 21:05, 8 July 2011 (UTC)<br />
<font color=purple><br />
::*Agree. Fixed it! <br />
</font><br />
<br />
=Basic Description=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*In the first sentence, change "items" to "pigeons" or vice versa for consistency.<br />
<br />
*In the second paragraph, I think that this quote is more confusing than helpful. I feel like you generalizing the same thing in your own words would be waaaaaay more helpful.<br />
::*It might be helpful to define "average value" and "maximum value" (maybe with a green mouse-over)<br />
<br />
*I'd delete "Although the two versions look very different, they are mathematically stating the same thing." and into the next paragraph, "To know why they are the same," and start with "Consider the main image instead". I think it's unnecessary to say.<br />
<br />
*Maybe change "bigger" to "greater"???? That sounds more mathy to me.<br />
<br />
*What's "its" referring to?<br />
::"Thus, '''its''' maximum value should be bigger than one as well, which means that there must be a pigeonhole contains more than one pigeons. Now we know that the two versions are actually talking about the same math principle."<br />
<br />
*Be careful with words like "pretty obvious". You're assuming a lot of the reader.<br />
<br />
*Move the sentence "Here are 10 exciting real life applications listed from easy to hard for you to have a better grasp on this famous principle." into the next section before the first example.<br />
</font><br />
<br />
:[[User:PhoebeJiang|Phoebe]] 21:24, 8 July 2011 (UTC)<br />
:<font color=purple> <br />
:*You have a lot of good points. I totally agree with you. <br />
:*Fixed all of them. Are they better now?</font><br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 02:35, 16 July 2011 (UTC) Phoebe, I'm Becky and I give feedback on many of the Math Images pages. I have a few suggestions for this page... <br />
* I would include mouseovers for "non empty" and "finite" because I think that if someone doesn't know what a maximum value or an average value is, they wont know either of those words either. <br />
* It's great that you introduce the general pigeonhole principle and then use explain the implications for the image. It's a logical order, and I think your approach is great! </font color><br />
<br />
=Interesting Applications=<br />
<font color=orangered> [[User:Rscott3|Richard]] 7/8<br />
*This section is awesome awesome awesome.<br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:04, 8 July 2011 (UTC)Thanks!</font><br />
*<font color=slateblue> [[User:Rebecca|Rebecca]] 02:58, 16 July 2011 (UTC) I agree- I like how you show people that these paradoxes must be true rather than formally proving them. It makes the page really interesting. </font color><br />
<br />
*Pictures would be really super cool here. The way its formatted right now makes it seem longer than it actually is, especially with the table of contents. One way that I'd think to format this is like the "More than just shadows" section of [[Solving Triangles]]. Assign a picture to each example, and make two columns where the picture and text alternate sides. The picture doesn't have to be super complicated. The birthday one could just be a cake or something. Make it look more visually appealing. <br />
::*This will also help the table of contents because you'd have to make each of the ten headings just bolded words, and not section titles.<br />
:::<font color=purple>[[User:PhoebeJiang|Phoebe]] 21:27, 8 July 2011 (UTC)Guess what! I'm thinking about the same thing!</font><br />
<br />
*Some of the example descriptions get a bit wordy. For the purposes of these comments I'll just talk about the first one as an example and then say which ones were more confusing.<br />
::*For the birthday one, you could make it more clear by changing "Under the worst condition when the first 366 students have their birthdays from January 1st to December 31th, the 367th person has to be born on any day of the year. Thus, there are definitely two of the students who have their birthday falling on the same day." to "Under the worst condition when each of the first 366 students have their birthdays on different days from January 1st to December 31th, the birthday of the 367th person must be a repeat of one of those days. Thus, there are definitely two of the students who have their birthday falling on the same day."<br />
<br />
::: <font color=purple>[[User:PhoebeJiang|Phoebe]] 22:34, 8 July 2011 (UTC)Yeah, yours is waaaay better. </font><br />
<br />
*Numbers 5 and 9 could be a lot clearer with good pictures.<br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:03, 8 July 2011 (UTC)Add some pictures. </font><br />
<br />
*Number 7's main statement is confusing to me. <br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:13, 8 July 2011 (UTC) Could you please be more specific about it? </font> <br />
:::<font color=orangered>I understand what you are trying to prove, but I think the statement is wordy. What if you say something like: " Some n number of people are at a party. There are always at least two people who shake hands with the same number of people."? But even with the way I worded it...It' awkward. [[User:Rscott3|Richard]] 7/12</font><br />
::*I really like how you relate this one back to the pigeon/pigeonhole metaphor.<br />
:::*<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:03, 8 July 2011 (UTC) Thanks. I though it may be easier to understand if I do this. </font><br />
<br />
*Number 8 is very confusing. That's the only one I don't understand.<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:55, 8 July 2011 (UTC) I made some changes. Try to make it as clear as possible. </font><br />
:::<font color=orangered>I'm still a bit confused by this. If he has to take at least one aspirin a day, does he take 14 consecutively in a period of 14 days? I think that's where I'm confused. What statement are you trying to make? Also, where did you get 59? [[User:Rscott3|Richard]] 7/12</font> <br />
::::<font color=purple> That is one possible answer. But he could also take 14 aspirin in less than 14 days, say he could take 14 aspirin in only 3 days. In other words, if he wants to try to avoid taking 14 aspirin during certain period, he can't do it. He may avoid taking 15 aspirin during a period of consecutive days. However, this statement is trying to say that you can always find a period of consecutive days where he takes exactly 14 aspirin. Am I being clear enough or not? Please ask me more questions if you are still confused. :P <br />
::::How did I get 59? Since you add 14 to every term in the first inequality, you'll get 45 + 14 = 59 for the very last term. <br />
::::Maybe I could generalize this statement instead of using numbers 45, 14, 30. (i.e. he has to take <math>n</math> aspirin over a <math>m</math> day period. Then there is definitely a period of consecutive days where he takes exactly <math>n - m -1 </math> aspirin.) Do it make more sense now? </font><br />
<br />
*Number 10a is awesome! Great, clear description!<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:55, 8 July 2011 (UTC) Good to know. Thanks! </font><br />
<br />
*For 10b, I didn't know exactly what you you were trying to show until you had already started to prove it. This one might be in need of some more clarity in the initial description of the proof and statement.<br />
::*Typo:"situation" should be "situations" in "Since there are over 32,000 possible colorings, we could not draw and check every one of the situation."<br />
</font><br />
:::<font color=purple> Fixed it. What do you think about this part now? </font><br />
<br />
<font color=slateblue> <br />
* [[User:Rebecca|Rebecca]] 02:49, 16 July 2011 (UTC) "Here are 6 exciting real life applications for you to have a better grasp on this famous principle." I would say "real world applications to give you a better grasp of this famous principle."<br />
* "Under the worst condition when each of the first 366 students have their birthdays..." I would say "In the most extreme condition" <br />
* "This example may sound impossible to believe but mathematics, more precisely, the seemingly meaningless pigeonhole principle tells you it could happen." I would say " This example may sound impossible to believe, but the seemingly obvious pigeonhole principle tells us it must be true." </font color><br />
<br />
=MME=<br />
==More Mathematical examples==<br />
<font color=orangered>[[User:Rscott3|Richard]] 7/8<br />
*Number 1 is confusing.<br />
<br />
*For number 2, wouldn't it just be easier to choose all of the odd numbers, knowing that they are not consecutive and that there are only 50, then we know that the 51st must be even and next to an odd number.</font><br />
<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 02:10, 9 July 2011 (UTC)Yes, you are right. </font><br />
<br />
==How to Construct==<br />
<font color=orangered> [[User:Rscott3|Richard]] 7/8 <br />
*I was a bit confused by these examples.<br />
<br />
*This might also be a good point to derive or prove the principle explicitly with the math for average and maximum values????</font><br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 03:09, 9 July 2011 (UTC) I tried to fixed those confusing examples. Maybe some of them are still not very clear. I'll work on them later. Please feel free to tell me where should I improve. Thanks!</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Pigeonhole_Principle&diff=25645Talk:Pigeonhole Principle2011-07-16T02:49:45Z<p>Rebecca: /* Interesting Applications */</p>
<hr />
<div><font color=orangered> Pictures will be so cool for this one! [[User:Rscott3|Richard]] 6/29</font><br />
:<font color=salmon> [[User:PhoebeJiang|Phoebe]] 18:35, 8 July 2011 (UTC)Yeah, I realized that too. I'm not finished with this page yet, so I'll work on it! Thanks!<br />
::Ps: We have pretty much the same font color~ lol </font><br />
<br />
=General Comments=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*This page is really really cool. You've got a ton of opportunities for applications and pictures.<br />
<br />
*I'd make you Interesting Applications Section a "Why It's Interesting" section. I think this is more standard for math images. You can go to the edit with form tab to start that section.<br />
<br />
*You really only use examples to go into the topic. Is there some graphical proof or derivation that you could include?</font><br />
<br />
<br />
:[[User:PhoebeJiang|Phoebe]] 21:06, 8 July 2011 (UTC)<br />
<font color=purple><br />
<br />
:*First of all, thank you for leaving comments!! I use a different color to distinguish us. <br />
<br />
:*As you can see, I intend to use those 10 examples to lead in, giving readers a basic idea of what Pigeonhole principle is and how it works. The principle itself is pretty self-explanatary, so I didn't include the proof of this principle. Then, after you know how this simple principle helps in daily life, you will see the MME section with more examples and tricks about constructing pigeonholes. This is how I conceive this page, from easy to hard, from the description of pigeonhole principle, to applications (lead in), and eventually the hardest part, MME. So do you think I should put the applications under "Why interesting" after MME? If so, I'm afraid readers will feel overwhelmed by MME section. What do you think?<br />
::<font color=orangered> Okay, I see what you mean and I understand where you're coming from. To me, this page starts out with a very intuitive topic/description, and then gets more complicated in the current MME. What if there were some middle ground? I'm thinking like describing what average value is mathematically or something to put at the beginning of the MME to sort of segway into harder examples. There's a lot of examples on this page, and as the reader, I think it gets to be more difficult to pick out which examples are the most important ones. I don't know.... [[User:Rscott3|Richard]] 7/12</font><br />
:::<font color=purple> Richard! Check this out. I want some simple and interesting examples to lead in and I also want to put some hard applications under "why interesting" as you suggested. So, I'm thinking about splitting them into two sections, leaving the first 4-5 examples where they are now and put the rest of the examples after MME. Plus, those ten examples seem to be really long together. And people could apply those tricks mentioned in MME to see how the tricks work via the hard examples at the end of the page. What do you think about this idea? :) [[User:PhoebeJiang|Phoebe]] 20:38, 13 July 2011 (UTC) </font><br />
<br />
:*Pigeonhole principle is basically about combinatorics, about numbers. This principle itself doesn't have much to do with pictures. I agree with you about the pictures. I personally like graphs than simply words and numbers, so I'm thinking about adding more illustrative pictures on it. <br />
</font><br />
<br />
:*<font color=orangered> Phoebe, this page is looking great! I can read it through again if you want me to, just let me know when it's ready! [[User:Rscott3|Richard]] 7/12</font><br />
::*<font color=purple> [[User:PhoebeJiang|Phoebe]] 03:16, 14 July 2011 (UTC) Yeah actually could you read it through one more time, please? Tell me where I need to explain more precisely. Thanks a lot! </font><br />
<br />
=Intro=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*I'd reorganize this paragraph to something like this:<br />
::A pigeon is looking for a spot in the grid, but each box in the grid, or pigeonhole, is occupied. Where should the poor pigeon on the outside go? No matter which box he chooses, he must share with another pigeon. If all of the pigeons fit into the grid, here is definitely a pigeonhole contains more than one pigeon. This concept is known as the '''pigeonhole principle'''.<br />
*I think it's important to introduce the topic here in this section(I added a sentence at the end in my edit above).<br />
</font><br />
<br />
<br />
::[[User:PhoebeJiang|Phoebe]] 21:05, 8 July 2011 (UTC)<br />
<font color=purple><br />
::*Agree. Fixed it! <br />
</font><br />
<br />
=Basic Description=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*In the first sentence, change "items" to "pigeons" or vice versa for consistency.<br />
<br />
*In the second paragraph, I think that this quote is more confusing than helpful. I feel like you generalizing the same thing in your own words would be waaaaaay more helpful.<br />
::*It might be helpful to define "average value" and "maximum value" (maybe with a green mouse-over)<br />
<br />
*I'd delete "Although the two versions look very different, they are mathematically stating the same thing." and into the next paragraph, "To know why they are the same," and start with "Consider the main image instead". I think it's unnecessary to say.<br />
<br />
*Maybe change "bigger" to "greater"???? That sounds more mathy to me.<br />
<br />
*What's "its" referring to?<br />
::"Thus, '''its''' maximum value should be bigger than one as well, which means that there must be a pigeonhole contains more than one pigeons. Now we know that the two versions are actually talking about the same math principle."<br />
<br />
*Be careful with words like "pretty obvious". You're assuming a lot of the reader.<br />
<br />
*Move the sentence "Here are 10 exciting real life applications listed from easy to hard for you to have a better grasp on this famous principle." into the next section before the first example.<br />
</font><br />
<br />
:[[User:PhoebeJiang|Phoebe]] 21:24, 8 July 2011 (UTC)<br />
:<font color=purple> <br />
:*You have a lot of good points. I totally agree with you. <br />
:*Fixed all of them. Are they better now?</font><br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 02:35, 16 July 2011 (UTC) Phoebe, I'm Becky and I give feedback on many of the Math Images pages. I have a few suggestions for this page... <br />
* I would include mouseovers for "non empty" and "finite" because I think that if someone doesn't know what a maximum value or an average value is, they wont know either of those words either. <br />
* It's great that you introduce the general pigeonhole principle and then use explain the implications for the image. It's a logical order, and I think your approach is great! </font color><br />
<br />
=Interesting Applications=<br />
<font color=orangered> [[User:Rscott3|Richard]] 7/8<br />
*This section is awesome awesome awesome.<br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:04, 8 July 2011 (UTC)Thanks!</font><br />
<br />
*Pictures would be really super cool here. The way its formatted right now makes it seem longer than it actually is, especially with the table of contents. One way that I'd think to format this is like the "More than just shadows" section of [[Solving Triangles]]. Assign a picture to each example, and make two columns where the picture and text alternate sides. The picture doesn't have to be super complicated. The birthday one could just be a cake or something. Make it look more visually appealing. <br />
::*This will also help the table of contents because you'd have to make each of the ten headings just bolded words, and not section titles.<br />
:::<font color=purple>[[User:PhoebeJiang|Phoebe]] 21:27, 8 July 2011 (UTC)Guess what! I'm thinking about the same thing!</font><br />
<br />
*Some of the example descriptions get a bit wordy. For the purposes of these comments I'll just talk about the first one as an example and then say which ones were more confusing.<br />
::*For the birthday one, you could make it more clear by changing "Under the worst condition when the first 366 students have their birthdays from January 1st to December 31th, the 367th person has to be born on any day of the year. Thus, there are definitely two of the students who have their birthday falling on the same day." to "Under the worst condition when each of the first 366 students have their birthdays on different days from January 1st to December 31th, the birthday of the 367th person must be a repeat of one of those days. Thus, there are definitely two of the students who have their birthday falling on the same day."<br />
<br />
::: <font color=purple>[[User:PhoebeJiang|Phoebe]] 22:34, 8 July 2011 (UTC)Yeah, yours is waaaay better. </font><br />
<br />
*Numbers 5 and 9 could be a lot clearer with good pictures.<br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:03, 8 July 2011 (UTC)Add some pictures. </font><br />
<br />
*Number 7's main statement is confusing to me. <br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:13, 8 July 2011 (UTC) Could you please be more specific about it? </font> <br />
:::<font color=orangered>I understand what you are trying to prove, but I think the statement is wordy. What if you say something like: " Some n number of people are at a party. There are always at least two people who shake hands with the same number of people."? But even with the way I worded it...It' awkward. [[User:Rscott3|Richard]] 7/12</font><br />
::*I really like how you relate this one back to the pigeon/pigeonhole metaphor.<br />
:::*<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:03, 8 July 2011 (UTC) Thanks. I though it may be easier to understand if I do this. </font><br />
<br />
*Number 8 is very confusing. That's the only one I don't understand.<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:55, 8 July 2011 (UTC) I made some changes. Try to make it as clear as possible. </font><br />
:::<font color=orangered>I'm still a bit confused by this. If he has to take at least one aspirin a day, does he take 14 consecutively in a period of 14 days? I think that's where I'm confused. What statement are you trying to make? Also, where did you get 59? [[User:Rscott3|Richard]] 7/12</font> <br />
::::<font color=purple> That is one possible answer. But he could also take 14 aspirin in less than 14 days, say he could take 14 aspirin in only 3 days. In other words, if he wants to try to avoid taking 14 aspirin during certain period, he can't do it. He may avoid taking 15 aspirin during a period of consecutive days. However, this statement is trying to say that you can always find a period of consecutive days where he takes exactly 14 aspirin. Am I being clear enough or not? Please ask me more questions if you are still confused. :P <br />
::::How did I get 59? Since you add 14 to every term in the first inequality, you'll get 45 + 14 = 59 for the very last term. <br />
::::Maybe I could generalize this statement instead of using numbers 45, 14, 30. (i.e. he has to take <math>n</math> aspirin over a <math>m</math> day period. Then there is definitely a period of consecutive days where he takes exactly <math>n - m -1 </math> aspirin.) Do it make more sense now? </font><br />
<br />
*Number 10a is awesome! Great, clear description!<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:55, 8 July 2011 (UTC) Good to know. Thanks! </font><br />
<br />
*For 10b, I didn't know exactly what you you were trying to show until you had already started to prove it. This one might be in need of some more clarity in the initial description of the proof and statement.<br />
::*Typo:"situation" should be "situations" in "Since there are over 32,000 possible colorings, we could not draw and check every one of the situation."<br />
</font><br />
:::<font color=purple> Fixed it. What do you think about this part now? </font><br />
<br />
<font color=slateblue> <br />
* [[User:Rebecca|Rebecca]] 02:49, 16 July 2011 (UTC) "Here are 6 exciting real life applications for you to have a better grasp on this famous principle." I would say "real world applications to give you a better grasp of this famous principle."<br />
* "Under the worst condition when each of the first 366 students have their birthdays..." I would say "In the most extreme condition" <br />
* "This example may sound impossible to believe but mathematics, more precisely, the seemingly meaningless pigeonhole principle tells you it could happen." I would say " This example may sound impossible to believe, but the seemingly obvious pigeonhole principle tells us it must be true." </font color><br />
<br />
=MME=<br />
==More Mathematical examples==<br />
<font color=orangered>[[User:Rscott3|Richard]] 7/8<br />
*Number 1 is confusing.<br />
<br />
*For number 2, wouldn't it just be easier to choose all of the odd numbers, knowing that they are not consecutive and that there are only 50, then we know that the 51st must be even and next to an odd number.</font><br />
<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 02:10, 9 July 2011 (UTC)Yes, you are right. </font><br />
<br />
==How to Construct==<br />
<font color=orangered> [[User:Rscott3|Richard]] 7/8 <br />
*I was a bit confused by these examples.<br />
<br />
*This might also be a good point to derive or prove the principle explicitly with the math for average and maximum values????</font><br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 03:09, 9 July 2011 (UTC) I tried to fixed those confusing examples. Maybe some of them are still not very clear. I'll work on them later. Please feel free to tell me where should I improve. Thanks!</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Pigeonhole_Principle&diff=25644Talk:Pigeonhole Principle2011-07-16T02:35:30Z<p>Rebecca: /* Basic Description */</p>
<hr />
<div><font color=orangered> Pictures will be so cool for this one! [[User:Rscott3|Richard]] 6/29</font><br />
:<font color=salmon> [[User:PhoebeJiang|Phoebe]] 18:35, 8 July 2011 (UTC)Yeah, I realized that too. I'm not finished with this page yet, so I'll work on it! Thanks!<br />
::Ps: We have pretty much the same font color~ lol </font><br />
<br />
=General Comments=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*This page is really really cool. You've got a ton of opportunities for applications and pictures.<br />
<br />
*I'd make you Interesting Applications Section a "Why It's Interesting" section. I think this is more standard for math images. You can go to the edit with form tab to start that section.<br />
<br />
*You really only use examples to go into the topic. Is there some graphical proof or derivation that you could include?</font><br />
<br />
<br />
:[[User:PhoebeJiang|Phoebe]] 21:06, 8 July 2011 (UTC)<br />
<font color=purple><br />
<br />
:*First of all, thank you for leaving comments!! I use a different color to distinguish us. <br />
<br />
:*As you can see, I intend to use those 10 examples to lead in, giving readers a basic idea of what Pigeonhole principle is and how it works. The principle itself is pretty self-explanatary, so I didn't include the proof of this principle. Then, after you know how this simple principle helps in daily life, you will see the MME section with more examples and tricks about constructing pigeonholes. This is how I conceive this page, from easy to hard, from the description of pigeonhole principle, to applications (lead in), and eventually the hardest part, MME. So do you think I should put the applications under "Why interesting" after MME? If so, I'm afraid readers will feel overwhelmed by MME section. What do you think?<br />
::<font color=orangered> Okay, I see what you mean and I understand where you're coming from. To me, this page starts out with a very intuitive topic/description, and then gets more complicated in the current MME. What if there were some middle ground? I'm thinking like describing what average value is mathematically or something to put at the beginning of the MME to sort of segway into harder examples. There's a lot of examples on this page, and as the reader, I think it gets to be more difficult to pick out which examples are the most important ones. I don't know.... [[User:Rscott3|Richard]] 7/12</font><br />
:::<font color=purple> Richard! Check this out. I want some simple and interesting examples to lead in and I also want to put some hard applications under "why interesting" as you suggested. So, I'm thinking about splitting them into two sections, leaving the first 4-5 examples where they are now and put the rest of the examples after MME. Plus, those ten examples seem to be really long together. And people could apply those tricks mentioned in MME to see how the tricks work via the hard examples at the end of the page. What do you think about this idea? :) [[User:PhoebeJiang|Phoebe]] 20:38, 13 July 2011 (UTC) </font><br />
<br />
:*Pigeonhole principle is basically about combinatorics, about numbers. This principle itself doesn't have much to do with pictures. I agree with you about the pictures. I personally like graphs than simply words and numbers, so I'm thinking about adding more illustrative pictures on it. <br />
</font><br />
<br />
:*<font color=orangered> Phoebe, this page is looking great! I can read it through again if you want me to, just let me know when it's ready! [[User:Rscott3|Richard]] 7/12</font><br />
::*<font color=purple> [[User:PhoebeJiang|Phoebe]] 03:16, 14 July 2011 (UTC) Yeah actually could you read it through one more time, please? Tell me where I need to explain more precisely. Thanks a lot! </font><br />
<br />
=Intro=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*I'd reorganize this paragraph to something like this:<br />
::A pigeon is looking for a spot in the grid, but each box in the grid, or pigeonhole, is occupied. Where should the poor pigeon on the outside go? No matter which box he chooses, he must share with another pigeon. If all of the pigeons fit into the grid, here is definitely a pigeonhole contains more than one pigeon. This concept is known as the '''pigeonhole principle'''.<br />
*I think it's important to introduce the topic here in this section(I added a sentence at the end in my edit above).<br />
</font><br />
<br />
<br />
::[[User:PhoebeJiang|Phoebe]] 21:05, 8 July 2011 (UTC)<br />
<font color=purple><br />
::*Agree. Fixed it! <br />
</font><br />
<br />
=Basic Description=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*In the first sentence, change "items" to "pigeons" or vice versa for consistency.<br />
<br />
*In the second paragraph, I think that this quote is more confusing than helpful. I feel like you generalizing the same thing in your own words would be waaaaaay more helpful.<br />
::*It might be helpful to define "average value" and "maximum value" (maybe with a green mouse-over)<br />
<br />
*I'd delete "Although the two versions look very different, they are mathematically stating the same thing." and into the next paragraph, "To know why they are the same," and start with "Consider the main image instead". I think it's unnecessary to say.<br />
<br />
*Maybe change "bigger" to "greater"???? That sounds more mathy to me.<br />
<br />
*What's "its" referring to?<br />
::"Thus, '''its''' maximum value should be bigger than one as well, which means that there must be a pigeonhole contains more than one pigeons. Now we know that the two versions are actually talking about the same math principle."<br />
<br />
*Be careful with words like "pretty obvious". You're assuming a lot of the reader.<br />
<br />
*Move the sentence "Here are 10 exciting real life applications listed from easy to hard for you to have a better grasp on this famous principle." into the next section before the first example.<br />
</font><br />
<br />
:[[User:PhoebeJiang|Phoebe]] 21:24, 8 July 2011 (UTC)<br />
:<font color=purple> <br />
:*You have a lot of good points. I totally agree with you. <br />
:*Fixed all of them. Are they better now?</font><br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 02:35, 16 July 2011 (UTC) Phoebe, I'm Becky and I give feedback on many of the Math Images pages. I have a few suggestions for this page... <br />
* I would include mouseovers for "non empty" and "finite" because I think that if someone doesn't know what a maximum value or an average value is, they wont know either of those words either. <br />
* It's great that you introduce the general pigeonhole principle and then use explain the implications for the image. It's a logical order, and I think your approach is great! </font color><br />
<br />
=Interesting Applications=<br />
<font color=orangered> [[User:Rscott3|Richard]] 7/8<br />
*This section is awesome awesome awesome.<br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:04, 8 July 2011 (UTC)Thanks!</font><br />
<br />
*Pictures would be really super cool here. The way its formatted right now makes it seem longer than it actually is, especially with the table of contents. One way that I'd think to format this is like the "More than just shadows" section of [[Solving Triangles]]. Assign a picture to each example, and make two columns where the picture and text alternate sides. The picture doesn't have to be super complicated. The birthday one could just be a cake or something. Make it look more visually appealing. <br />
::*This will also help the table of contents because you'd have to make each of the ten headings just bolded words, and not section titles.<br />
:::<font color=purple>[[User:PhoebeJiang|Phoebe]] 21:27, 8 July 2011 (UTC)Guess what! I'm thinking about the same thing!</font><br />
<br />
*Some of the example descriptions get a bit wordy. For the purposes of these comments I'll just talk about the first one as an example and then say which ones were more confusing.<br />
::*For the birthday one, you could make it more clear by changing "Under the worst condition when the first 366 students have their birthdays from January 1st to December 31th, the 367th person has to be born on any day of the year. Thus, there are definitely two of the students who have their birthday falling on the same day." to "Under the worst condition when each of the first 366 students have their birthdays on different days from January 1st to December 31th, the birthday of the 367th person must be a repeat of one of those days. Thus, there are definitely two of the students who have their birthday falling on the same day."<br />
<br />
::: <font color=purple>[[User:PhoebeJiang|Phoebe]] 22:34, 8 July 2011 (UTC)Yeah, yours is waaaay better. </font><br />
<br />
*Numbers 5 and 9 could be a lot clearer with good pictures.<br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:03, 8 July 2011 (UTC)Add some pictures. </font><br />
<br />
*Number 7's main statement is confusing to me. <br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:13, 8 July 2011 (UTC) Could you please be more specific about it? </font> <br />
:::<font color=orangered>I understand what you are trying to prove, but I think the statement is wordy. What if you say something like: " Some n number of people are at a party. There are always at least two people who shake hands with the same number of people."? But even with the way I worded it...It' awkward. [[User:Rscott3|Richard]] 7/12</font><br />
::*I really like how you relate this one back to the pigeon/pigeonhole metaphor.<br />
:::*<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:03, 8 July 2011 (UTC) Thanks. I though it may be easier to understand if I do this. </font><br />
<br />
*Number 8 is very confusing. That's the only one I don't understand.<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:55, 8 July 2011 (UTC) I made some changes. Try to make it as clear as possible. </font><br />
:::<font color=orangered>I'm still a bit confused by this. If he has to take at least one aspirin a day, does he take 14 consecutively in a period of 14 days? I think that's where I'm confused. What statement are you trying to make? Also, where did you get 59? [[User:Rscott3|Richard]] 7/12</font> <br />
::::<font color=purple> That is one possible answer. But he could also take 14 aspirin in less than 14 days, say he could take 14 aspirin in only 3 days. In other words, if he wants to try to avoid taking 14 aspirin during certain period, he can't do it. He may avoid taking 15 aspirin during a period of consecutive days. However, this statement is trying to say that you can always find a period of consecutive days where he takes exactly 14 aspirin. Am I being clear enough or not? Please ask me more questions if you are still confused. :P <br />
::::How did I get 59? Since you add 14 to every term in the first inequality, you'll get 45 + 14 = 59 for the very last term. <br />
::::Maybe I could generalize this statement instead of using numbers 45, 14, 30. (i.e. he has to take <math>n</math> aspirin over a <math>m</math> day period. Then there is definitely a period of consecutive days where he takes exactly <math>n - m -1 </math> aspirin.) Do it make more sense now? </font><br />
<br />
*Number 10a is awesome! Great, clear description!<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:55, 8 July 2011 (UTC) Good to know. Thanks! </font><br />
<br />
*For 10b, I didn't know exactly what you you were trying to show until you had already started to prove it. This one might be in need of some more clarity in the initial description of the proof and statement.<br />
::*Typo:"situation" should be "situations" in "Since there are over 32,000 possible colorings, we could not draw and check every one of the situation."<br />
</font><br />
:::<font color=purple> Fixed it. What do you think about this part now? </font><br />
<br />
=MME=<br />
==More Mathematical examples==<br />
<font color=orangered>[[User:Rscott3|Richard]] 7/8<br />
*Number 1 is confusing.<br />
<br />
*For number 2, wouldn't it just be easier to choose all of the odd numbers, knowing that they are not consecutive and that there are only 50, then we know that the 51st must be even and next to an odd number.</font><br />
<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 02:10, 9 July 2011 (UTC)Yes, you are right. </font><br />
<br />
==How to Construct==<br />
<font color=orangered> [[User:Rscott3|Richard]] 7/8 <br />
*I was a bit confused by these examples.<br />
<br />
*This might also be a good point to derive or prove the principle explicitly with the math for average and maximum values????</font><br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 03:09, 9 July 2011 (UTC) I tried to fixed those confusing examples. Maybe some of them are still not very clear. I'll work on them later. Please feel free to tell me where should I improve. Thanks!</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Pigeonhole_Principle&diff=25643Talk:Pigeonhole Principle2011-07-16T02:35:12Z<p>Rebecca: /* Basic Description */</p>
<hr />
<div><font color=orangered> Pictures will be so cool for this one! [[User:Rscott3|Richard]] 6/29</font><br />
:<font color=salmon> [[User:PhoebeJiang|Phoebe]] 18:35, 8 July 2011 (UTC)Yeah, I realized that too. I'm not finished with this page yet, so I'll work on it! Thanks!<br />
::Ps: We have pretty much the same font color~ lol </font><br />
<br />
=General Comments=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*This page is really really cool. You've got a ton of opportunities for applications and pictures.<br />
<br />
*I'd make you Interesting Applications Section a "Why It's Interesting" section. I think this is more standard for math images. You can go to the edit with form tab to start that section.<br />
<br />
*You really only use examples to go into the topic. Is there some graphical proof or derivation that you could include?</font><br />
<br />
<br />
:[[User:PhoebeJiang|Phoebe]] 21:06, 8 July 2011 (UTC)<br />
<font color=purple><br />
<br />
:*First of all, thank you for leaving comments!! I use a different color to distinguish us. <br />
<br />
:*As you can see, I intend to use those 10 examples to lead in, giving readers a basic idea of what Pigeonhole principle is and how it works. The principle itself is pretty self-explanatary, so I didn't include the proof of this principle. Then, after you know how this simple principle helps in daily life, you will see the MME section with more examples and tricks about constructing pigeonholes. This is how I conceive this page, from easy to hard, from the description of pigeonhole principle, to applications (lead in), and eventually the hardest part, MME. So do you think I should put the applications under "Why interesting" after MME? If so, I'm afraid readers will feel overwhelmed by MME section. What do you think?<br />
::<font color=orangered> Okay, I see what you mean and I understand where you're coming from. To me, this page starts out with a very intuitive topic/description, and then gets more complicated in the current MME. What if there were some middle ground? I'm thinking like describing what average value is mathematically or something to put at the beginning of the MME to sort of segway into harder examples. There's a lot of examples on this page, and as the reader, I think it gets to be more difficult to pick out which examples are the most important ones. I don't know.... [[User:Rscott3|Richard]] 7/12</font><br />
:::<font color=purple> Richard! Check this out. I want some simple and interesting examples to lead in and I also want to put some hard applications under "why interesting" as you suggested. So, I'm thinking about splitting them into two sections, leaving the first 4-5 examples where they are now and put the rest of the examples after MME. Plus, those ten examples seem to be really long together. And people could apply those tricks mentioned in MME to see how the tricks work via the hard examples at the end of the page. What do you think about this idea? :) [[User:PhoebeJiang|Phoebe]] 20:38, 13 July 2011 (UTC) </font><br />
<br />
:*Pigeonhole principle is basically about combinatorics, about numbers. This principle itself doesn't have much to do with pictures. I agree with you about the pictures. I personally like graphs than simply words and numbers, so I'm thinking about adding more illustrative pictures on it. <br />
</font><br />
<br />
:*<font color=orangered> Phoebe, this page is looking great! I can read it through again if you want me to, just let me know when it's ready! [[User:Rscott3|Richard]] 7/12</font><br />
::*<font color=purple> [[User:PhoebeJiang|Phoebe]] 03:16, 14 July 2011 (UTC) Yeah actually could you read it through one more time, please? Tell me where I need to explain more precisely. Thanks a lot! </font><br />
<br />
=Intro=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*I'd reorganize this paragraph to something like this:<br />
::A pigeon is looking for a spot in the grid, but each box in the grid, or pigeonhole, is occupied. Where should the poor pigeon on the outside go? No matter which box he chooses, he must share with another pigeon. If all of the pigeons fit into the grid, here is definitely a pigeonhole contains more than one pigeon. This concept is known as the '''pigeonhole principle'''.<br />
*I think it's important to introduce the topic here in this section(I added a sentence at the end in my edit above).<br />
</font><br />
<br />
<br />
::[[User:PhoebeJiang|Phoebe]] 21:05, 8 July 2011 (UTC)<br />
<font color=purple><br />
::*Agree. Fixed it! <br />
</font><br />
<br />
=Basic Description=<br />
<font color=orangered><br />
[[User:Rscott3|Richard]] 7/8<br />
*In the first sentence, change "items" to "pigeons" or vice versa for consistency.<br />
<br />
*In the second paragraph, I think that this quote is more confusing than helpful. I feel like you generalizing the same thing in your own words would be waaaaaay more helpful.<br />
::*It might be helpful to define "average value" and "maximum value" (maybe with a green mouse-over)<br />
<br />
*I'd delete "Although the two versions look very different, they are mathematically stating the same thing." and into the next paragraph, "To know why they are the same," and start with "Consider the main image instead". I think it's unnecessary to say.<br />
<br />
*Maybe change "bigger" to "greater"???? That sounds more mathy to me.<br />
<br />
*What's "its" referring to?<br />
::"Thus, '''its''' maximum value should be bigger than one as well, which means that there must be a pigeonhole contains more than one pigeons. Now we know that the two versions are actually talking about the same math principle."<br />
<br />
*Be careful with words like "pretty obvious". You're assuming a lot of the reader.<br />
<br />
*Move the sentence "Here are 10 exciting real life applications listed from easy to hard for you to have a better grasp on this famous principle." into the next section before the first example.<br />
</font><br />
<br />
:[[User:PhoebeJiang|Phoebe]] 21:24, 8 July 2011 (UTC)<br />
:<font color=purple> <br />
:*You have a lot of good points. I totally agree with you. <br />
:*Fixed all of them. Are they better now?</font><br />
<br />
<font color=slateblue> <br />
*[[User:Rebecca|Rebecca]] 02:35, 16 July 2011 (UTC) Phoebe, I'm Becky and I give feedback on many of the Math Images pages. I have a few suggestions for this page... <br />
* I would include mouseovers for "non empty" and "finite" because I think that if someone doesn't know what a maximum value or an average value is, they wont know either of those words either. <br />
* It's great that you introduce the general pigeonhole principle and then use explain the implications for the image. It's a logical order, and I think your approach is great!<br />
<br />
=Interesting Applications=<br />
<font color=orangered> [[User:Rscott3|Richard]] 7/8<br />
*This section is awesome awesome awesome.<br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:04, 8 July 2011 (UTC)Thanks!</font><br />
<br />
*Pictures would be really super cool here. The way its formatted right now makes it seem longer than it actually is, especially with the table of contents. One way that I'd think to format this is like the "More than just shadows" section of [[Solving Triangles]]. Assign a picture to each example, and make two columns where the picture and text alternate sides. The picture doesn't have to be super complicated. The birthday one could just be a cake or something. Make it look more visually appealing. <br />
::*This will also help the table of contents because you'd have to make each of the ten headings just bolded words, and not section titles.<br />
:::<font color=purple>[[User:PhoebeJiang|Phoebe]] 21:27, 8 July 2011 (UTC)Guess what! I'm thinking about the same thing!</font><br />
<br />
*Some of the example descriptions get a bit wordy. For the purposes of these comments I'll just talk about the first one as an example and then say which ones were more confusing.<br />
::*For the birthday one, you could make it more clear by changing "Under the worst condition when the first 366 students have their birthdays from January 1st to December 31th, the 367th person has to be born on any day of the year. Thus, there are definitely two of the students who have their birthday falling on the same day." to "Under the worst condition when each of the first 366 students have their birthdays on different days from January 1st to December 31th, the birthday of the 367th person must be a repeat of one of those days. Thus, there are definitely two of the students who have their birthday falling on the same day."<br />
<br />
::: <font color=purple>[[User:PhoebeJiang|Phoebe]] 22:34, 8 July 2011 (UTC)Yeah, yours is waaaay better. </font><br />
<br />
*Numbers 5 and 9 could be a lot clearer with good pictures.<br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:03, 8 July 2011 (UTC)Add some pictures. </font><br />
<br />
*Number 7's main statement is confusing to me. <br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 23:13, 8 July 2011 (UTC) Could you please be more specific about it? </font> <br />
:::<font color=orangered>I understand what you are trying to prove, but I think the statement is wordy. What if you say something like: " Some n number of people are at a party. There are always at least two people who shake hands with the same number of people."? But even with the way I worded it...It' awkward. [[User:Rscott3|Richard]] 7/12</font><br />
::*I really like how you relate this one back to the pigeon/pigeonhole metaphor.<br />
:::*<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:03, 8 July 2011 (UTC) Thanks. I though it may be easier to understand if I do this. </font><br />
<br />
*Number 8 is very confusing. That's the only one I don't understand.<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:55, 8 July 2011 (UTC) I made some changes. Try to make it as clear as possible. </font><br />
:::<font color=orangered>I'm still a bit confused by this. If he has to take at least one aspirin a day, does he take 14 consecutively in a period of 14 days? I think that's where I'm confused. What statement are you trying to make? Also, where did you get 59? [[User:Rscott3|Richard]] 7/12</font> <br />
::::<font color=purple> That is one possible answer. But he could also take 14 aspirin in less than 14 days, say he could take 14 aspirin in only 3 days. In other words, if he wants to try to avoid taking 14 aspirin during certain period, he can't do it. He may avoid taking 15 aspirin during a period of consecutive days. However, this statement is trying to say that you can always find a period of consecutive days where he takes exactly 14 aspirin. Am I being clear enough or not? Please ask me more questions if you are still confused. :P <br />
::::How did I get 59? Since you add 14 to every term in the first inequality, you'll get 45 + 14 = 59 for the very last term. <br />
::::Maybe I could generalize this statement instead of using numbers 45, 14, 30. (i.e. he has to take <math>n</math> aspirin over a <math>m</math> day period. Then there is definitely a period of consecutive days where he takes exactly <math>n - m -1 </math> aspirin.) Do it make more sense now? </font><br />
<br />
*Number 10a is awesome! Great, clear description!<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 23:55, 8 July 2011 (UTC) Good to know. Thanks! </font><br />
<br />
*For 10b, I didn't know exactly what you you were trying to show until you had already started to prove it. This one might be in need of some more clarity in the initial description of the proof and statement.<br />
::*Typo:"situation" should be "situations" in "Since there are over 32,000 possible colorings, we could not draw and check every one of the situation."<br />
</font><br />
:::<font color=purple> Fixed it. What do you think about this part now? </font><br />
<br />
=MME=<br />
==More Mathematical examples==<br />
<font color=orangered>[[User:Rscott3|Richard]] 7/8<br />
*Number 1 is confusing.<br />
<br />
*For number 2, wouldn't it just be easier to choose all of the odd numbers, knowing that they are not consecutive and that there are only 50, then we know that the 51st must be even and next to an odd number.</font><br />
<br />
::<font color=purple> [[User:PhoebeJiang|Phoebe]] 02:10, 9 July 2011 (UTC)Yes, you are right. </font><br />
<br />
==How to Construct==<br />
<font color=orangered> [[User:Rscott3|Richard]] 7/8 <br />
*I was a bit confused by these examples.<br />
<br />
*This might also be a good point to derive or prove the principle explicitly with the math for average and maximum values????</font><br />
::<font color=purple>[[User:PhoebeJiang|Phoebe]] 03:09, 9 July 2011 (UTC) I tried to fixed those confusing examples. Maybe some of them are still not very clear. I'll work on them later. Please feel free to tell me where should I improve. Thanks!</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=S11&diff=25642S112011-07-16T02:26:18Z<p>Rebecca: /* Current */</p>
<hr />
<div>__TOC__<br />
<br />
== Announcements ==<br />
For public-type help questions, see [[Help:Contents|Help]]. For Swat-specific ones, see [[Swarthmore summer research orientation]].<br />
<br />
<b>Remember to keep your projects sections short and up to date; only the last week of status changes should be mentioned. [[User:Smaurer1|Smaurer1]]</b><br />
<br />
===Group Discussion Questions===<br />
<br />
* [[Topics for conversations through Skype with RPI, SB, and/or Drexel]] Started 6/29.<br />
* [[Who are we writing for?]] Started 6/29.<br />
* [[Possibly expanding student Math Image roles]], to be addressed 7/6.<br />
<br />
===Questions:===<br />
*Things that are listed as Helper Pages but use the Image Page template<br />
:We need to decide whether these pages should be on the Helper Page template, the Image Page template, or both: {{Hide|1=<br />
:*[[Change of Coordinate Systems]] - Image template only; image template live<br />
:*[[Conic Section]] - both templates; image template not live<br />
:*[[Differentiability]] - both templates; image template not live<br />
:*[[Dot Product]] - Image template only; image template not live<br />
:*[[Gradients and Directional Derivatives]] - Image template only; image template not live<br />
:*[[Hyperbolic Geometry]] - Image template only; image template not live<br />
:*[[Inversion]] - Image template only; image template not live<br />
:*[[Iterated Functions]] - Image template only; image template not live<br />
:*[[Parametric Equations]] - Image template only; image template live<br />
:*[[Taylor Series]] - Image template only; image template not live<br />
:*[[Volume of Revolution]] - Image template only; image template live<br />
<br />
:<font color=dodgerblue>''(List complied by [[User:Kderosier|Kate]], June 16)''</font><br />
}}<br />
<br />
<br />
Older questions: {{Hide|1=<br />
*Harrison's question about text being cut off on Cross-cap: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 14:16, 8 June 2011 (UTC)<br />
**The text in MME on the [[Cross-cap]] page is getting truncated when viewed through edit with form, but still appears on the page.<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 00:49, 14 June 2011 (UTC): When I've encountered this problem previously, it's been because a set of double curly brackets wasn't closed.</font><br />
}}<br />
<br />
*Harrison's question about creating a list of not-yet-existent Helper Pages: {{Hide|1=<br />
Harrison, 5/26/11:<br />
:*<s>We need a list of empty pages: Penrose Tiles is only linked to one, now two, pages. Empty pages like this could well fade into obscurity.</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:09, 7 June 2011 (UTC): Such a list has been created. See [[Existing_Pages_Needing_Work#Empty_.28but_linked_to.29_Pages|here]].</font><br />
}}<br />
<br />
*Spam conversation: {{Hide|1=<br />
<font color=dodgerblue><br />
*[[User:Kderosier|Kate]] 14:38, 27 May 2011 (UTC): '''We have some new users who are creating a bunch of pages with links to illegally download or watch movies.''' At first, we though it might be someone from Sweet Briar practicing wiki-syntax, but now it's just starting to look like spam:<br />
**[[Watch_Sniper:_Reloaded_film_in_hd|This is the type of page I'm talking about]]<br />
**[[Special:Contributions/Calrivenick|List of pages created by Calrivenick]]<br />
**[[Special:Contributions/Cadedesi|List of pages created by Cadedesi]]<br />
</font><br />
:Let's talk about what to do this afternoon. [[User:Gene|Gene]] 15:19, 27 May 2011 (UTC)<br />
:<font color=dodgerblue>This problem has continued over the weekend. Someone spammed the talk page for Fun Topology with comments about buying Cialis and stuff. They also posted a lot more movie download pages under the Cadedesi username. I'm going to go through and delete again.</font><br />
:<font color=dodgerblue>The spam comments on Fun Topology were coming from this computer's IP address. </font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 14:34, 6 June 2011 (UTC): Haven't seen any more spam activity for a few days. I assume some computer people have handled the issue? I'm going to hide this conversation so that it's not taking up space on S11.</font><br />
}}<br />
<br />
*Citations/footnotes conversation: {{Hide|1=<br />
:I spent a really long time wandering around MediaWiki and Wikipedia this morning trying to figure out how to do footnotes/citations the way I wanted to - now that I know how, should I add instructions to one of the many help mages on Math Images? If so, which page? (Kate, 5/17)<br />
<br />
:<font color=red> Answer: put it here at [[Help:Wiki_Tricks|Wiki Tricks]] (XD, 5/17) </font><br />
<br />
:[[User:Smaurer1|Smaurer1]] 19:43, 17 May 2011 (UTC) Well, it's not clear that webarticles should have footnotes, although Wikipedia does. In text references may be better. This is surely something we should discuss as a group, and find out what last year's group decided, if they did. If there are footnotes, there has got to be a way to get back seamlessly to where you were before you jumped to the footnote.<br />
<br />
:Also, as for citations, we should be uniform in their format.<br />
<br />
:Finally, you can use 4 tildes to put your username and time stamp on your comments, and 3 tildes for just your username. <br />
<br />
:<font color=dodgerblue>Well, I wasn't doing comment-y type footnotes, I just wanted specific sentences to link to items in my References section. I think that format is better than full intext-citations, because it brings you to the source if that's what you're interested in, but it takes up less space if you're not. The references template we have comes equipped with little links to jump you back up, too- if you look at the [[Quipu#References|Quipu]] page, you can see that it lists each of the sections that reference is linked from, and those links bring you to the reference in that section. All in all, I think it's a clear and intuitive way to do references for both the writer and the reader (although, like most things, it doesn't play well with our hidden sections), and I'm going to go ahead and put the instructions up in WikiTricks. -[[User:Kderosier|Kate]] </font><br />
<br />
{{Hide|1=<br />
*What the help pages say now:<br />
**[[Tour_the_Math_Images_Project#Anatomy_of_a_page|The Tour page's "Anatomy of a page" section]]<br />
**[[Checklist_for_writing_pages#References_and_footnotes|The "References and footnotes" section on the checklist for writing pages]]<br />
*The way to do Wikipedia-like references:<br />
**[[Wiki_Tricks#How_to_do_Citations|Wiki Tricks - Citations section]]<br />
}}<br />
<br />
}}<br />
<br />
*Invisible Comments conversation: {{Hide|1= One of you asked "How do you put invisible comments in the source code?"<br />
<br />
:Answer: Same way you do in html, like this <nowiki><br />
:<!-- hidden stuff --><br />
:</nowiki><br />
:However, if you want to make comments about an article for its author, the comments are more likely to be seen if you either<br />
:* put it in the discussion page, or<br />
:* if it is important to put it right by the material commented on, put it in the article in color with your username and time stamp included.<br />
<br />
:Hidden comments in the source code are likely to be overlooked, except perhaps if they are written by the author him/herself, as a note for further development.<br />
}}<br />
}}<br />
<br />
== Current Individual Projects ==<br />
<br />
===Steve M (aka Prof Maurer)'s Role===<br />
{{Hide|1=<br />
My role is 2-fold:<br />
<br />
<ol><br />
<li> Come see me to sound me out (if you wish) on the mathematical appropriateness of an idea for a page, or for possible references.<br />
<br />
<li> Once you have a reasonable amount written, and want feedback on the quality and correctness of the mathematical exposition, ask me to look it over and then we will have a conference. (Abram and the oldies are as good as I am at discussion general organization and clarity issues.) <br />
</ol><br />
<br />
We have agreed to put a record on this S11 page of what we are doing and what help we want from others, but in addition tell me in person or by email if you want to conference with me.<br />
}}<br />
<br />
===Harrison's Projects===<br />
<br />
[[Harrison's detritus]]<br />
<br />
*[[User:Htasoff|Htasoff]] 23:44, 13 July 2011 (UTC) Pages will be submitted for final review in 1 - 3 days. A few, final comments are welcome. Real Projective Plane is still in the works, though.<br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:19, 14 July 2011 (UTC): Hey Harrison, do you know if that one picture in inverse trig that you got from somewhere on the internet is a picture we can use? Can you check please?</font><br />
<br />
===Richard's Projects===<br />
<br />
<br />
<font color=orangered> <br />
<br />
This weekend, I'll be reading pages to give feedback: [[Steiner's Chain]] [[Snell's Law]] [[Perko pair knots]] [[Pigeonhole Principle]] and an [[RPI11|RPI]] page<br />
<br />
:<font color=salmon>Hey Richard, thank you for leaving comments on pigeonhole principle. I've made some changes and left my ideas about the arrangement. Could you go through my page once again? I'd really appreciate it! [[User:PhoebeJiang|Phoebe]] 22:08, 14 July 2011 (UTC)</font><br />
<br />
*[[Ambiguous Case]]<br />
:*This page is the one that everyone should follow for feedback!<br />
:*Looking for final readthrough before it goes up for review! Then the lesson!!!![[User:Rscott3|Richard]] 7/14 </font color><br />
<br />
:APPLET INFO:[[User:Alimurreza|Alimurreza]] 02:53, 6 July 2011 (UTC)I am working on your applet. Check this out here @([http://mathforum.org/mathimages/index.php/DU11 Reza's work]).<br />
:APPLET UPDATE:[[User:Alimurreza|Alimurreza]] 02:41, 15 July 2011 (UTC)I am done with Ambiguous Case applet. Please, check the applet. Feel free to send me any feedback or change-request.<br />
:{{Hide|1=<br />
<br />
What i want mine to look like, but http://www.mccsc.edu/~aterwill/ambiguouscaseapplet/Ambiguous_Case_applet.html doesn't show the completed triangles.<br />
<br />
I like how this one shows the completed triangles<br />
http://www.mnwest.edu/fileadmin/static/website/dmatthews/Geogebra/AmbiguousCase01.html<br />
<br />
}}<br />
<br />
<br />
<br />
'''Completed Pages'''<br />
<br />
*[[Law of cosines]]<font color=orangered> [[User:Rscott3|Richard]] 6/23</font><br />
<br />
*[[Law of Sines]] [[User:AnnaP|AnnaP]] 7/7<br />
<br />
*[[Solving Triangles]] 7/12<br />
<br />
:Other ideas: {{Hide|1=<br />
*inscribed angles?<br />
<br />
*Normal Distribution?<br />
<br />
*Birthday Paradox?<br />
}}<br />
<br />
===Dayo's Projects===<br />
Current projects<br />
*[[Inscribed figures]] : there's a [[Compass & Straightedge Construction and the Impossible Constructions]] page, but I think that inscribed figures deserves its' own page. What do others think? <br />
::<font color=slateblue> [[User:Rebecca|Rebecca]] 01:07, 9 July 2011 (UTC) I left comments on the discussion page. </font color><br />
<br />
Future Projects: {{Hide|1=<br />
*[[Mathematics in architecture]]:make changes akin to [[Math for Computer Graphics and Computer Vision]], including:<br />
<br />
::*[[Cross sections]]: calculus application page, including examples of Tokyo international Forum, Suransuns Bridge, and other structures which could be thought of and put together easily in terms of their cross sections <br />
::*[[Torus]] edits, additions concerning the Torus in construction and architecture<br />
::*[[Domes]]:conic sections, arches, parabolas<br />
::*[[The Henderson Waves Bridge]]: sinusoids in architecture, parametric design<br />
::*[[Catenary]]: More real world examples: namely bridges<br />
::*[[Bridge of Peace]]: The equation(s) used to generate the surface, possibly words from the architect, very new, may be hard to get concrete technical information <br />
::*[[Kurilpa Bridge]]: Everyone have a look at the image and tell me what kind of actual subjects you could find in it, namely in the cables and tubes.<br />
::*Teaching Materials(6/30): ''growing up with science: projects'' could be the sort of activities we're looking for. I used these with a class, and think people should look at them.<br />
<br />
<br />
<br />
<br />
}}<br />
<br />
on hold: <br />
*[[Parametric Equations]]: integrating Xingda's page from [[S10]] into page.<br />
<br />
===Diana's Projects===<br />
<br />
====Current====<br />
*[[Logistic Bifurcation]]<br />
<br />
:<font color=darkred> I've put up comments. There are a few places that could use some work. [[User:AnnaP|AnnaP]] 7/10 </font> <br />
:<font color=slateblue> [[User:Rebecca|Rebecca]] 02:26, 16 July 2011 (UTC) This is a very impressive page. I put up a few small suggestions on the discussion page. </font color><br />
<br />
*[[Markus-Lyapunov Fractals]]<br />
:<font color=darkred> Approved [[User:AnnaP|AnnaP]] 7/14 </font><br />
<br />
====Ideas for later projects====<br />
{{Hide|1=<br />
*Chirikov-Taylor Maps<br />
**This seems like a natural extension of the Markus-Lyapunov Fractals page, but maybe the math involved in the two is too similar?<br />
*This aspect of pendular motion:<br />
**[[http://www.youtube.com/watch?v=yVkdfJ9PkRQ&feature=player_embedded|Varied-Length Pendulums]]<br />
**I'm not sure how or whether to use this -- does a ''moving'' image count as a "math image"? -- But it's incredible, and I'd love to explore it.<br />
*Kuen Surface<br />
**It's just really cool.<br />
}}<br />
<br />
===Kate's Projects===<br />
*[[User:Kderosier#Applet_Testing|Java Applets]]<br />
<br />
*[[Anne Burns' Mathscapes]] (Scrapped out of [[Mountains In Spring|three]] [[Mathscape|other]] [[Fractal Scene I|pages]]):<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 14:21, 14 July 2011 (UTC): Responded to Chris' comments. Feedback from others would be appreciated.</font><br />
<br />
*[[Perko pair knots]]:<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 21:00, 15 July 2011 (UTC): Have several changes I'm planning to make in response to verbal feedback from Abram, it'd be great if everyone else could hold off for a few days.</font><br />
<br />
*Finished pages: {{Hide|1=<br />
*[[Critical Points]]:<br />
:<font color=darkred> Approved, but I did have one note on whether or not you intended to add something. It's fine as is, but I wanted to put up a suggestion. [[User:AnnaP|AnnaP]] 16:24, 15 July 2011 (UTC) </font><br />
<br />
:*[[Summation Notation]]:<br />
::<font color=darkred> Approved [[User:AnnaP|AnnaP]] 16:24, 15 July 2011 (UTC) </font><br />
<br />
:*[[Bases]]:<br />
:: <font color=dodgerblue>[[User:Kderosier|Kate]] 17:31, 11 July 2011 (UTC): Changed things in response to Chris' comments.</font><br />
<br />
:* [[Quipu]]:<br />
::<font color=darkred> Put up as ready for the public 6/30 [[User:AnnaP|AnnaP]] </font><br />
<br />
:* [[Basic Trigonometric Functions]]:<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 18:11, 30 June 2011 (UTC): Changed the the things that were bolded.</font><br />
<br />
<br />
}}<br />
<br />
<br />
<font color=red>[[User:donko14|Anna]] Hey Kate-Thank you for all of your comments on my [[Steiner's Chain]] page, I really appreciate all of what you suggested, especially with this being my very first page. Your comments are extremely helpful not only in adjusting the content on this page, but as well as with how to construct the other pages I'm working on currently. THANKS!!</font><br />
::<font color=dodgerblue>np, glad you found them helpful! :) -[[User:Kderosier|Kate]] 14:21, 14 July 2011 (UTC)</font><br />
<br />
===Leah's Projects===<br />
*[[Bedsheet Problem]]<br />
not sure what to do with this page. <br />
<br />
*[[Boy's Surface]] <br />
WIP<br />
<br />
*[[Snell's Law]] feedback page<br />
::Need comments. Also, waiting on the final applet by Reza. 7/15<br />
::<font color=slateblue> I added a few comments and responded to old ones on the discussion page </font color><br />
<br />
*[[Witch of Agnesi]]<br />
up for final review. [[User:Ljeanlo1|Ljeanlo1]] 18:43, 15 July 2011 (UTC)<br />
<br />
*[[Dot Product]] <font color=darkred> Approved, 7/14 </font><br />
<br />
*[[Vector]] <font color=darkred> Approved, 7/10 </font><br />
<br />
==Requests to S10 Students==<br />
<br />
<br />
*<s>Can XD do a demo for MATLAB?</s> Done - [[Demo of MATLAB using the example of Bifurcation]]<br />
<br />
==Useful Links==<br />
[[S10]]<br />
<br />
[[SB11]]<br />
<br />
[[RPI11]]<br />
<br />
[[DU11]]<br />
<br />
[[Pages Ready for Final Review]]<br />
<br />
[[Feedback Requests]]<br />
<br />
[[Sample discussion page]]<br />
<br />
[[Math Tools Requests]] ''This page is a place where students whose primary focus is writing pages can post requests for applets, animations, and new images that they'd like to see the computer science students create.''<br />
<br />
[[Page Building Help]]<br />
<br />
[[Help:Wiki Tricks|Wiki Tricks]]<br />
<br />
[[From a Bunch of Old Timers]]<br />
<br />
[[List of summer 2010 pages]]<br />
<br />
http://en.wikipedia.org/wiki/Help:Displaying_a_formula<br />
<br />
[[PartnerHome]]<br />
<br />
[[Existing Pages Needing Work]]<br />
<br />
[[Site programming questions]]<br />
<br />
== Current Group Projects ==</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Logistic_Bifurcation&diff=25641Talk:Logistic Bifurcation2011-07-16T02:24:10Z<p>Rebecca: /* Response to Checklist */</p>
<hr />
<div>=Response to Checklist=<br />
<font color=purple>17:00, 7/7/11<br />
<font color=darkred> My comments are up [[User:AnnaP|AnnaP]] 7/10 </font><br />
<br />
<font color=darkred>'''Messages to the Future'''<br />
It might be kind of fun to include a hidden section at the end about how to plot the logistic map--maybe put in a request for a computer science oriented person to explain how to do it? You can also take a look at my mathematica code to plot it--you can download that by clicking [[http://www.sccs.swarthmore.edu/users/09/anna09/mathematica/LogMap.nb here]]</font><br />
<br />
'''References and Footnotes'''<br />
<br />
All of the images are cited, if you click on them. Most of them were created by me, anyway. I emailed the creators of the applet at the bottom of the page to get their permission, and it's very clearly cited on the page. No footnotes were necessary for the information on this page.<br />
<br />
'''Context'''<br />
<br />
The basic description is very clear about how logistic systems connect to biology and populations. It also shows how various oscillations would manifest, graphically in a population in a way that is easy to understand. "Why it's interesting" includes further discussion of real-world use and an interactive applet demonstrating self-similarity.<br />
<br />
'''Quality of Prose'''<br />
<br />
Because of the length of the page, I carefully used "signpost" sentences and paragraphs throughout the article, along with clear logical links from one paragraph to the next. Each section is clear about its purpose and direction. All of the more mathematical section is pretty heavy, and it's in the only order that makes sense, so I can't move the detailed math any further down.<br />
:*<font color=darkred> your first sentence "A section of a bifurcation diagram showing how logistic systems change as fecundity changes." might scare away readers by using "bifurcation" and "fecundity" Perhaps use a slightly less accurate, more generic first sentence? <br />
:*You don't need the word "recursively" here: "or apply it over and over recursively" Again, it's a word that will confuse some readers </font><br />
:*<font color=slateblue>[[User:Rebecca|Rebecca]] 02:24, 16 July 2011 (UTC) I would say "far from scattered" instead of "anything but scattered" in the bifurcation and chaos section. <br />
:* "Using a web diagram, we confirmed that, for the example of r = 2.9, the point we can find analytically is in fact the point the system approaches." I don't think you need the comma after "that." </font color><br />
'''Integration of Images'''<br />
<br />
The images are meticulously numbered, referenced in the text, linked between image and text, and explained in both the text and the captions.<br />
<br />
'''Connections'''<br />
<br />
This page links extensively to chaos and iterations, including a thorough discussion of how iteration can be applied to this topic. The idea of fractals is also discussed.<br />
<br />
'''Examples'''<br />
<br />
The logistic map is derived with clear explanations of steps. The mathematical discussion of bifurcation uses extensive examples in multiple forms -- diagrams, graphs, and analytical discussions. All new ideas are defined, discussed, or linked out to helper pages.<br />
<br />
'''Accuracy and Precision'''<br />
<br />
All terms are defined in text, bubbled out, or linked out. Mathematical ideas are expressed both in equations and pictorially, where possible. In the mathematical bifurcation section, because it is so long, great pains are taken to keep the reader on track and return consistently to the main ideas.<br />
<font color=darkred><br />
*The paragraph that begins with this sentence: "Earlier, we found that period-one fixed points exist in all logistic systems, whether or not they approach only one point. Now, we will see that the condition x(n+2) = xn also has a solution for logistic systems with r < 3. " Could use a bit of work. It'd be better to explain that a fixed point will certainly come back to itself when you iterate it. If you have f(x)=x, then f(f(x))=f(x)=x. So anything that is a solution to the first equation is also a solution to f(f(x))=x. Similarly, all two two-cycles will show up when you look for solutions to the period four equation f(f(f(f(x))))=x. An explanation in those terms in place of, or addition to, what you already have will make that section make more sense. </font> <br />
<font color=slateblue>[[User:Rebecca|Rebecca]] 01:42, 16 July 2011 (UTC) I don't know if you can just say "(hence the name)" when you're talking about bifurcation. I had to look up the fact that "furcate" is to divide into branches. I think mentioning that in the parentheses would be helpful. My vocabulary is pretty weak, but i think other people might have the same issue. </font color><br />
<br />
'''Layout'''<br />
I made the paragraphs as short as I could, put in breaks to make sure pictures didn't overlap with other sections, and tried to place image location to create the least possible interference with readability at any window size. Definitions are generally bubbled or linked out, with some in boldface.<br />
</font><br />
*<font color=darkred> Why don't you add an extra break between each paragraph in your basic description? That will help break up the text a bit better.<br />
*The paragraphs between images 3 and 4 and 5 and 6 could also use some extra spaces. <br />
*Image 5 is a bit distracting where it is, since you talk about it much lower than the image itself. Try to move it around.<br />
*Can you make the blurb on web diagrams it's own subsection, or make the phrase Web Diagrams at the beginning of that area bold to stand out? </font><br />
<br />
=General Comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 14:58, 1 July 2011 (UTC): Much clearer than before. Be careful with your "So"s - you begin a ''lot'' of sentences with "So". None of them are things I would object to individually, but the fact that they stood out to me probably means you're overusing them.</font><br />
<br />
*<font color=darkred>[[User:AnnaP|AnnaP]] 6/16 - Diana, have you seen the [[Iterated Functions]] Page? That page uses the logistic map for examples, and you might find that it's useful to link to that page (or lift some of the images) for examples.</font><br />
**<font color=purple> I had already linked to this, bit it was pretty subtle, so I've added it in more prominently.</font><br />
<br />
=Section-specific Comments=<br />
<br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:55, 1 July 2011 (UTC):<br />
*<s>Typo: ''into multiple values. '''i'''n the case of logistic bifurcation…''</s></font><br />
*<font color=dodgerblue>''The branching behavior of bifurcation occurs over the range of multiple logistic systems as their fecundities or maximum rates of change increase.''<br />
::I don't understand this sentence at all.</font><br />
*<font color=dodgerblue><s>''But to read this diagram, do not think of the branching action as a continuous motion. Instead consider a single vertical line through the image; it captures exactly one''<br />
::I think you should get rid of the "But" and the semi-colon should be a colon.</s></font><br />
*<font color=dodgerblue><s>The last picture in this section is helpful but kind of giant - what do you think about hiding it?</s></font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:53, 9 June 2011 (UTC):<br />
*<s>Out of curiosity, ''are'' there any populations whose size is chaotic?</s><br />
</font><br />
<font color=purple><br />
**Planning to put this in "Why It's Interesting."<br />
</font><br />
<br />
===Logistic Map===<br />
Old comments: {{Hide|1=<br />
<s><font color=dodgerblue><br />
*(How) does the number between 0 and 1 relate to an actual population? If there's 400 zebras in some area, is there a way to connect that number with the logistic function?<br />
</font><br />
<br />
<font color=dodgerblue><br />
*Is the function for a generic population, or is it customizable to specific populations?<br />
</font><br />
</s><br />
<br />
<font color=dodgerblue><br />
*<s>I think this section could make the difference between the logistic equation and the logistic map clearer. What are their specific purposes and uses?</s><br />
</font><br />
<font color=purple><br />
**I removed the logistic equation section and spent more time talking about what actually makes up the logistic map -- is it clearer now?<br />
</font><br />
::<font color=dodgerblue>Yeah, I think it does make more sense this way.</font><br />
<br />
*<font color=red>xd 20:44, 12 June 2011 (UTC) regarding Kate's comments, the x values are not exactly the population per ce. it is actually the ratio between two periods which is actually pretty short. I think wikipedia has a good explanation.</font><br />
}}<br />
<br />
===Bifurcation and Chaos===<br />
<br />
Old comments: {{Hide|1=<br />
<font color=dodgerblue><br />
*<s>I know I had to look up "fecundity" - perhaps this is a good place to use a green bubble?</s><font color=purple> done.</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*<s>''While both the '''initial population size''' and the '''fecundity rate''' of that population are variables in the logistic map, the '''rate of change''' is more mathematically powerful…''<br />
:fecundity rate = rate of (population?) change??? Or rate of change is more powerful than either initial pop. and fecundity rate? unclear.</s><br />
</font><br />
<font color=purple><br />
**In conjunction with everything I added to the "Basic Description," is this clear?<br />
</font><br />
::<font color=dodgerblue>Yup, I think it's clear.</font><br />
<br />
<font color=dodgerblue><br />
*instead of telling me not to think of continuous motion, I would have found it more helpful to be told not to think of one single community. But the rest of the explanation in that paragraph was very clear.<br />
</font><br />
<font color=purple><br />
**I added this in, but didn't really integrate that view in -- is what I stuck in sufficient?<br />
</font><br />
::<font color=dodgerblue>Yeah, I think this is one of those "for me personally, this explanation would be a tiny bit better" type things, but the way you have it now isn't confusing.</font><br />
<br />
<font color=dodgerblue><br />
*<s>The second paragraph in this section is perhaps a bit long - can it be split anywhere?</s><font color=purple> done.</font><br />
</font><br />
<br />
*<font color=red>xd 20:46, 12 June 2011 (UTC) I think this section is pretty good already. With the picture, the explanation is very clear. As said before, you can have a little section on how matlab plotted those pictures.</font><br />
}}<br />
<br />
==A More Mathematical Explanation==<br />
<br />
===Deriving the Logistic Map===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:55, 1 July 2011 (UTC):<br />
*''exactly one time interval'' - this phrasing seemed odd to me, I think it was the contrast of "exactly" with some unspecified length of time, like how "He's exactly an unknown height tall" would be weird.</font><br />
**<font color=purple>I couldn't figure out a great way to fix this. I realize it's strange, but I don't know a graceful way to specify that the "exactly" modifies "one" and not "interval." (Grammatically, "one" is technically what "exactly" modifies here, but it does read ambiguously.)</font><br />
:::<font color=dodgerblue>Okey dokey. It's not a big deal, the sentence is still perfectly understandable. ([[User:Kderosier|Kate]] 20:14, 6 July 2011 (UTC))</font><br />
<br />
Old comments: {{Hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:53, 9 June 2011 (UTC):<br />
*<s>I know the section heading says it, but I still would have appreciated an initial sentence telling me that we were about to begin deriving the LM.</s><font color=purple> good point. done.</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*<s>''In this way, the overall rate of change, R, is higher when xn is lower and lower when xn is higher.''<br />
:Why do we want it to be higher when xn is lower & v.v.? How do we know that this specific way of changing the rate is accurate to what happens in nature? Something like R=r cos(xn) would meet the stated goal of providing an R that changes, so why is r(1-xn) better?</s><br />
</font><br />
<font color=purple><br />
**Along with everything else I've added and the extra sentence here, does this make more sense?<br />
</font><br />
::<font color=dodgerblue>Yup! The pond pictures helped address that very well up top, and then you referred back to it in the derivation.</font><br />
<br />
<font color=dodgerblue><br />
<s>*Re: Eq. 4 - I'd like to see an intermediate step, so I'm not trying to do all the differentiating in my head. Also, I'm having a hard time reading the bit in the denominator - is that an x-sub-D or an x-sub-0?</s><br />
</font><br />
<br />
<font color=dodgerblue><br />
*<s>At this point, I'm really feeling like I'd like to have a bit more background on the logistic equation and where it comes from.</s><br />
</font><br />
<font color=purple><br />
**Ok, I've just removed all mention of the logistic equation. Is the article clear without it?<br />
</font><br />
::<font color=dodgerblue>Yeah, I think so. Might wanna get the opinion of someone who knows more of the math, but I think it reads fine.</font><br />
}}<br />
<br />
===A Mathematical View of Bifurcation===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:55, 1 July 2011 (UTC):</font><br />
*<font color=dodgerblue>The web diagram explanation is ''much'' clearer, yay!</font><br />
*<font color=dodgerblue><s>I don't understand the unlabeled equation that I'd probably call equation eight and a half…</s></font><br />
<font color=red>xd 7/6 One typo "Earlier, we found that period-one fixed points exist in all logistic systems, whether on not they approach only one point." I fixed it for you. </font><br />
Old comments: {{Hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:04, 17 June 2011 (UTC): I think I'm understanding the web diagrams now, but I still have a couple questions:<br />
*I think I figured out what k is, but you never address it, although it shows up in the legends of your graphs.</font><br />
**<font color=purple>I've addressed it in the caption of the first image that uses it; is this sufficient, or should I talk about it in the text?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): I think the caption's good enough, that's where people will look if they're confused about the picture.</font><br />
<br />
*<s><font color=dodgerblue>It would probably be a good idea to mention which equation goes with the parabola and which goes with the straight line the first time you reference one of those graphs, even though the reader can probably figure it out.</font></s><br />
**<font color=purple>Done, for all.</font><br />
<br />
*<font color=dodgerblue>Be more explicit about how/why the web diagram verifies that that point is a fixed point. It's because it spirals in towards it, right? I think it would be clearer if you said that.</font><br />
**<font color=purple>I've attempted to do this. Did I succeed?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>It would also be clearer if you state why we need the web diagram - how come looking at the picture and noting the intersection of the line and the parabola isn't good enough to find the fixed point?</font><br />
**<font color=purple>The web diagrams show where the '''system''' goes, whereas systems of equations just show intersections -- the web diagrams just show that what I'm saying is true. Is it clear now that this is why I'm using them?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>I need more explanation about how you can have a fixed point but not converge to a single value, and more explicit explanation about how "the web diagram for r = 3.4 on the right" shows that.</font><br />
**<font color=purple>Done? I think I did this...</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>Are you sure Eq. 7 is correct? What does the un-subscripted x mean?</font><br />
**<font color=purple>I think I fixed the issues here. I showed where I got it.</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): I think it's good.</font><br />
<br />
*<font color=dodgerblue>The first time you point us to a graph with k=2 (right after Eq. 7), it'd be helpful to be explicit about which intersections we're supposed to be looking at. The first time I read through, I was looking at the intersections of the parabola and the 4th degree polynomial, instead of the 4th degree polynomial and the line. Also, I think it is unhelpful/confusing to have unlabeled parabolas drawn in in all of these pictures - either give it a k=1 label like you do in the second to last one on the right or don't graph it.</font><br />
**<font color=purple>Ok, I haven't actually labeled all the curves, but I explain in the captions what you're seeing. Is that sufficient?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>This sentence confused me:</font><br />
::''We can see by the graph that, while both x(n+1) = xn and x(n+2) = xn have solutions, the two solutions are equal, so the system does not generate any new values. ''<br />
:<font color=dodgerblue>This sentence confused me so much the first five or so times I read it. I think it would be clearer if you first pointed out that the curve for k=2 only intersects the line once, and ''then'' point out that this solution is the same as the one provided by k=1.</font><br />
**<font color=purple>I think I've made this more clear.</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>There are too many unlabeled lines in the graph at the end on the bottom left (with r=3.54). Also, I don't see how you get four period oscillations out of that picture. When I look at it, it looks like the red polynomial intersects the line in 7 places, which I thought would correspond to oscillation between seven values.</font><br />
**<font color=purple>Again, please let me know if I've clarified this sufficiently. I think I have...</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
<font color=dodgerblue>Two overall comments for this section:<br />
*<s>Referring to your pictures only by location is confusing, especially for those of us who often mix up right and left. It would be so much easier if they were labeled.</s></font><br />
**<font color=purple>Done.</font><br />
*<font color=dodgerblue>I still don't understand what the web diagrams add to our understanding here - why are they better than just looking at the intersections of the lines and the polynomials?</font><br />
**<font color=purple>Mentioned above, I think I've made the use of both diagram clearer.</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
<br />
*<font color=red>xd 20:51, 12 June 2011 (UTC) I don't quite get this part. You are not done with this section are you?</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:53, 9 June 2011 (UTC):<br />
*I still don't really get what's going on in the two pictures near where you introduce "fixed point" - where did the parabola and the line come from? What's different about what's going on in the two pictures?<br />
</font><br />
<br />
*<font color=red>xd 20:16, 22 June 2011 (UTC) In your fig 2, what does that red label "k-1" mean? In addition, why is the y label x_n+k instead of x_n+1?</font><br />
<br />
}}<br />
<br />
===Special Cases===<br />
<br />
Old comments: {{Hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:04, 17 June 2011 (UTC):</font><br />
*''The web diagram to the left should help illustrate why: no matter what x0 begins the system, the values inevitably move toward zero.''<br />
::<font color=dodgerblue>Neither the web diagram nor this sentence helped illustrate that to me. Where is x0 in the web diagram? What parabola is being graphed there? Where is the zero it's moving towards? How do I know it's for every x0 even though only one blue line is graphed? What ''is'' x0 and why am I allowed to pick different values for it? I am exaggerating my confusion a little, but I know that you can explain it much better than this.</font><br />
**<font color=purple>I think the animation helps here.</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:34, 30 June 2011 (UTC): Animation is so helpful.</font><br />
*<font color=dodgerblue>None of the equations under 0<r<1 make any sense to me. Where do they come from? What does the random bar in Eq. 8 mean? I assume Eq. 8 came from the top of the page somewhere, but I don't really remember what it is. And how on earth did you get from the second equation in this section to the third?</font><br />
**<font color=purple>I put in something more like a full proof here. Does it make sense?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:34, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
}}<br />
<br />
==Why It's Interesting==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:55, 1 July 2011 (UTC):<br />
*This might be a personal preference, but I've been hiding applets, because the way they flicker when I scroll drives me crazy.</font><br />
**<font color=purple>Actually, that drives me crazy, too, but I'm leaving this one unhidden because it's at the bottom of the page, and so there's not much space in which the reader is scrolling. And it lets me direct the reader to the applet's actual position.</font><br />
:::<font color=dodgerblue>Reasonable. ([[User:Kderosier|Kate]] 20:15, 6 July 2011 (UTC)) </font><br />
*<font color=dodgerblue><s>The bit about chaos in nature was quite interesting. I think it might be a good idea to link to it from the top of the basic description - people may be interested in the pictures of fish in ponds and also the biology at the bottom but not the math in the middle.</s></font><br />
*<font color=dodgerblue><s>Typo: ''no matter how fari it is from x0,''</s></font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Logistic_Bifurcation&diff=25640Talk:Logistic Bifurcation2011-07-16T01:42:07Z<p>Rebecca: /* Response to Checklist */</p>
<hr />
<div>=Response to Checklist=<br />
<font color=purple>17:00, 7/7/11<br />
<font color=darkred> My comments are up [[User:AnnaP|AnnaP]] 7/10 </font><br />
<br />
<font color=darkred>'''Messages to the Future'''<br />
It might be kind of fun to include a hidden section at the end about how to plot the logistic map--maybe put in a request for a computer science oriented person to explain how to do it? You can also take a look at my mathematica code to plot it--you can download that by clicking [[http://www.sccs.swarthmore.edu/users/09/anna09/mathematica/LogMap.nb here]]</font><br />
<br />
'''References and Footnotes'''<br />
<br />
All of the images are cited, if you click on them. Most of them were created by me, anyway. I emailed the creators of the applet at the bottom of the page to get their permission, and it's very clearly cited on the page. No footnotes were necessary for the information on this page.<br />
<br />
'''Context'''<br />
<br />
The basic description is very clear about how logistic systems connect to biology and populations. It also shows how various oscillations would manifest, graphically in a population in a way that is easy to understand. "Why it's interesting" includes further discussion of real-world use and an interactive applet demonstrating self-similarity.<br />
<br />
'''Quality of Prose'''<br />
<br />
Because of the length of the page, I carefully used "signpost" sentences and paragraphs throughout the article, along with clear logical links from one paragraph to the next. Each section is clear about its purpose and direction. All of the more mathematical section is pretty heavy, and it's in the only order that makes sense, so I can't move the detailed math any further down.<br />
:*<font color=darkred> your first sentence "A section of a bifurcation diagram showing how logistic systems change as fecundity changes." might scare away readers by using "bifurcation" and "fecundity" Perhaps use a slightly less accurate, more generic first sentence? <br />
:*You don't need the word "recursively" here: "or apply it over and over recursively" Again, it's a word that will confuse some readers </font><br />
<br />
'''Integration of Images'''<br />
<br />
The images are meticulously numbered, referenced in the text, linked between image and text, and explained in both the text and the captions.<br />
<br />
'''Connections'''<br />
<br />
This page links extensively to chaos and iterations, including a thorough discussion of how iteration can be applied to this topic. The idea of fractals is also discussed.<br />
<br />
'''Examples'''<br />
<br />
The logistic map is derived with clear explanations of steps. The mathematical discussion of bifurcation uses extensive examples in multiple forms -- diagrams, graphs, and analytical discussions. All new ideas are defined, discussed, or linked out to helper pages.<br />
<br />
'''Accuracy and Precision'''<br />
<br />
All terms are defined in text, bubbled out, or linked out. Mathematical ideas are expressed both in equations and pictorially, where possible. In the mathematical bifurcation section, because it is so long, great pains are taken to keep the reader on track and return consistently to the main ideas.<br />
<font color=darkred><br />
*The paragraph that begins with this sentence: "Earlier, we found that period-one fixed points exist in all logistic systems, whether or not they approach only one point. Now, we will see that the condition x(n+2) = xn also has a solution for logistic systems with r < 3. " Could use a bit of work. It'd be better to explain that a fixed point will certainly come back to itself when you iterate it. If you have f(x)=x, then f(f(x))=f(x)=x. So anything that is a solution to the first equation is also a solution to f(f(x))=x. Similarly, all two two-cycles will show up when you look for solutions to the period four equation f(f(f(f(x))))=x. An explanation in those terms in place of, or addition to, what you already have will make that section make more sense. </font> <br />
<font color=slateblue>[[User:Rebecca|Rebecca]] 01:42, 16 July 2011 (UTC) I don't know if you can just say "(hence the name)" when you're talking about bifurcation. I had to look up the fact that "furcate" is to divide into branches. I think mentioning that in the parentheses would be helpful. My vocabulary is pretty weak, but i think other people might have the same issue. </font color><br />
<br />
'''Layout'''<br />
I made the paragraphs as short as I could, put in breaks to make sure pictures didn't overlap with other sections, and tried to place image location to create the least possible interference with readability at any window size. Definitions are generally bubbled or linked out, with some in boldface.<br />
</font><br />
*<font color=darkred> Why don't you add an extra break between each paragraph in your basic description? That will help break up the text a bit better.<br />
*The paragraphs between images 3 and 4 and 5 and 6 could also use some extra spaces. <br />
*Image 5 is a bit distracting where it is, since you talk about it much lower than the image itself. Try to move it around.<br />
*Can you make the blurb on web diagrams it's own subsection, or make the phrase Web Diagrams at the beginning of that area bold to stand out? </font><br />
<br />
=General Comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 14:58, 1 July 2011 (UTC): Much clearer than before. Be careful with your "So"s - you begin a ''lot'' of sentences with "So". None of them are things I would object to individually, but the fact that they stood out to me probably means you're overusing them.</font><br />
<br />
*<font color=darkred>[[User:AnnaP|AnnaP]] 6/16 - Diana, have you seen the [[Iterated Functions]] Page? That page uses the logistic map for examples, and you might find that it's useful to link to that page (or lift some of the images) for examples.</font><br />
**<font color=purple> I had already linked to this, bit it was pretty subtle, so I've added it in more prominently.</font><br />
<br />
=Section-specific Comments=<br />
<br />
==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:55, 1 July 2011 (UTC):<br />
*<s>Typo: ''into multiple values. '''i'''n the case of logistic bifurcation…''</s></font><br />
*<font color=dodgerblue>''The branching behavior of bifurcation occurs over the range of multiple logistic systems as their fecundities or maximum rates of change increase.''<br />
::I don't understand this sentence at all.</font><br />
*<font color=dodgerblue><s>''But to read this diagram, do not think of the branching action as a continuous motion. Instead consider a single vertical line through the image; it captures exactly one''<br />
::I think you should get rid of the "But" and the semi-colon should be a colon.</s></font><br />
*<font color=dodgerblue><s>The last picture in this section is helpful but kind of giant - what do you think about hiding it?</s></font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:53, 9 June 2011 (UTC):<br />
*<s>Out of curiosity, ''are'' there any populations whose size is chaotic?</s><br />
</font><br />
<font color=purple><br />
**Planning to put this in "Why It's Interesting."<br />
</font><br />
<br />
===Logistic Map===<br />
Old comments: {{Hide|1=<br />
<s><font color=dodgerblue><br />
*(How) does the number between 0 and 1 relate to an actual population? If there's 400 zebras in some area, is there a way to connect that number with the logistic function?<br />
</font><br />
<br />
<font color=dodgerblue><br />
*Is the function for a generic population, or is it customizable to specific populations?<br />
</font><br />
</s><br />
<br />
<font color=dodgerblue><br />
*<s>I think this section could make the difference between the logistic equation and the logistic map clearer. What are their specific purposes and uses?</s><br />
</font><br />
<font color=purple><br />
**I removed the logistic equation section and spent more time talking about what actually makes up the logistic map -- is it clearer now?<br />
</font><br />
::<font color=dodgerblue>Yeah, I think it does make more sense this way.</font><br />
<br />
*<font color=red>xd 20:44, 12 June 2011 (UTC) regarding Kate's comments, the x values are not exactly the population per ce. it is actually the ratio between two periods which is actually pretty short. I think wikipedia has a good explanation.</font><br />
}}<br />
<br />
===Bifurcation and Chaos===<br />
<br />
Old comments: {{Hide|1=<br />
<font color=dodgerblue><br />
*<s>I know I had to look up "fecundity" - perhaps this is a good place to use a green bubble?</s><font color=purple> done.</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*<s>''While both the '''initial population size''' and the '''fecundity rate''' of that population are variables in the logistic map, the '''rate of change''' is more mathematically powerful…''<br />
:fecundity rate = rate of (population?) change??? Or rate of change is more powerful than either initial pop. and fecundity rate? unclear.</s><br />
</font><br />
<font color=purple><br />
**In conjunction with everything I added to the "Basic Description," is this clear?<br />
</font><br />
::<font color=dodgerblue>Yup, I think it's clear.</font><br />
<br />
<font color=dodgerblue><br />
*instead of telling me not to think of continuous motion, I would have found it more helpful to be told not to think of one single community. But the rest of the explanation in that paragraph was very clear.<br />
</font><br />
<font color=purple><br />
**I added this in, but didn't really integrate that view in -- is what I stuck in sufficient?<br />
</font><br />
::<font color=dodgerblue>Yeah, I think this is one of those "for me personally, this explanation would be a tiny bit better" type things, but the way you have it now isn't confusing.</font><br />
<br />
<font color=dodgerblue><br />
*<s>The second paragraph in this section is perhaps a bit long - can it be split anywhere?</s><font color=purple> done.</font><br />
</font><br />
<br />
*<font color=red>xd 20:46, 12 June 2011 (UTC) I think this section is pretty good already. With the picture, the explanation is very clear. As said before, you can have a little section on how matlab plotted those pictures.</font><br />
}}<br />
<br />
==A More Mathematical Explanation==<br />
<br />
===Deriving the Logistic Map===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:55, 1 July 2011 (UTC):<br />
*''exactly one time interval'' - this phrasing seemed odd to me, I think it was the contrast of "exactly" with some unspecified length of time, like how "He's exactly an unknown height tall" would be weird.</font><br />
**<font color=purple>I couldn't figure out a great way to fix this. I realize it's strange, but I don't know a graceful way to specify that the "exactly" modifies "one" and not "interval." (Grammatically, "one" is technically what "exactly" modifies here, but it does read ambiguously.)</font><br />
:::<font color=dodgerblue>Okey dokey. It's not a big deal, the sentence is still perfectly understandable. ([[User:Kderosier|Kate]] 20:14, 6 July 2011 (UTC))</font><br />
<br />
Old comments: {{Hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:53, 9 June 2011 (UTC):<br />
*<s>I know the section heading says it, but I still would have appreciated an initial sentence telling me that we were about to begin deriving the LM.</s><font color=purple> good point. done.</font><br />
</font><br />
<br />
<font color=dodgerblue><br />
*<s>''In this way, the overall rate of change, R, is higher when xn is lower and lower when xn is higher.''<br />
:Why do we want it to be higher when xn is lower & v.v.? How do we know that this specific way of changing the rate is accurate to what happens in nature? Something like R=r cos(xn) would meet the stated goal of providing an R that changes, so why is r(1-xn) better?</s><br />
</font><br />
<font color=purple><br />
**Along with everything else I've added and the extra sentence here, does this make more sense?<br />
</font><br />
::<font color=dodgerblue>Yup! The pond pictures helped address that very well up top, and then you referred back to it in the derivation.</font><br />
<br />
<font color=dodgerblue><br />
<s>*Re: Eq. 4 - I'd like to see an intermediate step, so I'm not trying to do all the differentiating in my head. Also, I'm having a hard time reading the bit in the denominator - is that an x-sub-D or an x-sub-0?</s><br />
</font><br />
<br />
<font color=dodgerblue><br />
*<s>At this point, I'm really feeling like I'd like to have a bit more background on the logistic equation and where it comes from.</s><br />
</font><br />
<font color=purple><br />
**Ok, I've just removed all mention of the logistic equation. Is the article clear without it?<br />
</font><br />
::<font color=dodgerblue>Yeah, I think so. Might wanna get the opinion of someone who knows more of the math, but I think it reads fine.</font><br />
}}<br />
<br />
===A Mathematical View of Bifurcation===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:55, 1 July 2011 (UTC):</font><br />
*<font color=dodgerblue>The web diagram explanation is ''much'' clearer, yay!</font><br />
*<font color=dodgerblue><s>I don't understand the unlabeled equation that I'd probably call equation eight and a half…</s></font><br />
<font color=red>xd 7/6 One typo "Earlier, we found that period-one fixed points exist in all logistic systems, whether on not they approach only one point." I fixed it for you. </font><br />
Old comments: {{Hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:04, 17 June 2011 (UTC): I think I'm understanding the web diagrams now, but I still have a couple questions:<br />
*I think I figured out what k is, but you never address it, although it shows up in the legends of your graphs.</font><br />
**<font color=purple>I've addressed it in the caption of the first image that uses it; is this sufficient, or should I talk about it in the text?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): I think the caption's good enough, that's where people will look if they're confused about the picture.</font><br />
<br />
*<s><font color=dodgerblue>It would probably be a good idea to mention which equation goes with the parabola and which goes with the straight line the first time you reference one of those graphs, even though the reader can probably figure it out.</font></s><br />
**<font color=purple>Done, for all.</font><br />
<br />
*<font color=dodgerblue>Be more explicit about how/why the web diagram verifies that that point is a fixed point. It's because it spirals in towards it, right? I think it would be clearer if you said that.</font><br />
**<font color=purple>I've attempted to do this. Did I succeed?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>It would also be clearer if you state why we need the web diagram - how come looking at the picture and noting the intersection of the line and the parabola isn't good enough to find the fixed point?</font><br />
**<font color=purple>The web diagrams show where the '''system''' goes, whereas systems of equations just show intersections -- the web diagrams just show that what I'm saying is true. Is it clear now that this is why I'm using them?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>I need more explanation about how you can have a fixed point but not converge to a single value, and more explicit explanation about how "the web diagram for r = 3.4 on the right" shows that.</font><br />
**<font color=purple>Done? I think I did this...</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>Are you sure Eq. 7 is correct? What does the un-subscripted x mean?</font><br />
**<font color=purple>I think I fixed the issues here. I showed where I got it.</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): I think it's good.</font><br />
<br />
*<font color=dodgerblue>The first time you point us to a graph with k=2 (right after Eq. 7), it'd be helpful to be explicit about which intersections we're supposed to be looking at. The first time I read through, I was looking at the intersections of the parabola and the 4th degree polynomial, instead of the 4th degree polynomial and the line. Also, I think it is unhelpful/confusing to have unlabeled parabolas drawn in in all of these pictures - either give it a k=1 label like you do in the second to last one on the right or don't graph it.</font><br />
**<font color=purple>Ok, I haven't actually labeled all the curves, but I explain in the captions what you're seeing. Is that sufficient?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>This sentence confused me:</font><br />
::''We can see by the graph that, while both x(n+1) = xn and x(n+2) = xn have solutions, the two solutions are equal, so the system does not generate any new values. ''<br />
:<font color=dodgerblue>This sentence confused me so much the first five or so times I read it. I think it would be clearer if you first pointed out that the curve for k=2 only intersects the line once, and ''then'' point out that this solution is the same as the one provided by k=1.</font><br />
**<font color=purple>I think I've made this more clear.</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
*<font color=dodgerblue>There are too many unlabeled lines in the graph at the end on the bottom left (with r=3.54). Also, I don't see how you get four period oscillations out of that picture. When I look at it, it looks like the red polynomial intersects the line in 7 places, which I thought would correspond to oscillation between seven values.</font><br />
**<font color=purple>Again, please let me know if I've clarified this sufficiently. I think I have...</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
<font color=dodgerblue>Two overall comments for this section:<br />
*<s>Referring to your pictures only by location is confusing, especially for those of us who often mix up right and left. It would be so much easier if they were labeled.</s></font><br />
**<font color=purple>Done.</font><br />
*<font color=dodgerblue>I still don't understand what the web diagrams add to our understanding here - why are they better than just looking at the intersections of the lines and the polynomials?</font><br />
**<font color=purple>Mentioned above, I think I've made the use of both diagram clearer.</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:31, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
<br />
<br />
*<font color=red>xd 20:51, 12 June 2011 (UTC) I don't quite get this part. You are not done with this section are you?</font><br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:53, 9 June 2011 (UTC):<br />
*I still don't really get what's going on in the two pictures near where you introduce "fixed point" - where did the parabola and the line come from? What's different about what's going on in the two pictures?<br />
</font><br />
<br />
*<font color=red>xd 20:16, 22 June 2011 (UTC) In your fig 2, what does that red label "k-1" mean? In addition, why is the y label x_n+k instead of x_n+1?</font><br />
<br />
}}<br />
<br />
===Special Cases===<br />
<br />
Old comments: {{Hide|1=<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:04, 17 June 2011 (UTC):</font><br />
*''The web diagram to the left should help illustrate why: no matter what x0 begins the system, the values inevitably move toward zero.''<br />
::<font color=dodgerblue>Neither the web diagram nor this sentence helped illustrate that to me. Where is x0 in the web diagram? What parabola is being graphed there? Where is the zero it's moving towards? How do I know it's for every x0 even though only one blue line is graphed? What ''is'' x0 and why am I allowed to pick different values for it? I am exaggerating my confusion a little, but I know that you can explain it much better than this.</font><br />
**<font color=purple>I think the animation helps here.</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:34, 30 June 2011 (UTC): Animation is so helpful.</font><br />
*<font color=dodgerblue>None of the equations under 0<r<1 make any sense to me. Where do they come from? What does the random bar in Eq. 8 mean? I assume Eq. 8 came from the top of the page somewhere, but I don't really remember what it is. And how on earth did you get from the second equation in this section to the third?</font><br />
**<font color=purple>I put in something more like a full proof here. Does it make sense?</font><br />
:::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:34, 30 June 2011 (UTC): about to do another read-through for clarity, if I don't leave a new comment about this, assume it's ok.</font><br />
}}<br />
<br />
==Why It's Interesting==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 14:55, 1 July 2011 (UTC):<br />
*This might be a personal preference, but I've been hiding applets, because the way they flicker when I scroll drives me crazy.</font><br />
**<font color=purple>Actually, that drives me crazy, too, but I'm leaving this one unhidden because it's at the bottom of the page, and so there's not much space in which the reader is scrolling. And it lets me direct the reader to the applet's actual position.</font><br />
:::<font color=dodgerblue>Reasonable. ([[User:Kderosier|Kate]] 20:15, 6 July 2011 (UTC)) </font><br />
*<font color=dodgerblue><s>The bit about chaos in nature was quite interesting. I think it might be a good idea to link to it from the top of the basic description - people may be interested in the pictures of fish in ponds and also the biology at the bottom but not the math in the middle.</s></font><br />
*<font color=dodgerblue><s>Typo: ''no matter how fari it is from x0,''</s></font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=S11&diff=25639S112011-07-16T01:23:37Z<p>Rebecca: /* Leah's Projects */</p>
<hr />
<div>__TOC__<br />
<br />
== Announcements ==<br />
For public-type help questions, see [[Help:Contents|Help]]. For Swat-specific ones, see [[Swarthmore summer research orientation]].<br />
<br />
<b>Remember to keep your projects sections short and up to date; only the last week of status changes should be mentioned. [[User:Smaurer1|Smaurer1]]</b><br />
<br />
===Group Discussion Questions===<br />
<br />
* [[Topics for conversations through Skype with RPI, SB, and/or Drexel]] Started 6/29.<br />
* [[Who are we writing for?]] Started 6/29.<br />
* [[Possibly expanding student Math Image roles]], to be addressed 7/6.<br />
<br />
===Questions:===<br />
*Things that are listed as Helper Pages but use the Image Page template<br />
:We need to decide whether these pages should be on the Helper Page template, the Image Page template, or both: {{Hide|1=<br />
:*[[Change of Coordinate Systems]] - Image template only; image template live<br />
:*[[Conic Section]] - both templates; image template not live<br />
:*[[Differentiability]] - both templates; image template not live<br />
:*[[Dot Product]] - Image template only; image template not live<br />
:*[[Gradients and Directional Derivatives]] - Image template only; image template not live<br />
:*[[Hyperbolic Geometry]] - Image template only; image template not live<br />
:*[[Inversion]] - Image template only; image template not live<br />
:*[[Iterated Functions]] - Image template only; image template not live<br />
:*[[Parametric Equations]] - Image template only; image template live<br />
:*[[Taylor Series]] - Image template only; image template not live<br />
:*[[Volume of Revolution]] - Image template only; image template live<br />
<br />
:<font color=dodgerblue>''(List complied by [[User:Kderosier|Kate]], June 16)''</font><br />
}}<br />
<br />
<br />
Older questions: {{Hide|1=<br />
*Harrison's question about text being cut off on Cross-cap: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 14:16, 8 June 2011 (UTC)<br />
**The text in MME on the [[Cross-cap]] page is getting truncated when viewed through edit with form, but still appears on the page.<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 00:49, 14 June 2011 (UTC): When I've encountered this problem previously, it's been because a set of double curly brackets wasn't closed.</font><br />
}}<br />
<br />
*Harrison's question about creating a list of not-yet-existent Helper Pages: {{Hide|1=<br />
Harrison, 5/26/11:<br />
:*<s>We need a list of empty pages: Penrose Tiles is only linked to one, now two, pages. Empty pages like this could well fade into obscurity.</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:09, 7 June 2011 (UTC): Such a list has been created. See [[Existing_Pages_Needing_Work#Empty_.28but_linked_to.29_Pages|here]].</font><br />
}}<br />
<br />
*Spam conversation: {{Hide|1=<br />
<font color=dodgerblue><br />
*[[User:Kderosier|Kate]] 14:38, 27 May 2011 (UTC): '''We have some new users who are creating a bunch of pages with links to illegally download or watch movies.''' At first, we though it might be someone from Sweet Briar practicing wiki-syntax, but now it's just starting to look like spam:<br />
**[[Watch_Sniper:_Reloaded_film_in_hd|This is the type of page I'm talking about]]<br />
**[[Special:Contributions/Calrivenick|List of pages created by Calrivenick]]<br />
**[[Special:Contributions/Cadedesi|List of pages created by Cadedesi]]<br />
</font><br />
:Let's talk about what to do this afternoon. [[User:Gene|Gene]] 15:19, 27 May 2011 (UTC)<br />
:<font color=dodgerblue>This problem has continued over the weekend. Someone spammed the talk page for Fun Topology with comments about buying Cialis and stuff. They also posted a lot more movie download pages under the Cadedesi username. I'm going to go through and delete again.</font><br />
:<font color=dodgerblue>The spam comments on Fun Topology were coming from this computer's IP address. </font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 14:34, 6 June 2011 (UTC): Haven't seen any more spam activity for a few days. I assume some computer people have handled the issue? I'm going to hide this conversation so that it's not taking up space on S11.</font><br />
}}<br />
<br />
*Citations/footnotes conversation: {{Hide|1=<br />
:I spent a really long time wandering around MediaWiki and Wikipedia this morning trying to figure out how to do footnotes/citations the way I wanted to - now that I know how, should I add instructions to one of the many help mages on Math Images? If so, which page? (Kate, 5/17)<br />
<br />
:<font color=red> Answer: put it here at [[Help:Wiki_Tricks|Wiki Tricks]] (XD, 5/17) </font><br />
<br />
:[[User:Smaurer1|Smaurer1]] 19:43, 17 May 2011 (UTC) Well, it's not clear that webarticles should have footnotes, although Wikipedia does. In text references may be better. This is surely something we should discuss as a group, and find out what last year's group decided, if they did. If there are footnotes, there has got to be a way to get back seamlessly to where you were before you jumped to the footnote.<br />
<br />
:Also, as for citations, we should be uniform in their format.<br />
<br />
:Finally, you can use 4 tildes to put your username and time stamp on your comments, and 3 tildes for just your username. <br />
<br />
:<font color=dodgerblue>Well, I wasn't doing comment-y type footnotes, I just wanted specific sentences to link to items in my References section. I think that format is better than full intext-citations, because it brings you to the source if that's what you're interested in, but it takes up less space if you're not. The references template we have comes equipped with little links to jump you back up, too- if you look at the [[Quipu#References|Quipu]] page, you can see that it lists each of the sections that reference is linked from, and those links bring you to the reference in that section. All in all, I think it's a clear and intuitive way to do references for both the writer and the reader (although, like most things, it doesn't play well with our hidden sections), and I'm going to go ahead and put the instructions up in WikiTricks. -[[User:Kderosier|Kate]] </font><br />
<br />
{{Hide|1=<br />
*What the help pages say now:<br />
**[[Tour_the_Math_Images_Project#Anatomy_of_a_page|The Tour page's "Anatomy of a page" section]]<br />
**[[Checklist_for_writing_pages#References_and_footnotes|The "References and footnotes" section on the checklist for writing pages]]<br />
*The way to do Wikipedia-like references:<br />
**[[Wiki_Tricks#How_to_do_Citations|Wiki Tricks - Citations section]]<br />
}}<br />
<br />
}}<br />
<br />
*Invisible Comments conversation: {{Hide|1= One of you asked "How do you put invisible comments in the source code?"<br />
<br />
:Answer: Same way you do in html, like this <nowiki><br />
:<!-- hidden stuff --><br />
:</nowiki><br />
:However, if you want to make comments about an article for its author, the comments are more likely to be seen if you either<br />
:* put it in the discussion page, or<br />
:* if it is important to put it right by the material commented on, put it in the article in color with your username and time stamp included.<br />
<br />
:Hidden comments in the source code are likely to be overlooked, except perhaps if they are written by the author him/herself, as a note for further development.<br />
}}<br />
}}<br />
<br />
== Current Individual Projects ==<br />
<br />
===Steve M (aka Prof Maurer)'s Role===<br />
{{Hide|1=<br />
My role is 2-fold:<br />
<br />
<ol><br />
<li> Come see me to sound me out (if you wish) on the mathematical appropriateness of an idea for a page, or for possible references.<br />
<br />
<li> Once you have a reasonable amount written, and want feedback on the quality and correctness of the mathematical exposition, ask me to look it over and then we will have a conference. (Abram and the oldies are as good as I am at discussion general organization and clarity issues.) <br />
</ol><br />
<br />
We have agreed to put a record on this S11 page of what we are doing and what help we want from others, but in addition tell me in person or by email if you want to conference with me.<br />
}}<br />
<br />
===Harrison's Projects===<br />
<br />
[[Harrison's detritus]]<br />
<br />
*[[User:Htasoff|Htasoff]] 23:44, 13 July 2011 (UTC) Pages will be submitted for final review in 1 - 3 days. A few, final comments are welcome. Real Projective Plane is still in the works, though.<br />
<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 18:19, 14 July 2011 (UTC): Hey Harrison, do you know if that one picture in inverse trig that you got from somewhere on the internet is a picture we can use? Can you check please?</font><br />
<br />
===Richard's Projects===<br />
<br />
<br />
<font color=orangered> <br />
<br />
This weekend, I'll be reading pages to give feedback: [[Steiner's Chain]] [[Snell's Law]] [[Perko pair knots]] [[Pigeonhole Principle]] and an [[RPI11|RPI]] page<br />
<br />
:<font color=salmon>Hey Richard, thank you for leaving comments on pigeonhole principle. I've made some changes and left my ideas about the arrangement. Could you go through my page once again? I'd really appreciate it! [[User:PhoebeJiang|Phoebe]] 22:08, 14 July 2011 (UTC)</font><br />
<br />
*[[Ambiguous Case]]<br />
:*This page is the one that everyone should follow for feedback!<br />
:*Looking for final readthrough before it goes up for review! Then the lesson!!!![[User:Rscott3|Richard]] 7/14 </font color><br />
<br />
:APPLET INFO:[[User:Alimurreza|Alimurreza]] 02:53, 6 July 2011 (UTC)I am working on your applet. Check this out here @([http://mathforum.org/mathimages/index.php/DU11 Reza's work]).<br />
:APPLET UPDATE:[[User:Alimurreza|Alimurreza]] 02:41, 15 July 2011 (UTC)I am done with Ambiguous Case applet. Please, check the applet. Feel free to send me any feedback or change-request.<br />
:{{Hide|1=<br />
<br />
What i want mine to look like, but http://www.mccsc.edu/~aterwill/ambiguouscaseapplet/Ambiguous_Case_applet.html doesn't show the completed triangles.<br />
<br />
I like how this one shows the completed triangles<br />
http://www.mnwest.edu/fileadmin/static/website/dmatthews/Geogebra/AmbiguousCase01.html<br />
<br />
}}<br />
<br />
<br />
<br />
'''Completed Pages'''<br />
<br />
*[[Law of cosines]]<font color=orangered> [[User:Rscott3|Richard]] 6/23</font><br />
<br />
*[[Law of Sines]] [[User:AnnaP|AnnaP]] 7/7<br />
<br />
*[[Solving Triangles]] 7/12<br />
<br />
:Other ideas: {{Hide|1=<br />
*inscribed angles?<br />
<br />
*Normal Distribution?<br />
<br />
*Birthday Paradox?<br />
}}<br />
<br />
===Dayo's Projects===<br />
Current projects<br />
*[[Inscribed figures]] : there's a [[Compass & Straightedge Construction and the Impossible Constructions]] page, but I think that inscribed figures deserves its' own page. What do others think? <br />
::<font color=slateblue> [[User:Rebecca|Rebecca]] 01:07, 9 July 2011 (UTC) I left comments on the discussion page. </font color><br />
<br />
Future Projects: {{Hide|1=<br />
*[[Mathematics in architecture]]:make changes akin to [[Math for Computer Graphics and Computer Vision]], including:<br />
<br />
::*[[Cross sections]]: calculus application page, including examples of Tokyo international Forum, Suransuns Bridge, and other structures which could be thought of and put together easily in terms of their cross sections <br />
::*[[Torus]] edits, additions concerning the Torus in construction and architecture<br />
::*[[Domes]]:conic sections, arches, parabolas<br />
::*[[The Henderson Waves Bridge]]: sinusoids in architecture, parametric design<br />
::*[[Catenary]]: More real world examples: namely bridges<br />
::*[[Bridge of Peace]]: The equation(s) used to generate the surface, possibly words from the architect, very new, may be hard to get concrete technical information <br />
::*[[Kurilpa Bridge]]: Everyone have a look at the image and tell me what kind of actual subjects you could find in it, namely in the cables and tubes.<br />
::*Teaching Materials(6/30): ''growing up with science: projects'' could be the sort of activities we're looking for. I used these with a class, and think people should look at them.<br />
<br />
<br />
<br />
<br />
}}<br />
<br />
on hold: <br />
*[[Parametric Equations]]: integrating Xingda's page from [[S10]] into page.<br />
<br />
===Diana's Projects===<br />
<br />
====Current====<br />
*[[Logistic Bifurcation]]<br />
<br />
:<font color=darkred> I've put up comments. There are a few places that could use some work. [[User:AnnaP|AnnaP]] 7/10 </font> <br />
<br />
*[[Markus-Lyapunov Fractals]]<br />
:<font color=darkred> Approved [[User:AnnaP|AnnaP]] 7/14 </font><br />
<br />
====Ideas for later projects====<br />
{{Hide|1=<br />
*Chirikov-Taylor Maps<br />
**This seems like a natural extension of the Markus-Lyapunov Fractals page, but maybe the math involved in the two is too similar?<br />
*This aspect of pendular motion:<br />
**[[http://www.youtube.com/watch?v=yVkdfJ9PkRQ&feature=player_embedded|Varied-Length Pendulums]]<br />
**I'm not sure how or whether to use this -- does a ''moving'' image count as a "math image"? -- But it's incredible, and I'd love to explore it.<br />
*Kuen Surface<br />
**It's just really cool.<br />
}}<br />
<br />
===Kate's Projects===<br />
*[[User:Kderosier#Applet_Testing|Java Applets]]<br />
<br />
*[[Anne Burns' Mathscapes]] (Scrapped out of [[Mountains In Spring|three]] [[Mathscape|other]] [[Fractal Scene I|pages]]):<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 14:21, 14 July 2011 (UTC): Responded to Chris' comments. Feedback from others would be appreciated.</font><br />
<br />
*[[Perko pair knots]]:<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 21:00, 15 July 2011 (UTC): Have several changes I'm planning to make in response to verbal feedback from Abram, it'd be great if everyone else could hold off for a few days.</font><br />
<br />
*Finished pages: {{Hide|1=<br />
*[[Critical Points]]:<br />
:<font color=darkred> Approved, but I did have one note on whether or not you intended to add something. It's fine as is, but I wanted to put up a suggestion. [[User:AnnaP|AnnaP]] 16:24, 15 July 2011 (UTC) </font><br />
<br />
:*[[Summation Notation]]:<br />
::<font color=darkred> Approved [[User:AnnaP|AnnaP]] 16:24, 15 July 2011 (UTC) </font><br />
<br />
:*[[Bases]]:<br />
:: <font color=dodgerblue>[[User:Kderosier|Kate]] 17:31, 11 July 2011 (UTC): Changed things in response to Chris' comments.</font><br />
<br />
:* [[Quipu]]:<br />
::<font color=darkred> Put up as ready for the public 6/30 [[User:AnnaP|AnnaP]] </font><br />
<br />
:* [[Basic Trigonometric Functions]]:<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 18:11, 30 June 2011 (UTC): Changed the the things that were bolded.</font><br />
<br />
<br />
}}<br />
<br />
<br />
<font color=red>[[User:donko14|Anna]] Hey Kate-Thank you for all of your comments on my [[Steiner's Chain]] page, I really appreciate all of what you suggested, especially with this being my very first page. Your comments are extremely helpful not only in adjusting the content on this page, but as well as with how to construct the other pages I'm working on currently. THANKS!!</font><br />
::<font color=dodgerblue>np, glad you found them helpful! :) -[[User:Kderosier|Kate]] 14:21, 14 July 2011 (UTC)</font><br />
<br />
===Leah's Projects===<br />
*[[Bedsheet Problem]]<br />
not sure what to do with this page. <br />
<br />
*[[Boy's Surface]] <br />
WIP<br />
<br />
*[[Snell's Law]] feedback page<br />
::Need comments. Also, waiting on the final applet by Reza. 7/15<br />
::<font color=slateblue> I added a few comments and responded to old ones on the discussion page </font color><br />
<br />
*[[Witch of Agnesi]]<br />
up for final review. [[User:Ljeanlo1|Ljeanlo1]] 18:43, 15 July 2011 (UTC)<br />
<br />
*[[Dot Product]] <font color=darkred> Approved, 7/14 </font><br />
<br />
*[[Vector]] <font color=darkred> Approved, 7/10 </font><br />
<br />
==Requests to S10 Students==<br />
<br />
<br />
*<s>Can XD do a demo for MATLAB?</s> Done - [[Demo of MATLAB using the example of Bifurcation]]<br />
<br />
==Useful Links==<br />
[[S10]]<br />
<br />
[[SB11]]<br />
<br />
[[RPI11]]<br />
<br />
[[DU11]]<br />
<br />
[[Pages Ready for Final Review]]<br />
<br />
[[Feedback Requests]]<br />
<br />
[[Sample discussion page]]<br />
<br />
[[Math Tools Requests]] ''This page is a place where students whose primary focus is writing pages can post requests for applets, animations, and new images that they'd like to see the computer science students create.''<br />
<br />
[[Page Building Help]]<br />
<br />
[[Help:Wiki Tricks|Wiki Tricks]]<br />
<br />
[[From a Bunch of Old Timers]]<br />
<br />
[[List of summer 2010 pages]]<br />
<br />
http://en.wikipedia.org/wiki/Help:Displaying_a_formula<br />
<br />
[[PartnerHome]]<br />
<br />
[[Existing Pages Needing Work]]<br />
<br />
[[Site programming questions]]<br />
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== Current Group Projects ==</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Snell%27s_Law&diff=25638Talk:Snell's Law2011-07-16T01:19:29Z<p>Rebecca: /* Deriving Snell With Fermat */</p>
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<div>=General Comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:27, 6 July 2011 (UTC): Ok, so I took physics in high school, but it was a terrible class and I barely understood any of it, so I thought I'd give you some feedback from the perspective of someone who doesn't know or like physics. <br />
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:Your unhidden stuff is clear, but if I was just browsing, I probably wouldn't have read the hidden section. That's largely due to the fact that it's pretty much all physics and I just don't like physics, but I think your MME is also less clear than your Basic Description. I don't think you need to dumb it down or anything, you should be writing the section for someone who has a bit more physics than me anyway, but I think a little bit more outlining/sign-posting/telling the reader what you're doing in each section would be a good idea, and I pointed out a couple sections where you might want to go over the wording of your explanations with someone who understands what you're trying to say.<br />
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*<font color=violet> [[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Alright, that sounds like good feedback to me. I'll work on trying to make things a bit more understandable. For the math section I'll give a mini summary before I do any steps. So, hopefully that will help.</font> <br />
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:Anyway, I think you've got a really good start here. You did an especially good job of defining your terms in the basic description - clear and concise.</font><br />
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*<font color=blue>[[User:ifayanj|Dayo]] 16:53, 28 June 2011 (UTC) I would try to change the second sentence of the image description up top. It seems a bit awkward. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Is it still awkward now? If so, what do you suggest?</font><br />
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:I really like the page though, and think its' a good topic. If having too much physics is the problem I would try to say more about images or how it effects images (which it really does!) "The snell's law on the beach section": it's a really cool application, but I would try to put it under a different heading, maybe an, "applications and examples" section.</font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) No, I want the Snell's Law on the beach to lead into the idea of Fermat Principle and the derivation. It's just a quick analogy so that people can understand that light travel in the least time. I did provide examples later on and the application is more in the why it's interesting section.</font><br />
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*<font color=red>xd 14:25, 22 June 2011 (UTC) Is this too much physics? Of course. You are writing about a law in physics on Math Images Page. But if you want to continue this page, you have live with this. In addition, I think it would be advisable to look at wikipedia's page and think about what kind of new stuff you can offer than what is already there. If not, then I think you should take on a new project that is not explored very much.</font color><br />
::[[User:Ljeanlo1|Leah]] 19:35, 24 June 2011 (UTC)Although this is a physic topic, I just want to make sure it's capable of being a math image page.<br />
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=Section-specific comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC): ''Snell's Law is a mathematical formula that predicts the amount of bend.'' - amount of bend in what? Feels like the sentence stopped before it was over.</font><br />
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:[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Would it be better if I end off with "seen in the image"? <br />
::<font color=dodgerblue>Yeah, I think that'd be fine. Or you could say that it predicts the amount that light bends. You just need to tie the bending down somewhere, because it's not like Snell's Law is predicting the amount that like, a tree branch or a river or my left pinky finger bends. ([[User:Kderosier|Kate]] 14:51, 7 July 2011 (UTC))</font><br />
[[User:Ljeanlo1|Ljeanlo1]] 15:51, 13 July 2011 (UTC) Ok, got it. <br />
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==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''Geometrical optics will requires basic knowledge of geometry specifically on triangles.''<br />
::I think this sentence should be "Understanding geometrical optics requires basic knowledge of geometry and triangles."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence.<br />
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*<font color=dodgerblue>''In contrast, light can sometimes be treated as a wave which is found in physical optics, but that involves the interference and propagation of waves which will require more insight into physics.''<br />
::Even though you follow it by saying that physical optics won't be discussed, this sentence is a little intimidating to read. You might want to see if you can find a less detailed way of saying that there's other ways of understanding light.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC)I have broken this up and wrote that it will not be discussed. I think it's important to add little snippets of other topics in case anyone would like to learn about physical optics on a quick wiki search. Also, I took out the concept of physical optics and just said that light sometimes behaves in a different way. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) "geometrical optics where it's known that light travels in a straight line called a ray"--but you're talking about when it doesn't!<br />
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*[[User:Rebecca|Rebecca]] 01:45, 7 July 2011 (UTC) "Physical optics will not be discussed...." I would add "on this page."<br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC) I included this. <br />
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===Law of Reflection===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''The incident ray makes with the normal an angle of incidence.''<br />
::The wording here confused me, it might sound better to say "The angle that the incident ray makes with the normal is called the angle of incidence."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence. <br />
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*<font color=dodgerblue>I need a bit more explanation for why Image 3 shows distortion and Image 2 doesn't - to me, they both look like they're essentially the same thing as Image 1 - there's multiple light rays in each picture, and each ray follows the law of reflection. Is the point that in Image 2 the light rays enter and exit in parallel with each other? If so, shouldn't the light rays in Image 3 enter in parallel and then exit in different directions? (Right now, the rays in Image 3 look totally unrelated to each other to me.)</font><br />
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<s>*[[User:Rebecca|Rebecca]] 01:46, 7 July 2011 (UTC) "The reflected ray holds the same property of making an angle of reflection with the normal." I'm not sure if you need this sentence because if it reflects it seems sort of obvious that it would make an angle. </s><br />
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*<s> Bolding new words that you're defining really helps in this section.</s><br />
* [[User:Rebecca|Rebecca]] 01:14, 16 July 2011 (UTC) This section is great now. I think it's very clear. Only one question: is this actually a law of reflection? If so, what is the law specifically? If you can identify a law in here I think that would be helpful. Otherwise, I think the section would be more appropriately named "Reflection of Light" or something like that. <br />
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===Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):</font><br />
*<font color=dodgerblue>''It is 3.0 x 10^8 m/s '' - you should probably make that 8 an actual super script. I don't know how to type the html so that you can see the code, but I guess you can just look at this under edit - it should look like this: 10<sup>8</sup> </font><br />
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*<font color=dodgerblue>When you're typing "c" and "v" and "n", do you mean ''c'' and ''v'' and ''n''? </font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) I'll put it in italics instead of quote marks.<br />
:::<font color=dodgerblue>I mean, you don't have to. That's just how I would do it, and I know a lot of the time I mess up quotation marks with two single quotes and don't get italics where I want them, so I thought I'd ask.([[User:Kderosier|Kate]] 14:55, 7 July 2011 (UTC))</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC)No, it's ok. I think I should be consistent. <br />
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<s>*<font color=dodgerblue>''such as air and carbon dioxide, have an index of refractive'' - should that be "index of refraction"? I don't know the terminology, but that's what you called it when you bolded it.</font></s><br />
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*<font color=dodgerblue>The beginning of this section (explaining that light travels at different speeds in different materials) was good, and the ending seemed clear too (explaining different refractive indices and connecting them to the diagram), but I think you need to be more explicit in the middle about how light changing speeds changes the angle of the ray. I think I kind of remember it from physics, but if you want to write the basic description for someone who knows no physics, you're going to have to spell it out.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC) I added some more text to this section. I don't know if it's clear enough so have a look. <br />
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* "It is <math>3.0 x 10^8 \mathrm{m}/\mathrm{s}</math>" ?<br />
<font color=red>xd 14:23, 22 June 2011 (UTC) I think you mean <math>3.0 \times 10^8 \mathrm{m}/\mathrm{s}</math></font color><br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I fixed this. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) The speed of light differs when it travels through a certain medium" -- you mean ANOTHER medium, I bet.<br />
"index of refractive,"n""-- don't you mean "index of REFRACTION?<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) Sorry. I fixed these grammatical errors. <br />
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"The ratio of the speed of light in a vacuum, "c", and the speed of light in a medium, "v", is the index of refraction , "n"" -- it would help some of us if you wrote n = c/v.<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I have included the mathematical representation of the description. <br />
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Generally, clear writing.<br />
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===Definition===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*''Snell's law relates the angle of incidence and refraction along with the index of refraction for media. ''<br />
::I don't really understand this sentence. I don't know what you mean by "media", and I think maybe you mean "angles" because there's two of them? And I find the sentence structure "X relates Y and Z along with W" a little confusing. Something like "X gives the relationship between Y, Z, and W" or "X relates Y and Z to W" would be clearer, I think.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC) I have rearranged the sentence. <br />
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*<font color=dodgerblue>I'd really like for there to be some sort of words version of the law after you give the equation. What does the equation mean? Just that the amount of refraction is dependent upon the indices of refraction?</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC)I've added a word explanation of the Law at the beginning. Tell me what you think about it.<br />
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==A More Mathematical Explanation==<br />
<s>*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC): ''Below give two methods in deriving Snell's Law, additional information, and problems that you can solve. ''<br />
::This sentence doesn't mean what you want it to mean. Try "Given below are two methods…"</font><br />
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===Deriving Snell's Law with Refraction===<br />
<s><font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC):<br />
*I don't think you should just call it "Snell" in the subject heading here, it should be "Snell's Law"</font></s><br />
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<s>*<font color=dodgerblue>Typo: ''Speed is based on'' '''how''' ''much distance is traveled in an amount of time.''</font></s><br />
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*<s><font color=dodgerblue>You're missing punctuation between the sentence that begins "The wavelength in a medium…" and the one that begins "It was mentioned…"</font></s><br />
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<s>*<font color=dodgerblue>''Equate for the common hypotenuse gives:''<br />
::First, the equation after this isn't showing up. Second, I think maybe you mean "Solving for" and not "Equate"?</font></s><br />
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*<font color=dodgerblue>Are you sure your math in this section is right? In the last equation, n<sub>1</sub> and n<sub>2</sub> are on the same side as the thetas with the same index, but in the equation before that, they're still on the sides with the matching thetas, but are in the denominator. I don't know if I explained that well - what I'm trying to say is that it looks to me like you simplified <math>\frac{1}{n} \sin(\theta)</math> to <math>n \sin(\theta)</math>. </font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:37, 13 July 2011 (UTC) Do you think it's best that I put parentheses around theta. I don't really do that when I'm writing out my math on a piece of paper even though I know it's suppose to be there? <br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:27, 13 July 2011 (UTC)I have changed the syntax of the math so that the steps looks more clear. <br />
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<s>*[[User:Rebecca|Rebecca]] 01:47, 7 July 2011 (UTC) I would bold "period" when you define it.<br />
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===Total Internal Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:16, 6 July 2011 (UTC):<br />
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*I don't understand your first paragraph in this section. I think it's a combination of confusing wording and me having a hard time visualizing what you're talking about.</font><br />
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*<font color=dodgerblue>I don't think you really mean to write "sin<sub>1</sub>", but I don't know what you actually are trying to say.</font><br />
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*<font color=dodgerblue>I guess I really just don't understand this section. I don't know what the purpose of it is - I thought you said we were going to do two derivations of Snell's Law, but this doesn't look like a derivation. It'll probably help when you get your pictures in there, but it might be a good idea to go over the text with someone who understands the physics and try and make it clearer.</font><br />
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===Snell Law's on the Beach===<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I think the lifeguard example is a good one, but if you're using it just to begin the derivation, you should make that clearer at the start - I thought we were doing an example problem, but then when I saw the next heading, I was like, "huh? why is there a derivation here??"</font><br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) Lifeguard is one word.<br />
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* I think your diagram for the beach problem is helpful, but your black and red lines for "path with the least water" and "path with the least sand" aren't exactly true. For example, the black line shows just one choice of path with the least water. You could also run directly to the point where the T in "path with the least time" intersects the black line, and then run to the water and you'd still spend the same amount of time in the water. I'm not sure if there's a way to change this, and if not, don't worry too much. Just figured I'd point it out and maybe some of the other imagers have ideas. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 23:49, 13 July 2011 (UTC) I see what you mean, but I thought I would outlined the most common option a person would have if they were to point how the path with the least ____ (insert word). I'll ask other people what they think about it.</font> <br />
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====Deriving Snell With Fermat====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I found it kind of weird the way you said that it's usually "required" in middle school that you know d = rt. I think perhaps it would be better just to say "Recall that distance equals rate multiplied by time"</font><br />
<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) I took this sentence out and put in what you suggested.</font> <br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) "Usually in middle school, it's required that everyone know distance is equal to the rate times time (d=rt)." I would remove this sentence. I think it might intimidate people if they didn't learn this in middle school or they forgot it, and you don't really need it. Maybe also remove "Velocity is easy though." I think it's the same idea- if people don't immediately understand they will get discouraged. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC)<font color=violet>I took out both of these sentences and said to rename rate as velocity.</font><br />
:* [[User:Rebecca|Rebecca]] 01:18, 16 July 2011 (UTC) <font color=slateblue> I think you accidentally left "Velocity though is easy." </font color><br />
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* <s>When you say "So the total time from point A to point B is..." I think you need another sentence of explanation. Maybe try... "Using plugging these formulas for distance into the equation for time, we can find the total time from point A to point B. It is:" <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>Thanks. I used your sentence which was very clear.</font> </s><br />
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*<s> I don't think you're really crossing out the 1/2 in the next line... you're multiplying both sides by 2 to make the 1/2 disappear. To show this I think you need to add an extra step. Also, you proceed to say that the two expressions are the same.... but it's not that easy to see. You'll have to reduce it more to show that they're actually the same. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>I made it into more steps and included your suggestions about 2 vs. 1/2.</font> </s><br />
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==Why It's Interesting==<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:20, 6 July 2011 (UTC): I thought the mirages were definitely a reason why it's interesting! I didn't know that at all.</font><br />
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* <font color=slateblue>[[User:Rebecca|Rebecca]] 01:49, 7 July 2011 (UTC) I can't wait to see the new Why It's Interesting section and the applet! Nice work on this page. </font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:05, 13 July 2011 (UTC) I decided to put the total internal reflection part in this section, which I am revising. I plan to talk about fiber optic cables. Also, I want to expand on mirages if I can find a credible source. Lastly, people from Drexel suggest I do a section on ray tracing (this usually has to do with real/virtual images and what the eye sees.)</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Snell%27s_Law&diff=25637Talk:Snell's Law2011-07-16T01:18:24Z<p>Rebecca: /* Deriving Snell With Fermat */</p>
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<div>=General Comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:27, 6 July 2011 (UTC): Ok, so I took physics in high school, but it was a terrible class and I barely understood any of it, so I thought I'd give you some feedback from the perspective of someone who doesn't know or like physics. <br />
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:Your unhidden stuff is clear, but if I was just browsing, I probably wouldn't have read the hidden section. That's largely due to the fact that it's pretty much all physics and I just don't like physics, but I think your MME is also less clear than your Basic Description. I don't think you need to dumb it down or anything, you should be writing the section for someone who has a bit more physics than me anyway, but I think a little bit more outlining/sign-posting/telling the reader what you're doing in each section would be a good idea, and I pointed out a couple sections where you might want to go over the wording of your explanations with someone who understands what you're trying to say.<br />
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*<font color=violet> [[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Alright, that sounds like good feedback to me. I'll work on trying to make things a bit more understandable. For the math section I'll give a mini summary before I do any steps. So, hopefully that will help.</font> <br />
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:Anyway, I think you've got a really good start here. You did an especially good job of defining your terms in the basic description - clear and concise.</font><br />
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*<font color=blue>[[User:ifayanj|Dayo]] 16:53, 28 June 2011 (UTC) I would try to change the second sentence of the image description up top. It seems a bit awkward. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Is it still awkward now? If so, what do you suggest?</font><br />
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:I really like the page though, and think its' a good topic. If having too much physics is the problem I would try to say more about images or how it effects images (which it really does!) "The snell's law on the beach section": it's a really cool application, but I would try to put it under a different heading, maybe an, "applications and examples" section.</font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) No, I want the Snell's Law on the beach to lead into the idea of Fermat Principle and the derivation. It's just a quick analogy so that people can understand that light travel in the least time. I did provide examples later on and the application is more in the why it's interesting section.</font><br />
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*<font color=red>xd 14:25, 22 June 2011 (UTC) Is this too much physics? Of course. You are writing about a law in physics on Math Images Page. But if you want to continue this page, you have live with this. In addition, I think it would be advisable to look at wikipedia's page and think about what kind of new stuff you can offer than what is already there. If not, then I think you should take on a new project that is not explored very much.</font color><br />
::[[User:Ljeanlo1|Leah]] 19:35, 24 June 2011 (UTC)Although this is a physic topic, I just want to make sure it's capable of being a math image page.<br />
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=Section-specific comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC): ''Snell's Law is a mathematical formula that predicts the amount of bend.'' - amount of bend in what? Feels like the sentence stopped before it was over.</font><br />
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:[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Would it be better if I end off with "seen in the image"? <br />
::<font color=dodgerblue>Yeah, I think that'd be fine. Or you could say that it predicts the amount that light bends. You just need to tie the bending down somewhere, because it's not like Snell's Law is predicting the amount that like, a tree branch or a river or my left pinky finger bends. ([[User:Kderosier|Kate]] 14:51, 7 July 2011 (UTC))</font><br />
[[User:Ljeanlo1|Ljeanlo1]] 15:51, 13 July 2011 (UTC) Ok, got it. <br />
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==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''Geometrical optics will requires basic knowledge of geometry specifically on triangles.''<br />
::I think this sentence should be "Understanding geometrical optics requires basic knowledge of geometry and triangles."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence.<br />
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*<font color=dodgerblue>''In contrast, light can sometimes be treated as a wave which is found in physical optics, but that involves the interference and propagation of waves which will require more insight into physics.''<br />
::Even though you follow it by saying that physical optics won't be discussed, this sentence is a little intimidating to read. You might want to see if you can find a less detailed way of saying that there's other ways of understanding light.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC)I have broken this up and wrote that it will not be discussed. I think it's important to add little snippets of other topics in case anyone would like to learn about physical optics on a quick wiki search. Also, I took out the concept of physical optics and just said that light sometimes behaves in a different way. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) "geometrical optics where it's known that light travels in a straight line called a ray"--but you're talking about when it doesn't!<br />
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*[[User:Rebecca|Rebecca]] 01:45, 7 July 2011 (UTC) "Physical optics will not be discussed...." I would add "on this page."<br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC) I included this. <br />
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===Law of Reflection===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''The incident ray makes with the normal an angle of incidence.''<br />
::The wording here confused me, it might sound better to say "The angle that the incident ray makes with the normal is called the angle of incidence."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence. <br />
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*<font color=dodgerblue>I need a bit more explanation for why Image 3 shows distortion and Image 2 doesn't - to me, they both look like they're essentially the same thing as Image 1 - there's multiple light rays in each picture, and each ray follows the law of reflection. Is the point that in Image 2 the light rays enter and exit in parallel with each other? If so, shouldn't the light rays in Image 3 enter in parallel and then exit in different directions? (Right now, the rays in Image 3 look totally unrelated to each other to me.)</font><br />
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<s>*[[User:Rebecca|Rebecca]] 01:46, 7 July 2011 (UTC) "The reflected ray holds the same property of making an angle of reflection with the normal." I'm not sure if you need this sentence because if it reflects it seems sort of obvious that it would make an angle. </s><br />
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*<s> Bolding new words that you're defining really helps in this section.</s><br />
* [[User:Rebecca|Rebecca]] 01:14, 16 July 2011 (UTC) This section is great now. I think it's very clear. Only one question: is this actually a law of reflection? If so, what is the law specifically? If you can identify a law in here I think that would be helpful. Otherwise, I think the section would be more appropriately named "Reflection of Light" or something like that. <br />
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===Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):</font><br />
*<font color=dodgerblue>''It is 3.0 x 10^8 m/s '' - you should probably make that 8 an actual super script. I don't know how to type the html so that you can see the code, but I guess you can just look at this under edit - it should look like this: 10<sup>8</sup> </font><br />
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*<font color=dodgerblue>When you're typing "c" and "v" and "n", do you mean ''c'' and ''v'' and ''n''? </font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) I'll put it in italics instead of quote marks.<br />
:::<font color=dodgerblue>I mean, you don't have to. That's just how I would do it, and I know a lot of the time I mess up quotation marks with two single quotes and don't get italics where I want them, so I thought I'd ask.([[User:Kderosier|Kate]] 14:55, 7 July 2011 (UTC))</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC)No, it's ok. I think I should be consistent. <br />
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<s>*<font color=dodgerblue>''such as air and carbon dioxide, have an index of refractive'' - should that be "index of refraction"? I don't know the terminology, but that's what you called it when you bolded it.</font></s><br />
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*<font color=dodgerblue>The beginning of this section (explaining that light travels at different speeds in different materials) was good, and the ending seemed clear too (explaining different refractive indices and connecting them to the diagram), but I think you need to be more explicit in the middle about how light changing speeds changes the angle of the ray. I think I kind of remember it from physics, but if you want to write the basic description for someone who knows no physics, you're going to have to spell it out.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC) I added some more text to this section. I don't know if it's clear enough so have a look. <br />
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* "It is <math>3.0 x 10^8 \mathrm{m}/\mathrm{s}</math>" ?<br />
<font color=red>xd 14:23, 22 June 2011 (UTC) I think you mean <math>3.0 \times 10^8 \mathrm{m}/\mathrm{s}</math></font color><br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I fixed this. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) The speed of light differs when it travels through a certain medium" -- you mean ANOTHER medium, I bet.<br />
"index of refractive,"n""-- don't you mean "index of REFRACTION?<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) Sorry. I fixed these grammatical errors. <br />
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"The ratio of the speed of light in a vacuum, "c", and the speed of light in a medium, "v", is the index of refraction , "n"" -- it would help some of us if you wrote n = c/v.<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I have included the mathematical representation of the description. <br />
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Generally, clear writing.<br />
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===Definition===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*''Snell's law relates the angle of incidence and refraction along with the index of refraction for media. ''<br />
::I don't really understand this sentence. I don't know what you mean by "media", and I think maybe you mean "angles" because there's two of them? And I find the sentence structure "X relates Y and Z along with W" a little confusing. Something like "X gives the relationship between Y, Z, and W" or "X relates Y and Z to W" would be clearer, I think.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC) I have rearranged the sentence. <br />
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*<font color=dodgerblue>I'd really like for there to be some sort of words version of the law after you give the equation. What does the equation mean? Just that the amount of refraction is dependent upon the indices of refraction?</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC)I've added a word explanation of the Law at the beginning. Tell me what you think about it.<br />
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==A More Mathematical Explanation==<br />
<s>*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC): ''Below give two methods in deriving Snell's Law, additional information, and problems that you can solve. ''<br />
::This sentence doesn't mean what you want it to mean. Try "Given below are two methods…"</font><br />
</s><br />
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===Deriving Snell's Law with Refraction===<br />
<s><font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC):<br />
*I don't think you should just call it "Snell" in the subject heading here, it should be "Snell's Law"</font></s><br />
<br />
<s>*<font color=dodgerblue>Typo: ''Speed is based on'' '''how''' ''much distance is traveled in an amount of time.''</font></s><br />
<br />
*<s><font color=dodgerblue>You're missing punctuation between the sentence that begins "The wavelength in a medium…" and the one that begins "It was mentioned…"</font></s><br />
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<s>*<font color=dodgerblue>''Equate for the common hypotenuse gives:''<br />
::First, the equation after this isn't showing up. Second, I think maybe you mean "Solving for" and not "Equate"?</font></s><br />
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*<font color=dodgerblue>Are you sure your math in this section is right? In the last equation, n<sub>1</sub> and n<sub>2</sub> are on the same side as the thetas with the same index, but in the equation before that, they're still on the sides with the matching thetas, but are in the denominator. I don't know if I explained that well - what I'm trying to say is that it looks to me like you simplified <math>\frac{1}{n} \sin(\theta)</math> to <math>n \sin(\theta)</math>. </font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:37, 13 July 2011 (UTC) Do you think it's best that I put parentheses around theta. I don't really do that when I'm writing out my math on a piece of paper even though I know it's suppose to be there? <br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:27, 13 July 2011 (UTC)I have changed the syntax of the math so that the steps looks more clear. <br />
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<s>*[[User:Rebecca|Rebecca]] 01:47, 7 July 2011 (UTC) I would bold "period" when you define it.<br />
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===Total Internal Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:16, 6 July 2011 (UTC):<br />
<br />
*I don't understand your first paragraph in this section. I think it's a combination of confusing wording and me having a hard time visualizing what you're talking about.</font><br />
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*<font color=dodgerblue>I don't think you really mean to write "sin<sub>1</sub>", but I don't know what you actually are trying to say.</font><br />
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*<font color=dodgerblue>I guess I really just don't understand this section. I don't know what the purpose of it is - I thought you said we were going to do two derivations of Snell's Law, but this doesn't look like a derivation. It'll probably help when you get your pictures in there, but it might be a good idea to go over the text with someone who understands the physics and try and make it clearer.</font><br />
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===Snell Law's on the Beach===<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I think the lifeguard example is a good one, but if you're using it just to begin the derivation, you should make that clearer at the start - I thought we were doing an example problem, but then when I saw the next heading, I was like, "huh? why is there a derivation here??"</font><br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) Lifeguard is one word.<br />
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* I think your diagram for the beach problem is helpful, but your black and red lines for "path with the least water" and "path with the least sand" aren't exactly true. For example, the black line shows just one choice of path with the least water. You could also run directly to the point where the T in "path with the least time" intersects the black line, and then run to the water and you'd still spend the same amount of time in the water. I'm not sure if there's a way to change this, and if not, don't worry too much. Just figured I'd point it out and maybe some of the other imagers have ideas. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 23:49, 13 July 2011 (UTC) I see what you mean, but I thought I would outlined the most common option a person would have if they were to point how the path with the least ____ (insert word). I'll ask other people what they think about it.</font> <br />
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====Deriving Snell With Fermat====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I found it kind of weird the way you said that it's usually "required" in middle school that you know d = rt. I think perhaps it would be better just to say "Recall that distance equals rate multiplied by time"</font><br />
<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) I took this sentence out and put in what you suggested.</font> <br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) "Usually in middle school, it's required that everyone know distance is equal to the rate times time (d=rt)." I would remove this sentence. I think it might intimidate people if they didn't learn this in middle school or they forgot it, and you don't really need it. Maybe also remove "Velocity is easy though." I think it's the same idea- if people don't immediately understand they will get discouraged. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC)<font color=violet>I took out both of these sentences and said to rename rate as velocity.</font><br />
:* [[User:Rebecca|Rebecca]] 01:18, 16 July 2011 (UTC) <font color=slateblue> I think you accidentally left "Velocity though is easy." </font color><br />
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* When you say "So the total time from point A to point B is..." I think you need another sentence of explanation. Maybe try... "Using plugging these formulas for distance into the equation for time, we can find the total time from point A to point B. It is:"<br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>Thanks. I used your sentence which was very clear.</font> <br />
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* I don't think you're really crossing out the 1/2 in the next line... you're multiplying both sides by 2 to make the 1/2 disappear. To show this I think you need to add an extra step. Also, you proceed to say that the two expressions are the same.... but it's not that easy to see. You'll have to reduce it more to show that they're actually the same. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>I made it into more steps and included your suggestions about 2 vs. 1/2.</font><br />
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==Why It's Interesting==<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:20, 6 July 2011 (UTC): I thought the mirages were definitely a reason why it's interesting! I didn't know that at all.</font><br />
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* <font color=slateblue>[[User:Rebecca|Rebecca]] 01:49, 7 July 2011 (UTC) I can't wait to see the new Why It's Interesting section and the applet! Nice work on this page. </font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:05, 13 July 2011 (UTC) I decided to put the total internal reflection part in this section, which I am revising. I plan to talk about fiber optic cables. Also, I want to expand on mirages if I can find a credible source. Lastly, people from Drexel suggest I do a section on ray tracing (this usually has to do with real/virtual images and what the eye sees.)</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Snell%27s_Law&diff=25636Talk:Snell's Law2011-07-16T01:16:45Z<p>Rebecca: /* Law of Reflection */</p>
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<div>=General Comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:27, 6 July 2011 (UTC): Ok, so I took physics in high school, but it was a terrible class and I barely understood any of it, so I thought I'd give you some feedback from the perspective of someone who doesn't know or like physics. <br />
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:Your unhidden stuff is clear, but if I was just browsing, I probably wouldn't have read the hidden section. That's largely due to the fact that it's pretty much all physics and I just don't like physics, but I think your MME is also less clear than your Basic Description. I don't think you need to dumb it down or anything, you should be writing the section for someone who has a bit more physics than me anyway, but I think a little bit more outlining/sign-posting/telling the reader what you're doing in each section would be a good idea, and I pointed out a couple sections where you might want to go over the wording of your explanations with someone who understands what you're trying to say.<br />
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*<font color=violet> [[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Alright, that sounds like good feedback to me. I'll work on trying to make things a bit more understandable. For the math section I'll give a mini summary before I do any steps. So, hopefully that will help.</font> <br />
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:Anyway, I think you've got a really good start here. You did an especially good job of defining your terms in the basic description - clear and concise.</font><br />
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*<font color=blue>[[User:ifayanj|Dayo]] 16:53, 28 June 2011 (UTC) I would try to change the second sentence of the image description up top. It seems a bit awkward. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Is it still awkward now? If so, what do you suggest?</font><br />
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:I really like the page though, and think its' a good topic. If having too much physics is the problem I would try to say more about images or how it effects images (which it really does!) "The snell's law on the beach section": it's a really cool application, but I would try to put it under a different heading, maybe an, "applications and examples" section.</font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) No, I want the Snell's Law on the beach to lead into the idea of Fermat Principle and the derivation. It's just a quick analogy so that people can understand that light travel in the least time. I did provide examples later on and the application is more in the why it's interesting section.</font><br />
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*<font color=red>xd 14:25, 22 June 2011 (UTC) Is this too much physics? Of course. You are writing about a law in physics on Math Images Page. But if you want to continue this page, you have live with this. In addition, I think it would be advisable to look at wikipedia's page and think about what kind of new stuff you can offer than what is already there. If not, then I think you should take on a new project that is not explored very much.</font color><br />
::[[User:Ljeanlo1|Leah]] 19:35, 24 June 2011 (UTC)Although this is a physic topic, I just want to make sure it's capable of being a math image page.<br />
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=Section-specific comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC): ''Snell's Law is a mathematical formula that predicts the amount of bend.'' - amount of bend in what? Feels like the sentence stopped before it was over.</font><br />
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:[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Would it be better if I end off with "seen in the image"? <br />
::<font color=dodgerblue>Yeah, I think that'd be fine. Or you could say that it predicts the amount that light bends. You just need to tie the bending down somewhere, because it's not like Snell's Law is predicting the amount that like, a tree branch or a river or my left pinky finger bends. ([[User:Kderosier|Kate]] 14:51, 7 July 2011 (UTC))</font><br />
[[User:Ljeanlo1|Ljeanlo1]] 15:51, 13 July 2011 (UTC) Ok, got it. <br />
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==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''Geometrical optics will requires basic knowledge of geometry specifically on triangles.''<br />
::I think this sentence should be "Understanding geometrical optics requires basic knowledge of geometry and triangles."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence.<br />
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*<font color=dodgerblue>''In contrast, light can sometimes be treated as a wave which is found in physical optics, but that involves the interference and propagation of waves which will require more insight into physics.''<br />
::Even though you follow it by saying that physical optics won't be discussed, this sentence is a little intimidating to read. You might want to see if you can find a less detailed way of saying that there's other ways of understanding light.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC)I have broken this up and wrote that it will not be discussed. I think it's important to add little snippets of other topics in case anyone would like to learn about physical optics on a quick wiki search. Also, I took out the concept of physical optics and just said that light sometimes behaves in a different way. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) "geometrical optics where it's known that light travels in a straight line called a ray"--but you're talking about when it doesn't!<br />
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*[[User:Rebecca|Rebecca]] 01:45, 7 July 2011 (UTC) "Physical optics will not be discussed...." I would add "on this page."<br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC) I included this. <br />
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===Law of Reflection===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''The incident ray makes with the normal an angle of incidence.''<br />
::The wording here confused me, it might sound better to say "The angle that the incident ray makes with the normal is called the angle of incidence."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence. <br />
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*<font color=dodgerblue>I need a bit more explanation for why Image 3 shows distortion and Image 2 doesn't - to me, they both look like they're essentially the same thing as Image 1 - there's multiple light rays in each picture, and each ray follows the law of reflection. Is the point that in Image 2 the light rays enter and exit in parallel with each other? If so, shouldn't the light rays in Image 3 enter in parallel and then exit in different directions? (Right now, the rays in Image 3 look totally unrelated to each other to me.)</font><br />
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<s>*[[User:Rebecca|Rebecca]] 01:46, 7 July 2011 (UTC) "The reflected ray holds the same property of making an angle of reflection with the normal." I'm not sure if you need this sentence because if it reflects it seems sort of obvious that it would make an angle. </s><br />
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<font color=slateblue><br />
*<s> Bolding new words that you're defining really helps in this section.</s><br />
* [[User:Rebecca|Rebecca]] 01:14, 16 July 2011 (UTC) This section is great now. I think it's very clear. Only one question: is this actually a law of reflection? If so, what is the law specifically? If you can identify a law in here I think that would be helpful. Otherwise, I think the section would be more appropriately named "Reflection of Light" or something like that. <br />
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===Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):</font><br />
*<font color=dodgerblue>''It is 3.0 x 10^8 m/s '' - you should probably make that 8 an actual super script. I don't know how to type the html so that you can see the code, but I guess you can just look at this under edit - it should look like this: 10<sup>8</sup> </font><br />
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*<font color=dodgerblue>When you're typing "c" and "v" and "n", do you mean ''c'' and ''v'' and ''n''? </font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) I'll put it in italics instead of quote marks.<br />
:::<font color=dodgerblue>I mean, you don't have to. That's just how I would do it, and I know a lot of the time I mess up quotation marks with two single quotes and don't get italics where I want them, so I thought I'd ask.([[User:Kderosier|Kate]] 14:55, 7 July 2011 (UTC))</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC)No, it's ok. I think I should be consistent. <br />
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<s>*<font color=dodgerblue>''such as air and carbon dioxide, have an index of refractive'' - should that be "index of refraction"? I don't know the terminology, but that's what you called it when you bolded it.</font></s><br />
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*<font color=dodgerblue>The beginning of this section (explaining that light travels at different speeds in different materials) was good, and the ending seemed clear too (explaining different refractive indices and connecting them to the diagram), but I think you need to be more explicit in the middle about how light changing speeds changes the angle of the ray. I think I kind of remember it from physics, but if you want to write the basic description for someone who knows no physics, you're going to have to spell it out.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC) I added some more text to this section. I don't know if it's clear enough so have a look. <br />
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* "It is <math>3.0 x 10^8 \mathrm{m}/\mathrm{s}</math>" ?<br />
<font color=red>xd 14:23, 22 June 2011 (UTC) I think you mean <math>3.0 \times 10^8 \mathrm{m}/\mathrm{s}</math></font color><br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I fixed this. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) The speed of light differs when it travels through a certain medium" -- you mean ANOTHER medium, I bet.<br />
"index of refractive,"n""-- don't you mean "index of REFRACTION?<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) Sorry. I fixed these grammatical errors. <br />
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"The ratio of the speed of light in a vacuum, "c", and the speed of light in a medium, "v", is the index of refraction , "n"" -- it would help some of us if you wrote n = c/v.<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I have included the mathematical representation of the description. <br />
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Generally, clear writing.<br />
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===Definition===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*''Snell's law relates the angle of incidence and refraction along with the index of refraction for media. ''<br />
::I don't really understand this sentence. I don't know what you mean by "media", and I think maybe you mean "angles" because there's two of them? And I find the sentence structure "X relates Y and Z along with W" a little confusing. Something like "X gives the relationship between Y, Z, and W" or "X relates Y and Z to W" would be clearer, I think.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC) I have rearranged the sentence. <br />
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*<font color=dodgerblue>I'd really like for there to be some sort of words version of the law after you give the equation. What does the equation mean? Just that the amount of refraction is dependent upon the indices of refraction?</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC)I've added a word explanation of the Law at the beginning. Tell me what you think about it.<br />
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==A More Mathematical Explanation==<br />
<s>*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC): ''Below give two methods in deriving Snell's Law, additional information, and problems that you can solve. ''<br />
::This sentence doesn't mean what you want it to mean. Try "Given below are two methods…"</font><br />
</s><br />
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===Deriving Snell's Law with Refraction===<br />
<s><font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC):<br />
*I don't think you should just call it "Snell" in the subject heading here, it should be "Snell's Law"</font></s><br />
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<s>*<font color=dodgerblue>Typo: ''Speed is based on'' '''how''' ''much distance is traveled in an amount of time.''</font></s><br />
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*<s><font color=dodgerblue>You're missing punctuation between the sentence that begins "The wavelength in a medium…" and the one that begins "It was mentioned…"</font></s><br />
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<s>*<font color=dodgerblue>''Equate for the common hypotenuse gives:''<br />
::First, the equation after this isn't showing up. Second, I think maybe you mean "Solving for" and not "Equate"?</font></s><br />
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*<font color=dodgerblue>Are you sure your math in this section is right? In the last equation, n<sub>1</sub> and n<sub>2</sub> are on the same side as the thetas with the same index, but in the equation before that, they're still on the sides with the matching thetas, but are in the denominator. I don't know if I explained that well - what I'm trying to say is that it looks to me like you simplified <math>\frac{1}{n} \sin(\theta)</math> to <math>n \sin(\theta)</math>. </font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:37, 13 July 2011 (UTC) Do you think it's best that I put parentheses around theta. I don't really do that when I'm writing out my math on a piece of paper even though I know it's suppose to be there? <br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:27, 13 July 2011 (UTC)I have changed the syntax of the math so that the steps looks more clear. <br />
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<s>*[[User:Rebecca|Rebecca]] 01:47, 7 July 2011 (UTC) I would bold "period" when you define it.<br />
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===Total Internal Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:16, 6 July 2011 (UTC):<br />
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*I don't understand your first paragraph in this section. I think it's a combination of confusing wording and me having a hard time visualizing what you're talking about.</font><br />
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*<font color=dodgerblue>I don't think you really mean to write "sin<sub>1</sub>", but I don't know what you actually are trying to say.</font><br />
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*<font color=dodgerblue>I guess I really just don't understand this section. I don't know what the purpose of it is - I thought you said we were going to do two derivations of Snell's Law, but this doesn't look like a derivation. It'll probably help when you get your pictures in there, but it might be a good idea to go over the text with someone who understands the physics and try and make it clearer.</font><br />
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===Snell Law's on the Beach===<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I think the lifeguard example is a good one, but if you're using it just to begin the derivation, you should make that clearer at the start - I thought we were doing an example problem, but then when I saw the next heading, I was like, "huh? why is there a derivation here??"</font><br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) Lifeguard is one word.<br />
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* I think your diagram for the beach problem is helpful, but your black and red lines for "path with the least water" and "path with the least sand" aren't exactly true. For example, the black line shows just one choice of path with the least water. You could also run directly to the point where the T in "path with the least time" intersects the black line, and then run to the water and you'd still spend the same amount of time in the water. I'm not sure if there's a way to change this, and if not, don't worry too much. Just figured I'd point it out and maybe some of the other imagers have ideas. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 23:49, 13 July 2011 (UTC) I see what you mean, but I thought I would outlined the most common option a person would have if they were to point how the path with the least ____ (insert word). I'll ask other people what they think about it.</font> <br />
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====Deriving Snell With Fermat====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I found it kind of weird the way you said that it's usually "required" in middle school that you know d = rt. I think perhaps it would be better just to say "Recall that distance equals rate multiplied by time"</font><br />
<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) I took this sentence out and put in what you suggested.</font> <br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) "Usually in middle school, it's required that everyone know distance is equal to the rate times time (d=rt)." I would remove this sentence. I think it might intimidate people if they didn't learn this in middle school or they forgot it, and you don't really need it. Maybe also remove "Velocity is easy though." I think it's the same idea- if people don't immediately understand they will get discouraged. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC)<font color=violet>I took out both of these sentences and said to rename rate as velocity.</font><br />
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* When you say "So the total time from point A to point B is..." I think you need another sentence of explanation. Maybe try... "Using plugging these formulas for distance into the equation for time, we can find the total time from point A to point B. It is:"<br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>Thanks. I used your sentence which was very clear.</font> <br />
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* I don't think you're really crossing out the 1/2 in the next line... you're multiplying both sides by 2 to make the 1/2 disappear. To show this I think you need to add an extra step. Also, you proceed to say that the two expressions are the same.... but it's not that easy to see. You'll have to reduce it more to show that they're actually the same. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>I made it into more steps and included your suggestions about 2 vs. 1/2.</font><br />
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==Why It's Interesting==<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:20, 6 July 2011 (UTC): I thought the mirages were definitely a reason why it's interesting! I didn't know that at all.</font><br />
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* <font color=slateblue>[[User:Rebecca|Rebecca]] 01:49, 7 July 2011 (UTC) I can't wait to see the new Why It's Interesting section and the applet! Nice work on this page. </font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:05, 13 July 2011 (UTC) I decided to put the total internal reflection part in this section, which I am revising. I plan to talk about fiber optic cables. Also, I want to expand on mirages if I can find a credible source. Lastly, people from Drexel suggest I do a section on ray tracing (this usually has to do with real/virtual images and what the eye sees.)</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Snell%27s_Law&diff=25635Talk:Snell's Law2011-07-16T01:16:23Z<p>Rebecca: /* Law of Reflection */</p>
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<div>=General Comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:27, 6 July 2011 (UTC): Ok, so I took physics in high school, but it was a terrible class and I barely understood any of it, so I thought I'd give you some feedback from the perspective of someone who doesn't know or like physics. <br />
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:Your unhidden stuff is clear, but if I was just browsing, I probably wouldn't have read the hidden section. That's largely due to the fact that it's pretty much all physics and I just don't like physics, but I think your MME is also less clear than your Basic Description. I don't think you need to dumb it down or anything, you should be writing the section for someone who has a bit more physics than me anyway, but I think a little bit more outlining/sign-posting/telling the reader what you're doing in each section would be a good idea, and I pointed out a couple sections where you might want to go over the wording of your explanations with someone who understands what you're trying to say.<br />
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*<font color=violet> [[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Alright, that sounds like good feedback to me. I'll work on trying to make things a bit more understandable. For the math section I'll give a mini summary before I do any steps. So, hopefully that will help.</font> <br />
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:Anyway, I think you've got a really good start here. You did an especially good job of defining your terms in the basic description - clear and concise.</font><br />
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*<font color=blue>[[User:ifayanj|Dayo]] 16:53, 28 June 2011 (UTC) I would try to change the second sentence of the image description up top. It seems a bit awkward. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Is it still awkward now? If so, what do you suggest?</font><br />
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:I really like the page though, and think its' a good topic. If having too much physics is the problem I would try to say more about images or how it effects images (which it really does!) "The snell's law on the beach section": it's a really cool application, but I would try to put it under a different heading, maybe an, "applications and examples" section.</font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) No, I want the Snell's Law on the beach to lead into the idea of Fermat Principle and the derivation. It's just a quick analogy so that people can understand that light travel in the least time. I did provide examples later on and the application is more in the why it's interesting section.</font><br />
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*<font color=red>xd 14:25, 22 June 2011 (UTC) Is this too much physics? Of course. You are writing about a law in physics on Math Images Page. But if you want to continue this page, you have live with this. In addition, I think it would be advisable to look at wikipedia's page and think about what kind of new stuff you can offer than what is already there. If not, then I think you should take on a new project that is not explored very much.</font color><br />
::[[User:Ljeanlo1|Leah]] 19:35, 24 June 2011 (UTC)Although this is a physic topic, I just want to make sure it's capable of being a math image page.<br />
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=Section-specific comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC): ''Snell's Law is a mathematical formula that predicts the amount of bend.'' - amount of bend in what? Feels like the sentence stopped before it was over.</font><br />
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:[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Would it be better if I end off with "seen in the image"? <br />
::<font color=dodgerblue>Yeah, I think that'd be fine. Or you could say that it predicts the amount that light bends. You just need to tie the bending down somewhere, because it's not like Snell's Law is predicting the amount that like, a tree branch or a river or my left pinky finger bends. ([[User:Kderosier|Kate]] 14:51, 7 July 2011 (UTC))</font><br />
[[User:Ljeanlo1|Ljeanlo1]] 15:51, 13 July 2011 (UTC) Ok, got it. <br />
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==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''Geometrical optics will requires basic knowledge of geometry specifically on triangles.''<br />
::I think this sentence should be "Understanding geometrical optics requires basic knowledge of geometry and triangles."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence.<br />
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*<font color=dodgerblue>''In contrast, light can sometimes be treated as a wave which is found in physical optics, but that involves the interference and propagation of waves which will require more insight into physics.''<br />
::Even though you follow it by saying that physical optics won't be discussed, this sentence is a little intimidating to read. You might want to see if you can find a less detailed way of saying that there's other ways of understanding light.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC)I have broken this up and wrote that it will not be discussed. I think it's important to add little snippets of other topics in case anyone would like to learn about physical optics on a quick wiki search. Also, I took out the concept of physical optics and just said that light sometimes behaves in a different way. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) "geometrical optics where it's known that light travels in a straight line called a ray"--but you're talking about when it doesn't!<br />
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*[[User:Rebecca|Rebecca]] 01:45, 7 July 2011 (UTC) "Physical optics will not be discussed...." I would add "on this page."<br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC) I included this. <br />
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===Law of Reflection===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''The incident ray makes with the normal an angle of incidence.''<br />
::The wording here confused me, it might sound better to say "The angle that the incident ray makes with the normal is called the angle of incidence."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence. <br />
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*<font color=dodgerblue>I need a bit more explanation for why Image 3 shows distortion and Image 2 doesn't - to me, they both look like they're essentially the same thing as Image 1 - there's multiple light rays in each picture, and each ray follows the law of reflection. Is the point that in Image 2 the light rays enter and exit in parallel with each other? If so, shouldn't the light rays in Image 3 enter in parallel and then exit in different directions? (Right now, the rays in Image 3 look totally unrelated to each other to me.)</font><br />
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<s>*[[User:Rebecca|Rebecca]] 01:46, 7 July 2011 (UTC) "The reflected ray holds the same property of making an angle of reflection with the normal." I'm not sure if you need this sentence because if it reflects it seems sort of obvious that it would make an angle. </s><br />
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*<s> Bolding new words that you're defining really helps in this section.</s><br />
* [[User:Rebecca|Rebecca]] 01:14, 16 July 2011 (UTC) This section is great now. I think it's very clear. Only one question: is this actually a law of reflection? If so, what is the law specifically? If you can identify a law in here I think that would be helpful. Otherwise, I think the section would be more appropriately named "Reflection of Light" or something like that. <br />
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===Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):</font><br />
*<font color=dodgerblue>''It is 3.0 x 10^8 m/s '' - you should probably make that 8 an actual super script. I don't know how to type the html so that you can see the code, but I guess you can just look at this under edit - it should look like this: 10<sup>8</sup> </font><br />
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*<font color=dodgerblue>When you're typing "c" and "v" and "n", do you mean ''c'' and ''v'' and ''n''? </font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) I'll put it in italics instead of quote marks.<br />
:::<font color=dodgerblue>I mean, you don't have to. That's just how I would do it, and I know a lot of the time I mess up quotation marks with two single quotes and don't get italics where I want them, so I thought I'd ask.([[User:Kderosier|Kate]] 14:55, 7 July 2011 (UTC))</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC)No, it's ok. I think I should be consistent. <br />
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<s>*<font color=dodgerblue>''such as air and carbon dioxide, have an index of refractive'' - should that be "index of refraction"? I don't know the terminology, but that's what you called it when you bolded it.</font></s><br />
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*<font color=dodgerblue>The beginning of this section (explaining that light travels at different speeds in different materials) was good, and the ending seemed clear too (explaining different refractive indices and connecting them to the diagram), but I think you need to be more explicit in the middle about how light changing speeds changes the angle of the ray. I think I kind of remember it from physics, but if you want to write the basic description for someone who knows no physics, you're going to have to spell it out.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC) I added some more text to this section. I don't know if it's clear enough so have a look. <br />
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* "It is <math>3.0 x 10^8 \mathrm{m}/\mathrm{s}</math>" ?<br />
<font color=red>xd 14:23, 22 June 2011 (UTC) I think you mean <math>3.0 \times 10^8 \mathrm{m}/\mathrm{s}</math></font color><br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I fixed this. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) The speed of light differs when it travels through a certain medium" -- you mean ANOTHER medium, I bet.<br />
"index of refractive,"n""-- don't you mean "index of REFRACTION?<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) Sorry. I fixed these grammatical errors. <br />
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"The ratio of the speed of light in a vacuum, "c", and the speed of light in a medium, "v", is the index of refraction , "n"" -- it would help some of us if you wrote n = c/v.<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I have included the mathematical representation of the description. <br />
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Generally, clear writing.<br />
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===Definition===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*''Snell's law relates the angle of incidence and refraction along with the index of refraction for media. ''<br />
::I don't really understand this sentence. I don't know what you mean by "media", and I think maybe you mean "angles" because there's two of them? And I find the sentence structure "X relates Y and Z along with W" a little confusing. Something like "X gives the relationship between Y, Z, and W" or "X relates Y and Z to W" would be clearer, I think.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC) I have rearranged the sentence. <br />
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*<font color=dodgerblue>I'd really like for there to be some sort of words version of the law after you give the equation. What does the equation mean? Just that the amount of refraction is dependent upon the indices of refraction?</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC)I've added a word explanation of the Law at the beginning. Tell me what you think about it.<br />
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==A More Mathematical Explanation==<br />
<s>*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC): ''Below give two methods in deriving Snell's Law, additional information, and problems that you can solve. ''<br />
::This sentence doesn't mean what you want it to mean. Try "Given below are two methods…"</font><br />
</s><br />
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===Deriving Snell's Law with Refraction===<br />
<s><font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC):<br />
*I don't think you should just call it "Snell" in the subject heading here, it should be "Snell's Law"</font></s><br />
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<s>*<font color=dodgerblue>Typo: ''Speed is based on'' '''how''' ''much distance is traveled in an amount of time.''</font></s><br />
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*<s><font color=dodgerblue>You're missing punctuation between the sentence that begins "The wavelength in a medium…" and the one that begins "It was mentioned…"</font></s><br />
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<s>*<font color=dodgerblue>''Equate for the common hypotenuse gives:''<br />
::First, the equation after this isn't showing up. Second, I think maybe you mean "Solving for" and not "Equate"?</font></s><br />
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*<font color=dodgerblue>Are you sure your math in this section is right? In the last equation, n<sub>1</sub> and n<sub>2</sub> are on the same side as the thetas with the same index, but in the equation before that, they're still on the sides with the matching thetas, but are in the denominator. I don't know if I explained that well - what I'm trying to say is that it looks to me like you simplified <math>\frac{1}{n} \sin(\theta)</math> to <math>n \sin(\theta)</math>. </font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:37, 13 July 2011 (UTC) Do you think it's best that I put parentheses around theta. I don't really do that when I'm writing out my math on a piece of paper even though I know it's suppose to be there? <br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:27, 13 July 2011 (UTC)I have changed the syntax of the math so that the steps looks more clear. <br />
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<s>*[[User:Rebecca|Rebecca]] 01:47, 7 July 2011 (UTC) I would bold "period" when you define it.<br />
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===Total Internal Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:16, 6 July 2011 (UTC):<br />
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*I don't understand your first paragraph in this section. I think it's a combination of confusing wording and me having a hard time visualizing what you're talking about.</font><br />
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*<font color=dodgerblue>I don't think you really mean to write "sin<sub>1</sub>", but I don't know what you actually are trying to say.</font><br />
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*<font color=dodgerblue>I guess I really just don't understand this section. I don't know what the purpose of it is - I thought you said we were going to do two derivations of Snell's Law, but this doesn't look like a derivation. It'll probably help when you get your pictures in there, but it might be a good idea to go over the text with someone who understands the physics and try and make it clearer.</font><br />
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===Snell Law's on the Beach===<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I think the lifeguard example is a good one, but if you're using it just to begin the derivation, you should make that clearer at the start - I thought we were doing an example problem, but then when I saw the next heading, I was like, "huh? why is there a derivation here??"</font><br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) Lifeguard is one word.<br />
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* I think your diagram for the beach problem is helpful, but your black and red lines for "path with the least water" and "path with the least sand" aren't exactly true. For example, the black line shows just one choice of path with the least water. You could also run directly to the point where the T in "path with the least time" intersects the black line, and then run to the water and you'd still spend the same amount of time in the water. I'm not sure if there's a way to change this, and if not, don't worry too much. Just figured I'd point it out and maybe some of the other imagers have ideas. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 23:49, 13 July 2011 (UTC) I see what you mean, but I thought I would outlined the most common option a person would have if they were to point how the path with the least ____ (insert word). I'll ask other people what they think about it.</font> <br />
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====Deriving Snell With Fermat====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I found it kind of weird the way you said that it's usually "required" in middle school that you know d = rt. I think perhaps it would be better just to say "Recall that distance equals rate multiplied by time"</font><br />
<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) I took this sentence out and put in what you suggested.</font> <br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) "Usually in middle school, it's required that everyone know distance is equal to the rate times time (d=rt)." I would remove this sentence. I think it might intimidate people if they didn't learn this in middle school or they forgot it, and you don't really need it. Maybe also remove "Velocity is easy though." I think it's the same idea- if people don't immediately understand they will get discouraged. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC)<font color=violet>I took out both of these sentences and said to rename rate as velocity.</font><br />
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* When you say "So the total time from point A to point B is..." I think you need another sentence of explanation. Maybe try... "Using plugging these formulas for distance into the equation for time, we can find the total time from point A to point B. It is:"<br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>Thanks. I used your sentence which was very clear.</font> <br />
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* I don't think you're really crossing out the 1/2 in the next line... you're multiplying both sides by 2 to make the 1/2 disappear. To show this I think you need to add an extra step. Also, you proceed to say that the two expressions are the same.... but it's not that easy to see. You'll have to reduce it more to show that they're actually the same. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>I made it into more steps and included your suggestions about 2 vs. 1/2.</font><br />
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==Why It's Interesting==<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:20, 6 July 2011 (UTC): I thought the mirages were definitely a reason why it's interesting! I didn't know that at all.</font><br />
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* <font color=slateblue>[[User:Rebecca|Rebecca]] 01:49, 7 July 2011 (UTC) I can't wait to see the new Why It's Interesting section and the applet! Nice work on this page. </font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:05, 13 July 2011 (UTC) I decided to put the total internal reflection part in this section, which I am revising. I plan to talk about fiber optic cables. Also, I want to expand on mirages if I can find a credible source. Lastly, people from Drexel suggest I do a section on ray tracing (this usually has to do with real/virtual images and what the eye sees.)</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Snell%27s_Law&diff=25634Talk:Snell's Law2011-07-16T01:14:09Z<p>Rebecca: /* Law of Reflection */</p>
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<div>=General Comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:27, 6 July 2011 (UTC): Ok, so I took physics in high school, but it was a terrible class and I barely understood any of it, so I thought I'd give you some feedback from the perspective of someone who doesn't know or like physics. <br />
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:Your unhidden stuff is clear, but if I was just browsing, I probably wouldn't have read the hidden section. That's largely due to the fact that it's pretty much all physics and I just don't like physics, but I think your MME is also less clear than your Basic Description. I don't think you need to dumb it down or anything, you should be writing the section for someone who has a bit more physics than me anyway, but I think a little bit more outlining/sign-posting/telling the reader what you're doing in each section would be a good idea, and I pointed out a couple sections where you might want to go over the wording of your explanations with someone who understands what you're trying to say.<br />
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*<font color=violet> [[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Alright, that sounds like good feedback to me. I'll work on trying to make things a bit more understandable. For the math section I'll give a mini summary before I do any steps. So, hopefully that will help.</font> <br />
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:Anyway, I think you've got a really good start here. You did an especially good job of defining your terms in the basic description - clear and concise.</font><br />
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*<font color=blue>[[User:ifayanj|Dayo]] 16:53, 28 June 2011 (UTC) I would try to change the second sentence of the image description up top. It seems a bit awkward. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) Is it still awkward now? If so, what do you suggest?</font><br />
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:I really like the page though, and think its' a good topic. If having too much physics is the problem I would try to say more about images or how it effects images (which it really does!) "The snell's law on the beach section": it's a really cool application, but I would try to put it under a different heading, maybe an, "applications and examples" section.</font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 15:50, 13 July 2011 (UTC) No, I want the Snell's Law on the beach to lead into the idea of Fermat Principle and the derivation. It's just a quick analogy so that people can understand that light travel in the least time. I did provide examples later on and the application is more in the why it's interesting section.</font><br />
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*<font color=red>xd 14:25, 22 June 2011 (UTC) Is this too much physics? Of course. You are writing about a law in physics on Math Images Page. But if you want to continue this page, you have live with this. In addition, I think it would be advisable to look at wikipedia's page and think about what kind of new stuff you can offer than what is already there. If not, then I think you should take on a new project that is not explored very much.</font color><br />
::[[User:Ljeanlo1|Leah]] 19:35, 24 June 2011 (UTC)Although this is a physic topic, I just want to make sure it's capable of being a math image page.<br />
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=Section-specific comments=<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC): ''Snell's Law is a mathematical formula that predicts the amount of bend.'' - amount of bend in what? Feels like the sentence stopped before it was over.</font><br />
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:[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Would it be better if I end off with "seen in the image"? <br />
::<font color=dodgerblue>Yeah, I think that'd be fine. Or you could say that it predicts the amount that light bends. You just need to tie the bending down somewhere, because it's not like Snell's Law is predicting the amount that like, a tree branch or a river or my left pinky finger bends. ([[User:Kderosier|Kate]] 14:51, 7 July 2011 (UTC))</font><br />
[[User:Ljeanlo1|Ljeanlo1]] 15:51, 13 July 2011 (UTC) Ok, got it. <br />
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==Basic Description==<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''Geometrical optics will requires basic knowledge of geometry specifically on triangles.''<br />
::I think this sentence should be "Understanding geometrical optics requires basic knowledge of geometry and triangles."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence.<br />
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*<font color=dodgerblue>''In contrast, light can sometimes be treated as a wave which is found in physical optics, but that involves the interference and propagation of waves which will require more insight into physics.''<br />
::Even though you follow it by saying that physical optics won't be discussed, this sentence is a little intimidating to read. You might want to see if you can find a less detailed way of saying that there's other ways of understanding light.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC)I have broken this up and wrote that it will not be discussed. I think it's important to add little snippets of other topics in case anyone would like to learn about physical optics on a quick wiki search. Also, I took out the concept of physical optics and just said that light sometimes behaves in a different way. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) "geometrical optics where it's known that light travels in a straight line called a ray"--but you're talking about when it doesn't!<br />
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*[[User:Rebecca|Rebecca]] 01:45, 7 July 2011 (UTC) "Physical optics will not be discussed...." I would add "on this page."<br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:07, 13 July 2011 (UTC) I included this. <br />
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===Law of Reflection===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*<s>''The incident ray makes with the normal an angle of incidence.''<br />
::The wording here confused me, it might sound better to say "The angle that the incident ray makes with the normal is called the angle of incidence."</s></font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) Changed the sentence. <br />
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*<font color=dodgerblue>I need a bit more explanation for why Image 3 shows distortion and Image 2 doesn't - to me, they both look like they're essentially the same thing as Image 1 - there's multiple light rays in each picture, and each ray follows the law of reflection. Is the point that in Image 2 the light rays enter and exit in parallel with each other? If so, shouldn't the light rays in Image 3 enter in parallel and then exit in different directions? (Right now, the rays in Image 3 look totally unrelated to each other to me.)</font><br />
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<font color=slateblue><br />
<s>*[[User:Rebecca|Rebecca]] 01:46, 7 July 2011 (UTC) "The reflected ray holds the same property of making an angle of reflection with the normal." I'm not sure if you need this sentence because if it reflects it seems sort of obvious that it would make an angle. <br />
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<font color=slateblue><br />
* Bolding new words that you're defining really helps in this section.</s><br />
* [[User:Rebecca|Rebecca]] 01:14, 16 July 2011 (UTC) This section is great now. I think it's very clear. Only one question: is this actually a law of reflection? If so, what is the law specifically? If you can identify a law in here I think that would be helpful. Otherwise, I think the section would be more appropriately named "Reflection of Light" or something like that. <br />
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===Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):</font><br />
*<font color=dodgerblue>''It is 3.0 x 10^8 m/s '' - you should probably make that 8 an actual super script. I don't know how to type the html so that you can see the code, but I guess you can just look at this under edit - it should look like this: 10<sup>8</sup> </font><br />
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*<font color=dodgerblue>When you're typing "c" and "v" and "n", do you mean ''c'' and ''v'' and ''n''? </font><br />
::[[User:Ljeanlo1|Ljeanlo1]] 23:56, 6 July 2011 (UTC) I'll put it in italics instead of quote marks.<br />
:::<font color=dodgerblue>I mean, you don't have to. That's just how I would do it, and I know a lot of the time I mess up quotation marks with two single quotes and don't get italics where I want them, so I thought I'd ask.([[User:Kderosier|Kate]] 14:55, 7 July 2011 (UTC))</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC)No, it's ok. I think I should be consistent. <br />
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<s>*<font color=dodgerblue>''such as air and carbon dioxide, have an index of refractive'' - should that be "index of refraction"? I don't know the terminology, but that's what you called it when you bolded it.</font></s><br />
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*<font color=dodgerblue>The beginning of this section (explaining that light travels at different speeds in different materials) was good, and the ending seemed clear too (explaining different refractive indices and connecting them to the diagram), but I think you need to be more explicit in the middle about how light changing speeds changes the angle of the ray. I think I kind of remember it from physics, but if you want to write the basic description for someone who knows no physics, you're going to have to spell it out.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 16:41, 13 July 2011 (UTC) I added some more text to this section. I don't know if it's clear enough so have a look. <br />
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* "It is <math>3.0 x 10^8 \mathrm{m}/\mathrm{s}</math>" ?<br />
<font color=red>xd 14:23, 22 June 2011 (UTC) I think you mean <math>3.0 \times 10^8 \mathrm{m}/\mathrm{s}</math></font color><br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I fixed this. <br />
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[[User:Gene|Gene]] 19:13, 24 June 2011 (UTC) The speed of light differs when it travels through a certain medium" -- you mean ANOTHER medium, I bet.<br />
"index of refractive,"n""-- don't you mean "index of REFRACTION?<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) Sorry. I fixed these grammatical errors. <br />
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"The ratio of the speed of light in a vacuum, "c", and the speed of light in a medium, "v", is the index of refraction , "n"" -- it would help some of us if you wrote n = c/v.<br />
*[[User:Ljeanlo1|Leah]] 19:32, 24 June 2011 (UTC) I have included the mathematical representation of the description. <br />
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Generally, clear writing.<br />
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===Definition===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 16:39, 6 July 2011 (UTC):<br />
*''Snell's law relates the angle of incidence and refraction along with the index of refraction for media. ''<br />
::I don't really understand this sentence. I don't know what you mean by "media", and I think maybe you mean "angles" because there's two of them? And I find the sentence structure "X relates Y and Z along with W" a little confusing. Something like "X gives the relationship between Y, Z, and W" or "X relates Y and Z to W" would be clearer, I think.</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC) I have rearranged the sentence. <br />
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*<font color=dodgerblue>I'd really like for there to be some sort of words version of the law after you give the equation. What does the equation mean? Just that the amount of refraction is dependent upon the indices of refraction?</font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:16, 13 July 2011 (UTC)I've added a word explanation of the Law at the beginning. Tell me what you think about it.<br />
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==A More Mathematical Explanation==<br />
<s>*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC): ''Below give two methods in deriving Snell's Law, additional information, and problems that you can solve. ''<br />
::This sentence doesn't mean what you want it to mean. Try "Given below are two methods…"</font><br />
</s><br />
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===Deriving Snell's Law with Refraction===<br />
<s><font color=dodgerblue>[[User:Kderosier|Kate]] 17:05, 6 July 2011 (UTC):<br />
*I don't think you should just call it "Snell" in the subject heading here, it should be "Snell's Law"</font></s><br />
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<s>*<font color=dodgerblue>Typo: ''Speed is based on'' '''how''' ''much distance is traveled in an amount of time.''</font></s><br />
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*<s><font color=dodgerblue>You're missing punctuation between the sentence that begins "The wavelength in a medium…" and the one that begins "It was mentioned…"</font></s><br />
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<s>*<font color=dodgerblue>''Equate for the common hypotenuse gives:''<br />
::First, the equation after this isn't showing up. Second, I think maybe you mean "Solving for" and not "Equate"?</font></s><br />
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*<font color=dodgerblue>Are you sure your math in this section is right? In the last equation, n<sub>1</sub> and n<sub>2</sub> are on the same side as the thetas with the same index, but in the equation before that, they're still on the sides with the matching thetas, but are in the denominator. I don't know if I explained that well - what I'm trying to say is that it looks to me like you simplified <math>\frac{1}{n} \sin(\theta)</math> to <math>n \sin(\theta)</math>. </font><br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:37, 13 July 2011 (UTC) Do you think it's best that I put parentheses around theta. I don't really do that when I'm writing out my math on a piece of paper even though I know it's suppose to be there? <br />
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[[User:Ljeanlo1|Ljeanlo1]] 17:27, 13 July 2011 (UTC)I have changed the syntax of the math so that the steps looks more clear. <br />
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<s>*[[User:Rebecca|Rebecca]] 01:47, 7 July 2011 (UTC) I would bold "period" when you define it.<br />
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===Total Internal Refraction===<br />
<font color=dodgerblue>[[User:Kderosier|Kate]] 17:16, 6 July 2011 (UTC):<br />
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*I don't understand your first paragraph in this section. I think it's a combination of confusing wording and me having a hard time visualizing what you're talking about.</font><br />
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*<font color=dodgerblue>I don't think you really mean to write "sin<sub>1</sub>", but I don't know what you actually are trying to say.</font><br />
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*<font color=dodgerblue>I guess I really just don't understand this section. I don't know what the purpose of it is - I thought you said we were going to do two derivations of Snell's Law, but this doesn't look like a derivation. It'll probably help when you get your pictures in there, but it might be a good idea to go over the text with someone who understands the physics and try and make it clearer.</font><br />
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===Snell Law's on the Beach===<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I think the lifeguard example is a good one, but if you're using it just to begin the derivation, you should make that clearer at the start - I thought we were doing an example problem, but then when I saw the next heading, I was like, "huh? why is there a derivation here??"</font><br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) Lifeguard is one word.<br />
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* I think your diagram for the beach problem is helpful, but your black and red lines for "path with the least water" and "path with the least sand" aren't exactly true. For example, the black line shows just one choice of path with the least water. You could also run directly to the point where the T in "path with the least time" intersects the black line, and then run to the water and you'd still spend the same amount of time in the water. I'm not sure if there's a way to change this, and if not, don't worry too much. Just figured I'd point it out and maybe some of the other imagers have ideas. <br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 23:49, 13 July 2011 (UTC) I see what you mean, but I thought I would outlined the most common option a person would have if they were to point how the path with the least ____ (insert word). I'll ask other people what they think about it.</font> <br />
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====Deriving Snell With Fermat====<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:18, 6 July 2011 (UTC): I found it kind of weird the way you said that it's usually "required" in middle school that you know d = rt. I think perhaps it would be better just to say "Recall that distance equals rate multiplied by time"</font><br />
<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) I took this sentence out and put in what you suggested.</font> <br />
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*[[User:Rebecca|Rebecca]] 01:48, 7 July 2011 (UTC) "Usually in middle school, it's required that everyone know distance is equal to the rate times time (d=rt)." I would remove this sentence. I think it might intimidate people if they didn't learn this in middle school or they forgot it, and you don't really need it. Maybe also remove "Velocity is easy though." I think it's the same idea- if people don't immediately understand they will get discouraged. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC)<font color=violet>I took out both of these sentences and said to rename rate as velocity.</font><br />
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* When you say "So the total time from point A to point B is..." I think you need another sentence of explanation. Maybe try... "Using plugging these formulas for distance into the equation for time, we can find the total time from point A to point B. It is:"<br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>Thanks. I used your sentence which was very clear.</font> <br />
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* I don't think you're really crossing out the 1/2 in the next line... you're multiplying both sides by 2 to make the 1/2 disappear. To show this I think you need to add an extra step. Also, you proceed to say that the two expressions are the same.... but it's not that easy to see. You'll have to reduce it more to show that they're actually the same. <br />
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[[User:Ljeanlo1|Ljeanlo1]] 18:00, 13 July 2011 (UTC) <font color=violet>I made it into more steps and included your suggestions about 2 vs. 1/2.</font><br />
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==Why It's Interesting==<br />
*<font color=dodgerblue>[[User:Kderosier|Kate]] 17:20, 6 July 2011 (UTC): I thought the mirages were definitely a reason why it's interesting! I didn't know that at all.</font><br />
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* <font color=slateblue>[[User:Rebecca|Rebecca]] 01:49, 7 July 2011 (UTC) I can't wait to see the new Why It's Interesting section and the applet! Nice work on this page. </font color><br />
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<font color=violet>[[User:Ljeanlo1|Ljeanlo1]] 18:05, 13 July 2011 (UTC) I decided to put the total internal reflection part in this section, which I am revising. I plan to talk about fiber optic cables. Also, I want to expand on mirages if I can find a credible source. Lastly, people from Drexel suggest I do a section on ray tracing (this usually has to do with real/virtual images and what the eye sees.)</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Dimensions&diff=24416Talk:Dimensions2011-07-12T02:04:38Z<p>Rebecca: /* Basic Description */</p>
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<div>=General Comments=<br />
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=Section-specific Comments=<br />
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==Basic Description==<br />
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<font color=dodgerblue>[[User:Kderosier|Kate]] 15:33, 9 June 2011 (UTC):<br />
*It's mildly (very mildly) confusing to say that "forward ''and'' backward" together comprise one direction - I think it might be better to use "forward-backward", "left-right", and "up-down" to emphasize that each really is only one direction.<font color=Mediumblue>CHECK</font><br />
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*I'm not 100% sure what you mean by a dimension "corresponding" with a certain number of directions. I think it might be clearer to say that a certain dimensional space has that many directions of possible motion.<font color=Mediumblue>CHECK</font><br />
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*be consistent between things like "one dimensional", "3D", and "zeroth dimension"<font color=Mediumblue>I'm trying.</font><br />
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*font color=slateblue>[[User:Rebecca|Rebecca]] 02:04, 12 July 2011 (UTC) I'd like to see you add some pictures to this section. Even if they're just there to break up text (like a picture of mario), it think they would improve the section.<br />
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===Dimensions of Objects===<br />
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*<font color=dodgerblue>[[User:Kderosier|Kate]] 20:06, 11 July 2011 (UTC): I vehemently disagree with the current state of your second paragraph in this section, most specifically with the comment:<br />
::''Although one may contend that a string and a flattened quarter are 3 dimensional because they do still have length, width, and height, they are only analogies for an ideal 1 dimensional line and 2 dimensional disk within 3 dimensional space.''<br />
:'''This is just fundamentally untrue.''' A string and a flattened quarter are ''not'' "only analogies" for mathematical concepts - they are real, physical objects which can be ''used'' or ''interpreted'' as analogies. You ''cannot say'' that a physical object "is" an analogy! That's not what "analogy" means! <br />
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:I know you're concerned about not confusing people by going into detail about the difference between something being one dimensional and something ''representing'' a one dimensional object, but that is no excuse to totally abandon all accuracy to how things actually are! I contend that a reader will be ''more'' confused by this assertion that any and all strings and quarters are "only analogies" - readers have handled strings and quarters before, they've held them in their hands, and they understand them to be real, physical objects. When you say that these things are "only analogies", you're saying that ''each and every single string and flattened quarter in existence'' is not a physical object but rather a linguistic construction used to simplify one thing by comparing it to something familiar - a claim that is false and off-putting to the reader.<br />
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:Second, whatever explanation you choose to make about strings and quarters actually being three dimensional, I don't think it should come at the end as an after thought. This is an important issue, and you should mention it ''before'' making the comparisons.<br />
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<font color=Mediumblue>CHECK</font><br />
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<font color=Mediumblue>CHECK</font><br />
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<font color=dodgerblue><br />
*''On the disk, (best thought of as a filled in circle) there are two directions akin to up and down, right and left, making the disk two dimensional.''<br />
:I think the comma should come after the parenthetical, not before.<font color=Mediumblue>CHECK</font><br />
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<font color=dodgerblue><br />
*I think you should mention that although our representation of a line may have width, we are intending to represent an object with no width. Otherwise, when I think of a string, I can see that it actually does have three dimensions.</font><br />
:<font color=Mediumblue>I think that this is confusing. We seem to be contradicting ourselves. I think if we don't complicate it, it won't be as confusing.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 19:12, 10 June 2011 (UTC): Wait, so you're saying you think it's ''more'' confusing to explain that while a ''picture of a line'' may have height as well as length an actual ''line'' only has length? I disagree. I know that when I first ran into people talking about dimensions, I thought that it didn't make sense because even though a line that I drew in pencil or on the computer was thin enough that I probably couldn't measure it, it did have more than zero thickness. Zero thickness may be harder to visualize, but I think it's ''accurate'' and not ''contradictory''.<br />
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:::<font color=Mediumblue>I recognize the importance of explaining the imperfections in one's analogies. Nevertheless, it is trick to be able to do so without sounding hypocritical or confusing. I put this at the end of the paragraph in question, hopefully it is explanatory without being contradicting: Although one may contend that a string and a flattened quarter are 3 dimensional because they do still have length, width, and height, they are only analogies for an ideal 1 dimensional line and 2 dimensional disk within 3 dimensional space.</font><br />
::::<font color=dodgerblue>Disagree so much. See above.</font><br />
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*<font color=red>xd 21:08, 13 June 2011 (UTC) I don't think the sentence "the circle is a LINE joint front to back" is accurate. LINE extends infinitely to both direction. LINE segment has a starting and ending point. So in this case, if you insist on this analogy, you should say LINE SEGMENT instead of line.</font><font color=Mediumblue>CHECK</font><br />
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===Dimensions of Spaces===<br />
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<font color=dodgerblue><br />
*Is the Snake in the game really 1D? It clearly has height in the image. I understand the point you're trying to make, but I think there's got to be a better example. What about a movie projected on a screen?</font><br />
:<font color=Mediumblue>It's the only half-way decent image of the game I could find.</font><br />
::<font color=dodgerblue>I think you misunderstood me - it's not an issue with the quality of the picture. In that game, I maintain that the snake itself is 2D, as the blocks it's made out of have both height and width. <br />
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:<font color=Mediumblue>rectified</font><br />
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*<font color=slateblue>[[User:Rebecca|Rebecca]] 02:04, 12 July 2011 (UTC) Infinitely many dimensions exist, and when talking about and arbitrary dimension, the term "n-dimensional" is used. The use of multiple dimensions has many concrete applications as well. <br />
:* What about... "There are in fact an infinite number of dimensions, so when we talk about an arbitrary number of dimensions, we use the term "n-dimensional." Feel free to use your own wording, I just thought your original sentence was a bit clunky. </font color><br />
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==Four Dimensions==<br />
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<font color=dodgerblue>[[User:Kderosier|Kate]] 15:33, 9 June 2011 (UTC):<br />
*It'd be nice to have sort of a mission statement for this section - let the reader know that you're going to be building up to an understanding of four-dimensionality.<br />
</font><br />
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<font color=dodgerblue><br />
*Also, why are you enclosing your tuples in curly brackets? Isn't it typical to write points like (x), (x,y), (x,y,z), etc.?</font><br />
:<font color=Mediumblue>I don't know, maybe because that is how you do it in mathematica. Thanks for letting me know.</font><br />
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===1D===<br />
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<font color=dodgerblue><br />
*''Dimensions are represented mathematically by a coordinate variable. '''An''' point specified by one variable, such as x=8, can be plotted on the 1D number-line, also known as the x-axis, at the point {8}, as shown below. ''<br />
:This makes almost no sense to me. I don't think that your first sentence is accurate - the whole concept of a dimension isn't represented by a single coordinate. Although, do you mean that something like "X" in "x-axis" stands in for one direction? I thought you were saying something like (8) represented the concept of one-dimensionality. Also, typo at the beginning of the second sentence.<font color=Mediumblue>CHECK</font><br />
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===2D===<br />
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<font color=dodgerblue><br />
*This section is clearer than the 1D section, but check it for typos.<br />
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===3D===<br />
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<font color=dodgerblue><br />
*Again, check for typos.<br />
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*The image is a little confusing. I'd like it if the negative z axis continued beyond the horizontal dotted line. Also, your z-coordinate is given as positive 6, but the line appears to be going backwards.<font color=Mediumblue>After much editing, I fixed both the braces and the z-axis problems.</font><br />
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===4D===<br />
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<font color=dodgerblue><br />
*Since what you've (presumably) been trying to do all along is present an analog in lower dimensions, I think you should bring up the point about how 2D points can look the same when viewed in 1D earlier, and instead just refer back to it here.<br />
</font><font color=Mediumblue>I changed the example.</font><br />
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*As part of that example, I don't think you mean "when looked at from above", but rather something like "when looked at from the x-axis" or something. To me, above is out of the graph looking down (like looking out of an airplane).<br />
</font><font color=Mediumblue>I changed the example.</font><br />
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<font color=dodgerblue><br />
*I'm not sure this section would really explain 4D to me if I didn't already feel comfortable with it, but I can't really put my finger on what should be added. It just seems too short to adequately address the issue.<br />
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*<font color=red>xd 21:12, 13 June 2011 (UTC) Why don't you mention the 4th physical dimension being time. For example, the first three coordinates describes where the object is in space, and the forth variable describes where it is in time.</font><font color=Mediumblue>CHECK</font></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Anne_Burns%27_Mathscapes&diff=24415Talk:Anne Burns' Mathscapes2011-07-12T01:49:28Z<p>Rebecca: /* Plants */</p>
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<div>=General Comments=<br />
<br />
* <font color=slateblue> [[User:Rebecca|Rebecca]] 01:42, 12 July 2011 (UTC) I don't have any big suggestions for this page. I think it's great the way it is... there are just a few small things I would change. </font color=slateblue><br />
<br />
Old comments: {{Hide|1=<br />
<font color=red>xd 20:46, 14 June 2011 (UTC) If you want to expand on this page, I feel maybe you can do a few specific and yet simple example of how to recursively create plant or generate 3D mountain.</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 16:55, 15 June 2011 (UTC): That's a good idea, but I'm not sure my own computer skills are up to it. I think I'll ask the CS people if they can make an applet for it.</font><br />
}}<br />
<br />
=Section-specific comments=<br />
==Basic Description==<br />
<br />
Old comments: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Make this section start after the main image. Use: <nowiki><br style="clear: both" /></nowiki> before the section title to do this.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 16:59, 20 June 2011 (UTC): good tip, thanks!</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>I hate to be nit-picky, but reconsider your the sentence.</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>What is "''fractal methods''"? If it is a specific process, then define it. If not, then perhaps say something like: "... using fractal geometry."</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:00, 20 June 2011 (UTC): This paragraph was taken from one of the pre-existing pages that I got these pictures from. I agree that there's a lot of problems with it, I think I'll just scrap it and write my own.</font><br />
}}<br />
<br />
==A More Mathematical Explanation==<br />
===Plants===<br />
<br />
* "Notice that the second image didn't change, because it's string didn't contain an L." <br />
:*<font color=slateblue> [[User:Rebecca|Rebecca]] 01:49, 12 July 2011 (UTC) I would say "Notice that the second flower didn't change from Image 5 to Image 6 because the string didn't contain an L." It's just a little confusing because it could be read to mean that the second image is image 6.</font color><br />
<br />
Old comments: {{Hide|1=<br />
<s><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Explain "recursive replacement" because I didn't find it when I did a quick search on the Blue Fern page.<br />
</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>define: "trigonometric sums" and "3-D transformation".</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>The last sentence is too dense and technical heavy.</font> <br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"... Burns' plants aren't straight-forward fractals that are exactly self-similar into infinity"</font><br />
:<font color=Mediumblue>Awkward, try: "... Burns' plants are not (see below) fractals that are precisely and infinitely self-similar"</font><br />
::<font color=Mediumblue>"simple", "clear-cut", or "perfect" instead of "straight-forward", I recommend "perfect".</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"...some randomization is built in..."</font><br />
:<font color=Mediumblue>Would sound more natural if you said "... Burns uses some randomization in her equations ..."</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"... can be replaced by a smaller version of the original image, and so on and so on until the pictures are quite complicated."</font><br />
:<font color=Mediumblue>Not fond of the double use of "and so on". sounds too lackadaisical. Also, tense mix up with "are". Try rephrasing it like this: "... can be replaced by a smaller version of the original image, Which in turn can be replaced by an even smaller version, and so on until the pictures become quite complicated."</font><br />
</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:20, 6 July 2011 (UTC): Rewrote a bunch of things, addressed all of these points.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"The pictures can be made to look more natural by using random numbers to vary the length of the branches or the angle at which they connect."</font><br />
**<font color=Mediumblue>Good, clear explanation.</font><br />
<br />
<s><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"Another way to vary an image is to use the deReffye method. In this method, at each stage a branch can either continue to grow, die, or wait until the next stage. Each option has a certain probability, and all the probabilities add up to one."</font><br />
**<font color=Mediumblue>I recommend changing the first sentence to the active voice. If you choose not to, however, then combine the two into once sentence.</font><br />
**<font color=Mediumblue>Instead of just "vary an image" say what you are varying. Either that, or pick another word. You could try "introduce variation," which, though it may sound the same, is more of a complete proposition than simply "to vary".</font><br />
**<font color=Mediumblue>I'm confused by your explanation of the deReffye method. It took a bit of thought to connect the term "stage" with ''an iteration of the function''. Clarify this. Also, I recognize how branches can continue, or die (stop), put the stopping and starting confused me. I assume you don't mean that the branch will stop, and then smaller branches will be suspended above it in mid air where it starts again, which is the first notion that came to mind. If I am correct, you are referring to a branch not being given intermittent size branches, but, rather, skipping that iteration and continuing straight to twigs. Explain that this is what you mean (If indeed it is).</font><br />
**<font color=Mediumblue>Instead of "option" try "outcome".</font><br />
**<font color=Mediumblue>I believe it is only important to say that the probabilities add to 1 if you then explain that is means that there is a 100% chance that every branch will follow at least one of these options (and here I mean option, not outcome). Nevertheless, it is already implied that every branch does at least one of these, so the remark is unnecessary.</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"You can also make the probabilities change over time, so that at later stages, the branches are more likely to die (and thus the plant eventually stops growing)."</font><br />
**<font color=Mediumblue>Introducing the pronoun "you" does not fit with the trend established so far in this section. Also, ditch the parenthesis.</font><br />
</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): Section re-written. Some of the questions you asked were things I just don't know, because she wasn't clear about it in my source material, but I addressed all the other points.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>The arrangement of the tree images is awkward. try doing two on a first line and one on a second below that. This would be particularly appropriate given that the first two images serve as examples for a different process than that represented in the third image.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): I actually think this is fine, and given that I'm hoping to add an applet later, I'm going to leave things where they are for now.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>I don't understand your explanation of string-rewriting.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): Re-written and images added. Hopefully it's clearer now.</font><br />
}}<br />
<br />
===Clouds & Mountains===<br />
<br />
Old comments: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>First paragraph has lots of unexplained terms:</font><br />
**<font color=Mediumblue>"two-dimensional height field"</font><br />
**<font color=Mediumblue>"projected" (in what sense)</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:12, 6 July 2011 (UTC): I can't answer this question, the source doesn't say.</font><br />
**<font color=Mediumblue>"three-dimensional image into two-dimensional space"</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"Over time, the random numbers added to the heights are scaled down."</font><br />
**<font color=Mediumblue>You never introduced what part of this model corresponds to the height, and how so.</font><br />
**<font color=Mediumblue>In addition to your next sentence, which is good, further explain how scaling down the magnitude of the random number as the iterations increase creates a form that has a bumpiness that is on the same scale as the part of the surface it takes up. Namely, features that impact a large portion of the form are large, while the bumps that impact only a small fraction of the form are small.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>last paragraph could use some more explanation. It made sense to me, but I can see it being clearer if more things are explained, and if you go through the process a bit more slowly.</font><br />
**<font color=Mediumblue>Explain that the z-axis is the up and down direction.</font><br />
**<font color=Mediumblue>Explain what is being done with the trig and calc: perhaps: "trig and calc are used to rotate the form so it is viewed side-on, rather than from above, then it is projected, turned into a 2D image, etc. ..."</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:12, 6 July 2011 (UTC): I can't answer this question, the source doesn't say.</font><br />
<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:14, 6 July 2011 (UTC): I'm just going to interpret this as being that I need to rewrite this section, and hide the specifics.</font><br />
}}<br />
<br />
==Why It's Interesting==<br />
<br />
*<s>[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Also add that, "Burns' images reveal the fractal geometry behind many natural phenomena."</font></s></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Anne_Burns%27_Mathscapes&diff=24414Talk:Anne Burns' Mathscapes2011-07-12T01:46:04Z<p>Rebecca: /* General Comments */</p>
<hr />
<div>=General Comments=<br />
<br />
* <font color=slateblue> [[User:Rebecca|Rebecca]] 01:42, 12 July 2011 (UTC) I don't have any big suggestions for this page. I think it's great the way it is... there are just a few small things I would change. </font color=slateblue><br />
<br />
Old comments: {{Hide|1=<br />
<font color=red>xd 20:46, 14 June 2011 (UTC) If you want to expand on this page, I feel maybe you can do a few specific and yet simple example of how to recursively create plant or generate 3D mountain.</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 16:55, 15 June 2011 (UTC): That's a good idea, but I'm not sure my own computer skills are up to it. I think I'll ask the CS people if they can make an applet for it.</font><br />
}}<br />
<br />
=Section-specific comments=<br />
==Basic Description==<br />
<br />
Old comments: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Make this section start after the main image. Use: <nowiki><br style="clear: both" /></nowiki> before the section title to do this.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 16:59, 20 June 2011 (UTC): good tip, thanks!</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>I hate to be nit-picky, but reconsider your the sentence.</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>What is "''fractal methods''"? If it is a specific process, then define it. If not, then perhaps say something like: "... using fractal geometry."</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:00, 20 June 2011 (UTC): This paragraph was taken from one of the pre-existing pages that I got these pictures from. I agree that there's a lot of problems with it, I think I'll just scrap it and write my own.</font><br />
}}<br />
<br />
==A More Mathematical Explanation==<br />
===Plants===<br />
<br />
Old comments: {{Hide|1=<br />
<s><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Explain "recursive replacement" because I didn't find it when I did a quick search on the Blue Fern page.<br />
</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>define: "trigonometric sums" and "3-D transformation".</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>The last sentence is too dense and technical heavy.</font> <br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"... Burns' plants aren't straight-forward fractals that are exactly self-similar into infinity"</font><br />
:<font color=Mediumblue>Awkward, try: "... Burns' plants are not (see below) fractals that are precisely and infinitely self-similar"</font><br />
::<font color=Mediumblue>"simple", "clear-cut", or "perfect" instead of "straight-forward", I recommend "perfect".</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"...some randomization is built in..."</font><br />
:<font color=Mediumblue>Would sound more natural if you said "... Burns uses some randomization in her equations ..."</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"... can be replaced by a smaller version of the original image, and so on and so on until the pictures are quite complicated."</font><br />
:<font color=Mediumblue>Not fond of the double use of "and so on". sounds too lackadaisical. Also, tense mix up with "are". Try rephrasing it like this: "... can be replaced by a smaller version of the original image, Which in turn can be replaced by an even smaller version, and so on until the pictures become quite complicated."</font><br />
</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:20, 6 July 2011 (UTC): Rewrote a bunch of things, addressed all of these points.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"The pictures can be made to look more natural by using random numbers to vary the length of the branches or the angle at which they connect."</font><br />
**<font color=Mediumblue>Good, clear explanation.</font><br />
<br />
<s><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"Another way to vary an image is to use the deReffye method. In this method, at each stage a branch can either continue to grow, die, or wait until the next stage. Each option has a certain probability, and all the probabilities add up to one."</font><br />
**<font color=Mediumblue>I recommend changing the first sentence to the active voice. If you choose not to, however, then combine the two into once sentence.</font><br />
**<font color=Mediumblue>Instead of just "vary an image" say what you are varying. Either that, or pick another word. You could try "introduce variation," which, though it may sound the same, is more of a complete proposition than simply "to vary".</font><br />
**<font color=Mediumblue>I'm confused by your explanation of the deReffye method. It took a bit of thought to connect the term "stage" with ''an iteration of the function''. Clarify this. Also, I recognize how branches can continue, or die (stop), put the stopping and starting confused me. I assume you don't mean that the branch will stop, and then smaller branches will be suspended above it in mid air where it starts again, which is the first notion that came to mind. If I am correct, you are referring to a branch not being given intermittent size branches, but, rather, skipping that iteration and continuing straight to twigs. Explain that this is what you mean (If indeed it is).</font><br />
**<font color=Mediumblue>Instead of "option" try "outcome".</font><br />
**<font color=Mediumblue>I believe it is only important to say that the probabilities add to 1 if you then explain that is means that there is a 100% chance that every branch will follow at least one of these options (and here I mean option, not outcome). Nevertheless, it is already implied that every branch does at least one of these, so the remark is unnecessary.</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"You can also make the probabilities change over time, so that at later stages, the branches are more likely to die (and thus the plant eventually stops growing)."</font><br />
**<font color=Mediumblue>Introducing the pronoun "you" does not fit with the trend established so far in this section. Also, ditch the parenthesis.</font><br />
</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): Section re-written. Some of the questions you asked were things I just don't know, because she wasn't clear about it in my source material, but I addressed all the other points.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>The arrangement of the tree images is awkward. try doing two on a first line and one on a second below that. This would be particularly appropriate given that the first two images serve as examples for a different process than that represented in the third image.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): I actually think this is fine, and given that I'm hoping to add an applet later, I'm going to leave things where they are for now.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>I don't understand your explanation of string-rewriting.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): Re-written and images added. Hopefully it's clearer now.</font><br />
}}<br />
<br />
===Clouds & Mountains===<br />
<br />
Old comments: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>First paragraph has lots of unexplained terms:</font><br />
**<font color=Mediumblue>"two-dimensional height field"</font><br />
**<font color=Mediumblue>"projected" (in what sense)</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:12, 6 July 2011 (UTC): I can't answer this question, the source doesn't say.</font><br />
**<font color=Mediumblue>"three-dimensional image into two-dimensional space"</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"Over time, the random numbers added to the heights are scaled down."</font><br />
**<font color=Mediumblue>You never introduced what part of this model corresponds to the height, and how so.</font><br />
**<font color=Mediumblue>In addition to your next sentence, which is good, further explain how scaling down the magnitude of the random number as the iterations increase creates a form that has a bumpiness that is on the same scale as the part of the surface it takes up. Namely, features that impact a large portion of the form are large, while the bumps that impact only a small fraction of the form are small.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>last paragraph could use some more explanation. It made sense to me, but I can see it being clearer if more things are explained, and if you go through the process a bit more slowly.</font><br />
**<font color=Mediumblue>Explain that the z-axis is the up and down direction.</font><br />
**<font color=Mediumblue>Explain what is being done with the trig and calc: perhaps: "trig and calc are used to rotate the form so it is viewed side-on, rather than from above, then it is projected, turned into a 2D image, etc. ..."</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:12, 6 July 2011 (UTC): I can't answer this question, the source doesn't say.</font><br />
<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:14, 6 July 2011 (UTC): I'm just going to interpret this as being that I need to rewrite this section, and hide the specifics.</font><br />
}}<br />
<br />
==Why It's Interesting==<br />
<br />
*<s>[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Also add that, "Burns' images reveal the fractal geometry behind many natural phenomena."</font></s></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Anne_Burns%27_Mathscapes&diff=24413Talk:Anne Burns' Mathscapes2011-07-12T01:42:53Z<p>Rebecca: /* General Comments */</p>
<hr />
<div>=General Comments=<br />
<br />
* <font color=slateblue> [[User:Rebecca|Rebecca]] 01:42, 12 July 2011 (UTC) I don't even have any suggestions for this page. I think it's great the way it is. </font color=slateblue><br />
<br />
Old comments: {{Hide|1=<br />
<font color=red>xd 20:46, 14 June 2011 (UTC) If you want to expand on this page, I feel maybe you can do a few specific and yet simple example of how to recursively create plant or generate 3D mountain.</font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 16:55, 15 June 2011 (UTC): That's a good idea, but I'm not sure my own computer skills are up to it. I think I'll ask the CS people if they can make an applet for it.</font><br />
}}<br />
<br />
=Section-specific comments=<br />
==Basic Description==<br />
<br />
Old comments: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Make this section start after the main image. Use: <nowiki><br style="clear: both" /></nowiki> before the section title to do this.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 16:59, 20 June 2011 (UTC): good tip, thanks!</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>I hate to be nit-picky, but reconsider your the sentence.</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>What is "''fractal methods''"? If it is a specific process, then define it. If not, then perhaps say something like: "... using fractal geometry."</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:00, 20 June 2011 (UTC): This paragraph was taken from one of the pre-existing pages that I got these pictures from. I agree that there's a lot of problems with it, I think I'll just scrap it and write my own.</font><br />
}}<br />
<br />
==A More Mathematical Explanation==<br />
===Plants===<br />
<br />
Old comments: {{Hide|1=<br />
<s><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Explain "recursive replacement" because I didn't find it when I did a quick search on the Blue Fern page.<br />
</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>define: "trigonometric sums" and "3-D transformation".</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>The last sentence is too dense and technical heavy.</font> <br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"... Burns' plants aren't straight-forward fractals that are exactly self-similar into infinity"</font><br />
:<font color=Mediumblue>Awkward, try: "... Burns' plants are not (see below) fractals that are precisely and infinitely self-similar"</font><br />
::<font color=Mediumblue>"simple", "clear-cut", or "perfect" instead of "straight-forward", I recommend "perfect".</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"...some randomization is built in..."</font><br />
:<font color=Mediumblue>Would sound more natural if you said "... Burns uses some randomization in her equations ..."</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"... can be replaced by a smaller version of the original image, and so on and so on until the pictures are quite complicated."</font><br />
:<font color=Mediumblue>Not fond of the double use of "and so on". sounds too lackadaisical. Also, tense mix up with "are". Try rephrasing it like this: "... can be replaced by a smaller version of the original image, Which in turn can be replaced by an even smaller version, and so on until the pictures become quite complicated."</font><br />
</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:20, 6 July 2011 (UTC): Rewrote a bunch of things, addressed all of these points.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"The pictures can be made to look more natural by using random numbers to vary the length of the branches or the angle at which they connect."</font><br />
**<font color=Mediumblue>Good, clear explanation.</font><br />
<br />
<s><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"Another way to vary an image is to use the deReffye method. In this method, at each stage a branch can either continue to grow, die, or wait until the next stage. Each option has a certain probability, and all the probabilities add up to one."</font><br />
**<font color=Mediumblue>I recommend changing the first sentence to the active voice. If you choose not to, however, then combine the two into once sentence.</font><br />
**<font color=Mediumblue>Instead of just "vary an image" say what you are varying. Either that, or pick another word. You could try "introduce variation," which, though it may sound the same, is more of a complete proposition than simply "to vary".</font><br />
**<font color=Mediumblue>I'm confused by your explanation of the deReffye method. It took a bit of thought to connect the term "stage" with ''an iteration of the function''. Clarify this. Also, I recognize how branches can continue, or die (stop), put the stopping and starting confused me. I assume you don't mean that the branch will stop, and then smaller branches will be suspended above it in mid air where it starts again, which is the first notion that came to mind. If I am correct, you are referring to a branch not being given intermittent size branches, but, rather, skipping that iteration and continuing straight to twigs. Explain that this is what you mean (If indeed it is).</font><br />
**<font color=Mediumblue>Instead of "option" try "outcome".</font><br />
**<font color=Mediumblue>I believe it is only important to say that the probabilities add to 1 if you then explain that is means that there is a 100% chance that every branch will follow at least one of these options (and here I mean option, not outcome). Nevertheless, it is already implied that every branch does at least one of these, so the remark is unnecessary.</font><br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"You can also make the probabilities change over time, so that at later stages, the branches are more likely to die (and thus the plant eventually stops growing)."</font><br />
**<font color=Mediumblue>Introducing the pronoun "you" does not fit with the trend established so far in this section. Also, ditch the parenthesis.</font><br />
</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): Section re-written. Some of the questions you asked were things I just don't know, because she wasn't clear about it in my source material, but I addressed all the other points.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>The arrangement of the tree images is awkward. try doing two on a first line and one on a second below that. This would be particularly appropriate given that the first two images serve as examples for a different process than that represented in the third image.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): I actually think this is fine, and given that I'm hoping to add an applet later, I'm going to leave things where they are for now.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>I don't understand your explanation of string-rewriting.</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 20:32, 6 July 2011 (UTC): Re-written and images added. Hopefully it's clearer now.</font><br />
}}<br />
<br />
===Clouds & Mountains===<br />
<br />
Old comments: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>First paragraph has lots of unexplained terms:</font><br />
**<font color=Mediumblue>"two-dimensional height field"</font><br />
**<font color=Mediumblue>"projected" (in what sense)</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:12, 6 July 2011 (UTC): I can't answer this question, the source doesn't say.</font><br />
**<font color=Mediumblue>"three-dimensional image into two-dimensional space"</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>"Over time, the random numbers added to the heights are scaled down."</font><br />
**<font color=Mediumblue>You never introduced what part of this model corresponds to the height, and how so.</font><br />
**<font color=Mediumblue>In addition to your next sentence, which is good, further explain how scaling down the magnitude of the random number as the iterations increase creates a form that has a bumpiness that is on the same scale as the part of the surface it takes up. Namely, features that impact a large portion of the form are large, while the bumps that impact only a small fraction of the form are small.</font><br />
<br />
*[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>last paragraph could use some more explanation. It made sense to me, but I can see it being clearer if more things are explained, and if you go through the process a bit more slowly.</font><br />
**<font color=Mediumblue>Explain that the z-axis is the up and down direction.</font><br />
**<font color=Mediumblue>Explain what is being done with the trig and calc: perhaps: "trig and calc are used to rotate the form so it is viewed side-on, rather than from above, then it is projected, turned into a 2D image, etc. ..."</font><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:12, 6 July 2011 (UTC): I can't answer this question, the source doesn't say.</font><br />
<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 23:14, 6 July 2011 (UTC): I'm just going to interpret this as being that I need to rewrite this section, and hide the specifics.</font><br />
}}<br />
<br />
==Why It's Interesting==<br />
<br />
*<s>[[User:Htasoff|Htasoff]] 15:35, 20 June 2011 (UTC)<font color=Mediumblue>Also add that, "Burns' images reveal the fractal geometry behind many natural phenomena."</font></s></div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=S11&diff=24412S112011-07-12T01:36:14Z<p>Rebecca: /* Harrison's Projects */</p>
<hr />
<div>__TOC__<br />
<br />
== Announcements ==<br />
For public-type help questions, see [[Help:Contents|Help]]. For Swat-specific ones, see [[Swarthmore summer research orientation]].<br />
<br />
<b>Remember to keep your projects sections short and up to date; only the last week of status changes should be mentioned. [[User:Smaurer1|Smaurer1]]</b><br />
<br />
===Group Discussion Questions===<br />
<br />
* [[Topics for conversations through Skype with RPI, SB, and/or Drexel]] Started 6/29.<br />
* [[Who are we writing for?]] Started 6/29.<br />
* [[Possibly expanding student Math Image roles]], to be addressed 7/6.<br />
<br />
===Questions:===<br />
*Things that are listed as Helper Pages but use the Image Page template<br />
:We need to decide whether these pages should be on the Helper Page template, the Image Page template, or both: {{Hide|1=<br />
:*[[Change of Coordinate Systems]] - Image template only; image template live<br />
:*[[Conic Section]] - both templates; image template not live<br />
:*[[Differentiability]] - both templates; image template not live<br />
:*[[Dot Product]] - Image template only; image template not live<br />
:*[[Gradients and Directional Derivatives]] - Image template only; image template not live<br />
:*[[Hyperbolic Geometry]] - Image template only; image template not live<br />
:*[[Inversion]] - Image template only; image template not live<br />
:*[[Iterated Functions]] - Image template only; image template not live<br />
:*[[Parametric Equations]] - Image template only; image template live<br />
:*[[Taylor Series]] - Image template only; image template not live<br />
:*[[Volume of Revolution]] - Image template only; image template live<br />
<br />
:<font color=dodgerblue>''(List complied by [[User:Kderosier|Kate]], June 16)''</font><br />
}}<br />
<br />
<br />
Older questions: {{Hide|1=<br />
*Harrison's question about text being cut off on Cross-cap: {{Hide|1=<br />
*[[User:Htasoff|Htasoff]] 14:16, 8 June 2011 (UTC)<br />
**The text in MME on the [[Cross-cap]] page is getting truncated when viewed through edit with form, but still appears on the page.<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 00:49, 14 June 2011 (UTC): When I've encountered this problem previously, it's been because a set of double curly brackets wasn't closed.</font><br />
}}<br />
<br />
*Harrison's question about creating a list of not-yet-existent Helper Pages: {{Hide|1=<br />
Harrison, 5/26/11:<br />
:*<s>We need a list of empty pages: Penrose Tiles is only linked to one, now two, pages. Empty pages like this could well fade into obscurity.</s><br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:09, 7 June 2011 (UTC): Such a list has been created. See [[Existing_Pages_Needing_Work#Empty_.28but_linked_to.29_Pages|here]].</font><br />
}}<br />
<br />
*Spam conversation: {{Hide|1=<br />
<font color=dodgerblue><br />
*[[User:Kderosier|Kate]] 14:38, 27 May 2011 (UTC): '''We have some new users who are creating a bunch of pages with links to illegally download or watch movies.''' At first, we though it might be someone from Sweet Briar practicing wiki-syntax, but now it's just starting to look like spam:<br />
**[[Watch_Sniper:_Reloaded_film_in_hd|This is the type of page I'm talking about]]<br />
**[[Special:Contributions/Calrivenick|List of pages created by Calrivenick]]<br />
**[[Special:Contributions/Cadedesi|List of pages created by Cadedesi]]<br />
</font><br />
:Let's talk about what to do this afternoon. [[User:Gene|Gene]] 15:19, 27 May 2011 (UTC)<br />
:<font color=dodgerblue>This problem has continued over the weekend. Someone spammed the talk page for Fun Topology with comments about buying Cialis and stuff. They also posted a lot more movie download pages under the Cadedesi username. I'm going to go through and delete again.</font><br />
:<font color=dodgerblue>The spam comments on Fun Topology were coming from this computer's IP address. </font><br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 14:34, 6 June 2011 (UTC): Haven't seen any more spam activity for a few days. I assume some computer people have handled the issue? I'm going to hide this conversation so that it's not taking up space on S11.</font><br />
}}<br />
<br />
*Citations/footnotes conversation: {{Hide|1=<br />
:I spent a really long time wandering around MediaWiki and Wikipedia this morning trying to figure out how to do footnotes/citations the way I wanted to - now that I know how, should I add instructions to one of the many help mages on Math Images? If so, which page? (Kate, 5/17)<br />
<br />
:<font color=red> Answer: put it here at [[Help:Wiki_Tricks|Wiki Tricks]] (XD, 5/17) </font><br />
<br />
:[[User:Smaurer1|Smaurer1]] 19:43, 17 May 2011 (UTC) Well, it's not clear that webarticles should have footnotes, although Wikipedia does. In text references may be better. This is surely something we should discuss as a group, and find out what last year's group decided, if they did. If there are footnotes, there has got to be a way to get back seamlessly to where you were before you jumped to the footnote.<br />
<br />
:Also, as for citations, we should be uniform in their format.<br />
<br />
:Finally, you can use 4 tildes to put your username and time stamp on your comments, and 3 tildes for just your username. <br />
<br />
:<font color=dodgerblue>Well, I wasn't doing comment-y type footnotes, I just wanted specific sentences to link to items in my References section. I think that format is better than full intext-citations, because it brings you to the source if that's what you're interested in, but it takes up less space if you're not. The references template we have comes equipped with little links to jump you back up, too- if you look at the [[Quipu#References|Quipu]] page, you can see that it lists each of the sections that reference is linked from, and those links bring you to the reference in that section. All in all, I think it's a clear and intuitive way to do references for both the writer and the reader (although, like most things, it doesn't play well with our hidden sections), and I'm going to go ahead and put the instructions up in WikiTricks. -[[User:Kderosier|Kate]] </font><br />
<br />
{{Hide|1=<br />
*What the help pages say now:<br />
**[[Tour_the_Math_Images_Project#Anatomy_of_a_page|The Tour page's "Anatomy of a page" section]]<br />
**[[Checklist_for_writing_pages#References_and_footnotes|The "References and footnotes" section on the checklist for writing pages]]<br />
*The way to do Wikipedia-like references:<br />
**[[Wiki_Tricks#How_to_do_Citations|Wiki Tricks - Citations section]]<br />
}}<br />
<br />
}}<br />
<br />
*Invisible Comments conversation: {{Hide|1= One of you asked "How do you put invisible comments in the source code?"<br />
<br />
:Answer: Same way you do in html, like this <nowiki><br />
:<!-- hidden stuff --><br />
:</nowiki><br />
:However, if you want to make comments about an article for its author, the comments are more likely to be seen if you either<br />
:* put it in the discussion page, or<br />
:* if it is important to put it right by the material commented on, put it in the article in color with your username and time stamp included.<br />
<br />
:Hidden comments in the source code are likely to be overlooked, except perhaps if they are written by the author him/herself, as a note for further development.<br />
}}<br />
}}<br />
<br />
== Current Individual Projects ==<br />
<br />
===Steve M (aka Prof Maurer)'s Role===<br />
{{Hide|1=<br />
My role is 2-fold:<br />
<br />
<ol><br />
<li> Come see me to sound me out (if you wish) on the mathematical appropriateness of an idea for a page, or for possible references.<br />
<br />
<li> Once you have a reasonable amount written, and want feedback on the quality and correctness of the mathematical exposition, ask me to look it over and then we will have a conference. (Abram and the oldies are as good as I am at discussion general organization and clarity issues.) <br />
</ol><br />
<br />
We have agreed to put a record on this S11 page of what we are doing and what help we want from others, but in addition tell me in person or by email if you want to conference with me.<br />
}}<br />
<br />
===Harrison's Projects===<br />
<br />
*[[Real Projective Plane]]<br />
**[[User:Htasoff|Htasoff]] 18:47, 11 July 2011 (UTC) Will look at organization of page when my book arrives.<br />
<br />
*[[Cross-cap]]<br />
::--[[User:Alimurreza|Alimurreza]] 02:47, 6 July 2011 (UTC)Please, check this out here @ ([http://mathforum.org/mathimages/index.php/DU11 Reza's work]). It is done.<br />
<br />
*[[Mobius Strip]], a page originally from 2009<br />
::[[User:Htasoff|Htasoff]] 18:47, 11 July 2011 (UTC) pretty much ready, some final comments are good.<br />
::<font color=slateblue>[[User:Rebecca|Rebecca]] 01:36, 12 July 2011 (UTC) I left some comments on the discussion page, but overall I think it looks great. </font color><br />
<br />
*[[Topology Glossary]]<br />
:*Used to be [[Non-orientability|non-orientable]]<br />
::[[User:Htasoff|Htasoff]] 18:47, 11 July 2011 (UTC) adding some basic info. Will need to be developed by future writers.<br />
<br />
*[[Rope around the Earth]]<br />
::[[User:AnnaP|AnnaP]] <font color=darkred> 7/7 I've responded to your comments again </font> <br />
::[[User:Htasoff|Htasoff]] 18:47, 11 July 2011 (UTC) Done with page, trying to get it up.<br />
<br />
*[[Dimensions]]<br />
::[[User:Htasoff|Htasoff]] 18:47, 11 July 2011 (UTC) pretty much ready, some final comments are good.<br />
<br />
*[[Congruent triangles]]<br />
::[[User:Htasoff|Htasoff]] 18:47, 11 July 2011 (UTC) Steve thinks that proofs would be good. Will need to be developed by future writers. Other than that, pretty much ready.<br />
<br />
*[[Basic_Trigonometric_Functions#Inverse_Trig_Functions|Inverse Trig section of Basic Trig helper page]]<br />
:Completed & approved.<br />
<br />
*[[Radians]] <br />
: <font color=darkred> Since you have an open question on your discussion page (asking how to make your helper page link to the pages that link it) I have removed it from the "ready for final review" page. 7/7 [[User:AnnaP|AnnaP]] </font><br />
::[[User:Htasoff|Htasoff]] 18:47, 11 July 2011 (UTC) pretty much ready, need help with helper page template.<br />
<br />
*[[Dinosaur]] :-)<br />
<br />
===Richard's Projects===<br />
<br />
<br />
<font color=orangered> <br />
<br />
*[[Ambiguous Case]]<br />
:*This page is the one that everyone should follow for feedback!<br />
:*Starting to address the comments on the discussion page one by one. [[User:Rscott3|Richard]] 7/7 </font color><br />
:*<font color=slateblue> [[User:Rebecca|Rebecca]] 00:30, 8 July 2011 (UTC) I reread the page, and I think it is looking much improved! I love the addition of the demonstration and the new pictures. I do agree with Abram's most recent comment about mentioning that we're dealing with an acute angle in this page. <br />
</font><br />
<br />
:APPLET INFO:[[User:Alimurreza|Alimurreza]] 02:53, 6 July 2011 (UTC)I am working on your applet. Check this out here @([http://mathforum.org/mathimages/index.php/DU11 Reza's work]).<br />
:{{Hide|1=<br />
<br />
What i want mine to look like, but http://www.mccsc.edu/~aterwill/ambiguouscaseapplet/Ambiguous_Case_applet.html doesn't show the completed triangles.<br />
<br />
I like how this one shows the completed triangles<br />
http://www.mnwest.edu/fileadmin/static/website/dmatthews/Geogebra/AmbiguousCase01.html<br />
<br />
}}<br />
<br />
*[[Solving Triangles]]<br />
<font color=orangered><br />
:*Put up for second final review! Score![[User:Rscott3|Richard]] 7/11<br />
</font><br />
====Completed Pages====<br />
<br />
*[[Law of cosines]]<font color=orangered> [[User:Rscott3|Richard]] 6/23</font><br />
<br />
*[[Law of Sines]] [[User:AnnaP|AnnaP]] 7/7<br />
<br />
<br />
:Other ideas: {{Hide|1=<br />
*inscribed angles?<br />
<br />
*Normal Distribution?<br />
<br />
*Birthday Paradox?<br />
}}<br />
<br />
===Dayo's Projects===<br />
Current projects<br />
*[[Inscribed figures]] : there's a [[Compass & Straightedge Construction and the Impossible Constructions]] page, but I think that inscribed figures deserves its' own page. What do others think? <br />
::<font color=red>xd 7/6 how is this related to the Compass & Straightedge page? </font><br />
::<font color=slateblue> [[User:Rebecca|Rebecca]] 01:07, 9 July 2011 (UTC) I left comments on the discussion page. </font color><br />
<br />
*[[Torus]] edits, additions concerning the Torus in construction and architecture<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 17:41, 6 July 2011 (UTC): Hey Dayo, I was doing some commenting this morning, and I was wondering which parts of this page you'd worked on, so I could give you feedback?</font><br />
*Teaching Materials(6/30): ''growing up with science: projects'' could be the sort of activities we're looking for. I used these with a class, and think people should look at them.<br />
<br />
<br />
Future Projects: {{Hide|1=<br />
*[[Mathematics in architecture]]:make changes akin to [[Math for Computer Graphics and Computer Vision]], including:<br />
<br />
*[[Domes]]:conic sections, arches, parabolas<br />
<br />
*[[The Henderson Waves Bridge]]: sinusoids in architecture, parametric design<br />
<br />
*[[Catenary]]: More real world examples: namely bridges<br />
<br />
*[[Bridge of Peace]]: The equation(s) used to generate the surface, possibly words from the architect, very new, may be hard to get concrete technical information <br />
<br />
*[[Kurilpa Bridge]]: Everyone have a look at the image and tell me what kind of actual subjects you could find in it, namely in the cables and tubes.<br />
<br />
<br />
<br />
<br />
}}<br />
<br />
on hold: <br />
*[[Parametric Equations]]: integrating Xingda's page from [[S10]] into page.<br />
<br />
===Diana's Projects===<br />
<br />
====Current====<br />
*[[Logistic Bifurcation]]<br />
<br />
:<font color=darkred> I've put up comments. There are a few places that could use some work. [[User:AnnaP|AnnaP]] 7/10 </font> <br />
<br />
*[[Markus-Lyapunov Fractals]]<br />
:<font color=darkred> I have posted a few minor comments. This page is in very good shape. [[User:AnnaP|AnnaP]] 7/10 </font><br />
<br />
====Ideas for later projects====<br />
{{Hide|1=<br />
*Chirikov-Taylor Maps<br />
**This seems like a natural extension of the Markus-Lyapunov Fractals page, but maybe the math involved in the two is too similar?<br />
*This aspect of pendular motion:<br />
**[[http://www.youtube.com/watch?v=yVkdfJ9PkRQ&feature=player_embedded|Varied-Length Pendulums]]<br />
**I'm not sure how or whether to use this -- does a ''moving'' image count as a "math image"? -- But it's incredible, and I'd love to explore it.<br />
*Kuen Surface<br />
**It's just really cool.<br />
}}<br />
<br />
===Kate's Projects===<br />
*[[User:Kderosier#Applet_Testing|Java Applets]]<br />
<br />
*[[Critical Points]]:<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 19:02, 11 July 2011 (UTC): Made small changes based on feedback from Anna. I'm planning to come back and add information about Taylor polynomials for functions in multiple variables in the fall, when I can get my notes from Math 35 out of storage.</font><br />
<br />
*[[Summation Notation]]:<br />
:<font color=dodgerblue>Made changes based on feedback from Anna. Would really appreciate comments on the example given in the "More on dummy variables" section.</font><br />
<br />
*[[Anne Burns' Mathscapes]] (Scrapped out of [[Mountains In Spring|three]] [[Mathscape|other]] [[Fractal Scene I|pages]]):<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 23:08, 6 July 2011 (UTC): I'd like people to look over this page. I'm still planning on getting an applet done at some point.</font><br />
<br />
*[[Bases]]:<br />
: <font color=dodgerblue>[[User:Kderosier|Kate]] 17:31, 11 July 2011 (UTC): Changed things in response to Chris' comments.</font><br />
<br />
*[[Perko pair knots]]:<br />
:<font color=dodgerblue>[[User:Kderosier|Kate]] 21:04, 7 July 2011 (UTC): Have started drawing up the images for the proof. 39/81 images complete. Please hold back on feedback until I get these pictures done.</font><br />
::{{Hide|1=<br />
::<font color=darkred>You wanted rollover images on this page, right? I've figured out the Java code necessary to put them in, could you please check my user page to confirm if it is what you wanted? Also feel free to email me any images you need to be made into an applet like it. [[User:Rguo|Rguo]]</font><br />
::<font color=dodgerblue>This is exactly what I want! I'm gonna need about 40 of these done in a week or two from now - might be easier if you taught me how to do it, I don't want to make you do all of that tedious stuff for me. -[[User:Kderosier|Kate]] 20:47, 28 June 2011 (UTC)</font><br />
::<font color=darkred> [http://www.pages.drexel.edu/~rg458/mathimages/MouseOver.java Here's the Java file] you'll need to place into a Java Class Library project -- make sure it's in the default package. I went back to add comments to point where you'll need to change the link/image URLs and how to get the files you'll need to upload to the Wiki. The only downside is that I'm fairly certain you're going need to change the class/project name for each version of a rollover you'll want. [[User:Rguo|Rguo]]</font><br />
}}<br />
<br />
*Finished pages: {{Hide|1=<br />
:* [[Quipu]]:<br />
::<font color=darkred> Put up as ready for the public 6/30 [[User:AnnaP|AnnaP]] </font><br />
<br />
:* [[Basic Trigonometric Functions]]:<br />
::<font color=dodgerblue>[[User:Kderosier|Kate]] 18:11, 30 June 2011 (UTC): Changed the the things that were bolded.</font><br />
<br />
<br />
}}<br />
<br />
===Leah's Projects===<br />
*[[Bedsheet Problem]]<br />
::sigh, sadly still in the works. WIP<br />
<br />
*[[Witch of Agnesi]]<br />
working on Anna's comments hoping to post up for final review again by tomorrow. <br />
<br />
*[[Dot Product]] <br />
re-post it for final review 7/11<br />
<br />
*[[Vector]] <font color=darkred> Approved, 7/10 </font><br />
<br />
*[[Snell's Law]] feedback page<br />
working on Kate's comments and adding problems. <br />
<br />
*[[Boy's Surface]] <br />
WIP<br />
<br />
==Requests to S10 Students==<br />
<br />
<br />
*<s>Can XD do a demo for MATLAB?</s> Done - [[Demo of MATLAB using the example of Bifurcation]]<br />
<br />
==Useful Links==<br />
[[S10]]<br />
<br />
[[SB11]]<br />
<br />
[[RPI11]]<br />
<br />
[[DU11]]<br />
<br />
[[Pages Ready for Final Review]]<br />
<br />
[[Feedback Requests]]<br />
<br />
[[Sample discussion page]]<br />
<br />
[[Math Tools Requests]] ''This page is a place where students whose primary focus is writing pages can post requests for applets, animations, and new images that they'd like to see the computer science students create.''<br />
<br />
[[Page Building Help]]<br />
<br />
[[Help:Wiki Tricks|Wiki Tricks]]<br />
<br />
[[From a Bunch of Old Timers]]<br />
<br />
[[List of summer 2010 pages]]<br />
<br />
http://en.wikipedia.org/wiki/Help:Displaying_a_formula<br />
<br />
[[PartnerHome]]<br />
<br />
[[Existing Pages Needing Work]]<br />
<br />
[[Site programming questions]]<br />
<br />
== Current Group Projects ==</div>Rebeccahttps://mathimages.swarthmore.edu/index.php?title=Talk:Mobius_Strip&diff=24411Talk:Mobius Strip2011-07-12T01:34:35Z<p>Rebecca: /* Why It's Interesting */</p>
<hr />
<div>[[User:Htasoff|Htasoff]] 14:39, 7 June 2011 (UTC)<br />
<br />
Video removed due to copy right issues.<br />
<br />
=Basic Description=<br />
*"if perpendicular arrows were drawn in the surface to the surface pointing upward, moving them along specific paths in the shape would return them to the starting point as a mirror image of the position they were in when they began."<br />
<font color=red>xd 14:56, 22 June 2011 (UTC) You need to explain this better with a picture. Also the sentence is awkward. I cannot picture the arrows simply with these. Make sure you mean exactly what you mean when you say "drawn IN the surface". Define "specific paths". Do you mean they end up at a position that is the "mirror image (about what? the strip? or the path) of the position" they started with OR the arrows end up as the "mirror image" of themselves. The bubble for "perpendicular" is not very necessary. </font><br />
<s>* <font color=slateblue>[[User:Rebecca|Rebecca]] 22:51, 27 June 2011 (UTC) No comma after that in the sentence "Being non-orientable means that, if..." <br />
* Also, I agree with XD. The sentence is confusing, and a picture will help.<br />
* Is it true that the edge can be referred to as a circle? If a circle is "highly distorted" is it still a circle? (This is a question because I don't actually have any idea). </font color><br />
*<font color=Mediumblue>CHECK</font> </s><br />
<br />
* <font color=slateblue> [[User:Rebecca|Rebecca]] 01:32, 12 July 2011 (UTC) Technically shouldn't be capitalized. </font color><br />
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=More Mathematical Description=<br />
<s> *[[User:Rebecca|Rebecca]] 23:23, 27 June 2011 (UTC)<font color=slateblue> I thought this section was good. I think the descriptions under the images are cool.</font color> </s><br />
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=Why It's Interesting=<br />
*<font color=slateblue> [[User:Rebecca|Rebecca]] 23:23, 27 June 2011 (UTC) You could try to embed of a movie of someone playing with a mobius strip in the . I think this would be a great addition to the page. </font color> <font color=Mediumblue>There was one originally, but I had to take it down due to copyright issues.</font><br />
*<font color=slateblue> [[User:Rebecca|Rebecca]] 01:34, 12 July 2011 (UTC) Is there another one you could use? Or are they all protected?</font color><br />
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=Applications=<br />
* <font color=slateblue> [[User:Rebecca|Rebecca]] 01:29, 12 July 2011 (UTC) I think the applications section would be more appropriately titled "Mobius strips in the real world" or something along those lines. "Applications" makes me think you're going to talk about applying the content of the page to problems. <br />
* When you talk about Escher's picture, why not include it? It's a very cool picture. <br />
</font color><br />
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=Old Comments=<br />
{{hide|1=<br />
==Abram 7/7==<br />
Nice job with the edits. So to clarify the bit I explained to you a bit confusingly before, if you look at your description of Experiment #2, you write, "In general we would expect... But this is not so with the Mobius strip". I was thinking the first two paragraphs could be structured that same way, for example:<br />
:''Normally, surfaces have two sides. You could paint each side of a (hollow) sphere or a rubber band a different color. But if you take a rectangular strip of paper and... you get something that doesn't follow that rule...''<br />
<br />
But you could ignore this suggestion too, and I think it's ready for public.<br />
<br />
The one change I made to the page was rewriting "A Mobius strip ''has'' a non-orientable surface" as "A Mobius strip ''is'' a non orientable surface."<br />
<br />
==Lizah 7/7==<br />
Hi Chris,<br />
<br />
Thanks for the suggestions. I corrected all the typos you pointed out and effected most of the changes you suggested.<br />
<br />
//I would title the first section Mobius Strip. A comma is needed after “also referred to as a Mobius band”.//<br />
<br />
ok<br />
<br />
//I would take out “we” in initial explanation. For example, “Take a rectangular strip of paper. Make a half twist and join the ends. The result is a Mobius strip."//<br />
<br />
I sought a third opinion on this because I felt like saying "take a rectangular..." would sound a bit imperative and distant. On the other hand, starting with "If we..." kind of includes the reader. I'll seek more opinions on this.<br />
<br />
//Basic Description: "but on the opposite side of the paper". If it's at the same point, how can it be on the opposite side?//<br />
I put opposite in quotation marks to imply that opposite does not exactly mean oppostie in this case, but more like the other side of the paper (though by definition, the Mobius strip technically has no other side)<br />
<br />
//You title this "strange properties" but then make only one statement before the four experiments. The ant sentence relates to the first experiment, which then hangs alone since the other three experiments directly follow.//<br />
I changed the first sentence altogether so that it introduces the video instead.<br />
<br />
//Is there a graphic that can help demonstrate its use in resistors, etc.?//<br />
<br />
So far I haven't found one, but I'll keep looking.<br />
<br />
//Applications should be a topic on its own, not a part of “A more mathematical explanation.//<br />
<br />
I got rid of the section "a more mathematical explanation" because the Mobius strip has no really intimidating hard math.<br />
<br />
//Were there other artists you found that used them as well? Otherwise, cite only M.C. Escher.//<br />
<br />
Martin Gardner wrote an amusing short story based on the Mobius strip called "No-sided Professor." I'll mention him too.<br />
<br />
Thanks again for the helpful suggestions you put forth<br />
<br />
== Abram 7/7 ==<br />
Really nice job with the edits. I won't address them one by one because they're all great. I agree with Chris's suggestions, and I think they should be easy to implement.<br />
<br />
I have three more suggestions, two of which I feel strongly about and one of which is less important (the less important one is at the end).<br />
* I'm glad you decided to put just about everything in the basic description. The parametrization section, though, ''should'' be relegated to a section titled "A more mathematical description." <br />
* In your description of experiment 1, mention that you already referred to this property in your opening paragraphs (just to really make it clear how central this feature is).<br />
* The opening paragraphs are great, except that I think they could do a better job emphasizing how weird a Mobius strip is. I can imagine someone reading, "Logically, this is only possible..." and not registering, "Hey, that's really bizarre." One way to change the emphasis would be to ''begin'' this section by describing how "normal" shapes like spheres and rubber bands have two sides. This will set up a contrast with the Mobius strip. But there are all sorts of other ways to build in this emphasis as well.<br />
<br />
==Chris Taranta 7/6==<br />
This is a really fun topic that is accessible even to younger students, making it more likely they’ll stick with the math. Nice job on this.<br />
<br />
I would title the first section Mobius Strip. A comma is needed after “also referred to as a Mobius band”. <br />
<br />
I would take out “we” in initial explanation. For example, “Take a rectangular strip of paper. Make a half twist and join the ends. The result is a Mobius strip."<br />
<br />
Basic Description: "but on the opposite side of the paper". If it's at the same point, how can it be on the opposite side?<br />
<br />
Strange Properties<br />
The four experiments from the video form the content for this section. Your introductory sentence refers to only one of them. I would instead have the first sentence set up the video. Credit for video?<br />
<br />
You title this "strange properties" but then make only one statement before the four experiments. The ant sentence relates to the first experiment, which then hangs alone since the other three experiments directly follow. <br />
<br />
⁋1 Sentence 3: “the tape” replaces “he tape”<br />
Sentence 4: Is there a graphic that can help demonstrate its use in resistors, etc.?<br />
<br />
⁋2 Sentence 1: “M.C. Escher” replaces “MC. Escther”. Were there other artists you found that used them as well? Otherwise, cite only M.C. Escher.<br />
<br />
⁋3 I would not use the word “also” here. I’d simply begin with “The universal…”<br />
<br />
Applications should be a topic on its own, not a part of “A more mathematical explanation.”<br />
<br />
<br />
==Lizah 7/4==<br />
<br />
Hey Anna,<br />
<br />
I effected the changes you suggested. Could you please take a look again?<br />
<br />
==Anna 7/4==<br />
<br />
Hi Lizah,<br />
<br />
I have a few comments. I'd really like to see the "strange properties" moved up to the basic description section. Also, I do think that it would flow much better if you put the experiment results immediately after the descriptions/numbering. Right now that's a little disjointed. <br />
<br />
I'll look at it again after you make those changes. <br />
<br />
==Lizah 7/1==<br />
Hey Abram and Anna,<br />
<br />
Thanks once again for the helpful suggestions.<br />
//You have these cool YouTube experiments that you describe in words. In your textual description of each experiment, say which experiment number in the video that textual description corresponds to//<br />
<br />
This was also suggested during my meeting with Gene and Anna. I just put the experiment numbers and a brief description of what is going on in each experiment next to the video. In the paragraph that follows the video, I describe the results of each experiment. <br />
<br />
//[this sentence you already have in the basic description]//<br />
<br />
I see what you mean. I'll get rid of it to avoid unecessary repitition.<br />
<br />
//Move everything except the parametrization to the basic description. It's really cool stuff that can be easily understood without knowing any fancy math.//<br />
<br />
I'm still debating about this because of the issue of how long should the basic decription be. You're probably familiar with Gene's emaphasis on really short basic descriptions, but at the same time, if it is really something 'fancy', why not put it in the basic description? I'll seek a third opinion on these.<br />
<br />
//Move the bit about the ant needing to walk around twice to the first paragraph, because this is one of the central features of a Mobius strip//<br />
<br />
ok<br />
<br />
//u and v are described accurately or a bit confusingly in your parametrization. u represents position along the length of the strip from the arbitrary "starting point" along the x-axis. this is slightly different from your current "u describes the length of the strip", because the length of the strip is a property of the strip as a whole, and is equal to 2*pi, while position along the length of the strip varies from point to point. A similar change in the description of v would be helpful.//<br />
<br />
I changed the wording. Please chheck it out. I hope it makes it clearer.<br />
<br />
//In your two sentence description, can you maybe include a mouse over for what you mean by "true surface"? It's unclear what you mean.//<br />
<br />
I got rid of that sentence altogether. I realize that my meaning is clearer without it.<br />
<br />
<br />
//I'd cut out the phrase "in very light words."<br />
Can you add the recycling sign next to where you mention it?//<br />
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<br />
Duly done. We talked about this in our meeting.<br />
<br />
Thanks for the suggestions<br />
<br />
<br />
<br />
==Abram 7/1==<br />
The page looks great. I have several suggestions, but most of them should be pretty quick to implement.<br />
<br />
* Move everything except the parametrization to the basic description. It's really cool stuff that can be easily understood without knowing any fancy math.<br />
* <br />
. One way to do this is to write something like: <br />
: ''If we were to draw a line through the centre of the strip without lifting the pencil off the paper, we would come back to the starting point but on the opposite side of the paper'' [this sentence you already have in the basic description]''. Your pencil point would have to go around the strip two full times before it returned to its original position.''<br />
* You have these cool YouTube experiments that you describe in words. In your textual description of each experiment, say which experiment number in the video that textual description corresponds to.<br />
<br />
One important mathematical detail:<br />
* u and v are described accurately or a bit confusingly in your parametrization. u represents position along the length of the strip from the arbitrary "starting point" along the x-axis. this is slightly different from your current "u describes the length of the strip", because the length of the strip is a property of the strip as a whole, and is equal to 2*pi, while position along the length of the strip varies from point to point. A similar change in the description of v would be helpful.<br />
* It may be helpful to mention that u also represents angle from the positive x-axis.<br />
<br />
==Anna 6/26==<br />
In your two sentence description, can you maybe include a mouse over for what you mean by "true surface"? It's unclear what you mean. Your explanation in the "mathematical description" section is very good, though. <br />
<br />
I'd cut out the phrase "in very light words."<br />
<br />
Can you add the recycling sign next to where you mention it?<br />
<br />
==David 6/25==<br />
<br />
I realize you are still working on this page, but I love mobius strips so much I had to check it out.<br />
<br />
A couple of things; can you find an animation that will show how a mobius strip has only one side? Also for the cutting explanations can you find an animation that will show that as well,it is difficult to imagine what you are talking about because the mobius strip itself is counterintuitive and then when you slice it up it is even more complex to grasp.<br />
<br />
==Lizah 6/26==<br />
<br />
Thanks for the suggestion David. I agree with you that picturing the properties of a Mobius strip can be somewhat difficult but I found this cool youtube video that illustrates all the properties described. You can check it out! And please feel free to make whatever changes you feel are necessary on the page.<br />
<br />
}}</div>Rebecca