Talk:Straight Line and its construction

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Individuals' statuses

Smaurer1 17:48, 16 June 2010 (UTC) Well, we did have a talk, and among other things I suggested lots of revisions to the linkage history section, where engineering terms like "beam", "tension" have to be explained. When Xingda does a revision and says he wants me to look at it again, I will. I wouldn't call it 90% done.

Iris's comments(7/15)

More explanation needed

  • In the second paragraph of what is a straight line?-a question rarely asked, add an explanation for cartesian coordinates
  • In the second paragraph of what is a straight line?-a question rarely asked, last sentence, what if two points were on the sphere but very close to each other? Explain how the distance is a part of the great circle
  • First sentence of The quest to draw a straight line - the practical need, you did not define what a straight line is. Either define it in the previous paragraph, or define it in the beginning of this paragraph
  • what is mechanical linkage in The quest to draw a straight line - the practical need,? add balloon
  • In your explanation of Image 3, add a sentence to this paragraph why or how the steam engine is related to straight line construction
  • In your explanation of how the steam engine works (the hidden part after explanation of image 3), explain why the vertical movement of the piston is ideal
  • In james watt's breakthrough section, I thought the piston had to move in a vertical direction(as you explained in previous paragraphs). Why did James Watt try to convert linear motion into circular motion?? This seems contradictory & problem seems a bad word choice
  • the motion of point p section, explain why the very first paragraph is important to this page about constructing straight lines. It seems irrelevant without any explanation
  • In the motion of point p - algebraic description derivation, the last part seems unfinished. If it is complicated, can you at least show the result? Or the relationship between x, y coordinates of P? It's not clear what you were trying to derive
  • Is the second paragraph of the first planar straight line linkage section really relevant?
  • In the inversive geometry in peaucellier section, what is inversive pairs, inversive center? add a balloon for each
  • In Hart's linkage section, where did you get OP/BD=m, OQ/AC=1-m? If you are assigning OP/BD=m, say so, and show why OQ/AC=1-m
  • In the same section, at the end, explain that OP*OQ is constant and explain how this is related to straight line
  • in Other straight line mechanism how did you get r_1\beta=r_2\alpha??

Coordination between picture and text

  • 2nd paragraph of what is a straight line?, refer to image 1 & image 2
  • In your explanation of Image 3, explain in more detail where the cylinder with piston is
  • In your explanation of Image 5, the sentence the piston rod is confined between.... in the up-and-down motion is hard to find in the picture. Explain better?.
  • In motion of point p-parametric description derivation, the vector AD can be written as (c,d) only if point A is assigned (0,0). Add this
  • In the same section, in your explanation for Image 12, I can't find \theta. Draw it in image 12

Word choice problems

  • In The motion of point P - Algebraic description you use the word between the coordinates of P. Maybe you meant between the 'x- and y- coordinates of P'??
  • in the same section, what does closed form mean?
  • in the [[show/hide]], write show derivation of ____. what are you trying to derive?? This also works for the hide/show of parametric description
  • There were some grammar mistakes and typos, but I won't write them down here

Becky's comments(7/21)

Break up long paragraphs

  • Break up introduction paragraph at "These are questions that seem..."
  • Break up What is a straight line paragraph at "So what is a straightness anyway?"
  • Break up the paragraph above Image 4 and 5 at what used to be "Now considering that the..."
  • Break up the planar linkage in action paragraph at "Mr. Prim's blowing engin..."


  • Remove the content in the parenthesis in the paragraph that explains how the engine works. It is fine and less confusing without it.
  • Give the imitation paragraph a heading and explain more explicitly what Watt left out in the patent.
  • Switch the order of the first wo paragraphs from the the Peaucellier-lipkin section.
  • Rephrase the conclusion so it sounds less preachy.

Active Comments

Major strengths of the page

  • Great job framing the nature of the problem, its solution, and its importance
  • Good sequencing of material
  • Inclusion of lots of images, especially representing the same image in several different ways
  • Good integration of mathematical content and non-strictly mathematical applications
  • The layout is hugely improved (Anna 7/14)
Abram, 6/4

Layout Issues

  • Anna, there are a lot layout issues hidden below that you brought up that seem satisfactorily fixed, but they are here in case you want to review them.
  • The two beginning pictures appear twice right next to each other. I don't see a reason for that.
Which picture are you referring to? (Xingda 6/28)
Anna, are you referring to the first two pictures of steam engines? I'm *really* confused by the second picture of a steam engine. I didn't realize until *today* that the second picture isn't supposed to be a double-action steam engine (or maybe it is, and I'm even more confused?). (Abram, 6/30)
I think the source of the confusion the sentence "Improvements were made. Firstly, "double-action" engines were made, part of which is shown in the picture on the right" which in fact the picture is on top. So I change it to "...picture on top". (Xingda, 7/7)
This seems not to be an issue any more. (Abram, 7/16)
  • When there is text between the two pictures, the text gets all broken up if you make the browser window too small. I suggest you move one of the images around so this doesn't happen.
Issue addressed (Xingda 6/28)
This also seems ok now. Anna? (Abram, 7/16)
  • You've got a lot of what I like to call "paragraphs of doom." These are big blocks of text that are quiet difficult to read for no other reason that the fact that they are big. I strongly encourage breaking them up into smaller pieces. In writing for the web, it's important to keep paragraphs to basically one idea each.
I would appreciate some specific suggestions. (Xingda, 7/7)
Your other changes have actually help to break up the text much better. I would suggest finding a spot to break up the paragraph underneath image 10. Perhaps put in a break right before the sentence that starts "The link ABCD..." (Anna 7/14)
issue addressed (Xingda 7/15)
Looks good. (Abram, 7/16)
Also the paragraph underneath image 22 could really benefit from each sentence being it's own line with some extra space, since the equations are crowding into each other.
Looks fixed. (Abram, 7/16)
  • Can you mention why we're above to see the steam engine picture before we do? Right now, it overwhelms the reader.
The point that I am introducing the mechanics of engine is to make the readers to realize that we are not doing this straight line thing for nothing. It is not that mathematicians have nothing better to do and decide to come up with this question. The practical need was a much better incentive for people to solve this problem. In addition, the mechanics problems are interesting. It would be very awkward and abrupt if, without any background information, I just say "oh, Watt came up with a straight linkage but it was not good and this is why. Then this French guy came up with this and that worked." People will ask why are we even bothered by all these. (Xingda 6/28)
Including the information about the steam engine and other practical applications is one of the strongest things about the page. I think Anna is saying that because the reader encounters the picture first, and then may have to scroll down to see any text in the browser window that talks about steam engines, the reader could be initially confused by the picture. (Abram, 6/28)
I don't quite get it. I have a paragraph before I started using diagrams. We need to talk about this. (Xingda 6/29)
It seems like the display has changed so much that this conversation is now out of date. (Abram, 7/16)
On this note, I do agree with Abram about potentially hiding some portion of this text.
I deleted 3 diagrams and one short paragraph. (Xingda 6/28)
There has been lots of shortening/hiding already, and the main discussion about that is happening somewhere else now anyway. (Abram, 7/16)
  • When you've got two equations that end up on top of each other (for example, the one starting Substituting, followed by Hence in the motion of P section), add an extra space in for easy reading.
Issue addressed (Xingda 6/28)
Looks good. (Abram, 7/16)
  • A few of your diagrams showing these constructions would actually be more useful if they were smaller. That way, the reader can see them closer to the text and better connect them with the math.
Issue addressed (Xingda 6/28)
It's much better now! (Anna 7/14)
  • Two or more images side by side causing formatting funkiness
Specifically, Images 11 and 12 can't fit in the browser window side by side, even when I fill up my laptop screen (it's 13 inches btw). Can you either make them on separate lines, or make them both a bit smaller.
The same issue is happening at Images 19,20 and 21. (Anna 7/14)
issue addressed (Xingda 7/15)
Looks good. (Abram, 7/16)

(Anna 6/25)

  • Format equation references using the template Prof. Maurer worked out if we actually decide to keep all the equations (see discussion about parameterization section). (Abram, 6/30)
Issue addressed (Xingda, 7/7)
The format still looks a bit different than the template we decided on. We've been putting the label "Eq. 1" *before* the image. (Abram, 7/14)
must we all adhere to that? i mean on text books such labeling always follows the equations.
issue addressed (Xingda 7/19)
Looks good. (Abram, 7/21)
  • Why are the images for the algebraic and parametric description of P not hidden by default? It seems like the only reason one would ever look at these images would be if one wanted to read the hidden derivation. (Abram, 7/14)
reason 1. even if i put it under hide, it will show because it is on the first line. reason 2. they are there to remind the reader that there are stuff hidden and don't over look that. (Xingda 7/15)
reason 1. It seems worth it to find some way around this technical glitch, so that people don't have to see the image if they aren't reading the proof. reason 2. It seems that between the all the introductory text and the new handy-dandy hide template, readers will get it. (Abram, 7/16)
  • This would be less of a big deal if the images were much smaller. Basically, each image that you use for a proof fills up literally half the vertical viewing space on my 13" laptop. The images could be much smaller and still be readable. (Abram, 7/14)
Some of the images seem smaller. Images 14, 15, and 18, and kind of Image 16, are still huge. (Abram, 7/16)
i cannot do it. it just does not hide and it won't hide the math as more. I mean the pictures there do not bother anyone it is actually good for the smarter of the readers because once they look at the picture, they know what is coming and they don't even need to see the detailed math. it is like an experienced researcher knows what is in the a paper by simply looking at the abstract (Xingda 7/19)
I thought Iris had some way around this? Anyway, images 14, 15, 16, and 18 could still be smaller. (Abram, 7/21)
i shrank the images. but i tried iris's way and it won't do. i think it is because it is in a table (Xingda 7/22)
Images 14 and 15 could still be 25% smaller or so. (Abram, 7/23)

Amount of material

We may come back to this issue, but for now, it's good.

  • All the content is interesting, but a lot of it can be hidden or removed with no less of continuity in the page. Examples include the paragraph beginning "the picture above shows a patent drawing" as well as Phineas Crowther's application of Watts's linkage. The page will seem less overwhelming if this auxilliary material is hidden by default (Abram, 6/4).
I deleted three diagrams including that paragraph you referred to and the Crowther's engine as well (Xingda 6/28)

Cool. There's still a *huge* amount of material in this page, which brings up 2 issues. First, a lot of the material isn't relevant to the main point of the page. For instance, a paragraph-long description of how a steam engine works, including details about why the pump is there isn't necessary -- the second paragraph (beginning "Anyway, the piston...") is enough to make it clear why this problem is important. In a printed book, or very long magazine article, including so much content might be appropriate (after all, it is all interesting information), but this is a website, and that changes everything.

The second issue is that if you do want to include all the information that is currently in the page, there's going to be a truly inordinate amount of work to do on this page. We're talking about a few questions in almost every single paragraph about the ideas/content, plus sentence-by-sentence editing over the entire content of the page to help clarify the wording, etc.

We can talk about this more if you want. I can also make specific suggestions for content to remove. An alternative to removing content would be to hide a bunch of content, and just not worry about cleaning it up this summer. (Abram, 6/30)

I would like to talk. (Xingda, 7/7)
OK, we talked about this, and there has been huge improvement. (Abram, 7/14)

Philosophical discussion about straightness is a bit confusing

The basic description of the page is really interesting. It just throws me off-balance makes it seem like the page will be devoted in equal parts to a philosophical discussion about a) what defines straightness and b) how to make straight things. In fact, 90% page is devoted to the question of how to create a linkage that will force a point to move in a straight line. For a similar reason, it seems a little bit strange to right, "Hopefully, you will start questioning the flatness of a plane, roundness of a circle and the nature of a point. This was how real science and amazing discoveries were made and this is how you should learn and appreciate them." (This sentence is also really preachy).

Moreover, I'm not sure that the section on "What is a straight line - a question rarely asked" is actually that helpful. In the space of one small paragraph, you introduce two or three different ideas, none of which are actually all that relevant to the main purpose of the page. The problem may just be bringing up great circles. It seems weird to bring up this *caveat* to the definition of a sraight line as the shortest distance between two points, when the definition of straightness is not the main point of the page. It's not that having tangential information is bad, and I also like the idea of starting with this question of straightness. That is all fine. And again, it's all interesting. It's just that it's hard for me as a reader to know what you're getting at.

Later, you mention that creasing a paper is an easy way to create a straight line. This is *great* material, and should be moved to the same area where you are discussing the definition of straightness. This example is a great way of giving the reader a sense that, "Oh, making a straight line is really easy, but making a linkage that forces points to move in a straight line is really hard", especially if you point this out explicitly. (Abram, 7/14)

1. the purpose of the page is restated as "This page explores the answer to the question "how do you construct something straight without a straight edge?" " so we don't get hung up on "what is straight line" business.

This looks good, except that the page is really about creating a linkage that forces a line to move in a straight point, not about the general topic of constructing something straight without a straightedge. (Abram, 7/16)

now it reads "This page explores the answer to the question "how do you construct a straight line without a straight edge?"" i think we dont have to talk about linkage that early. (Xingda 7/19)
Now that you mention linkages in the Question Rarely Asked section, I agree. The only problem is that *that* sentence about linkages (in the Question Rarely Asked section) is confusing. The sentence is "However, to achieve our ultimate goal, the linkage that produces a straight line motion..." but it seems to come out of left field. You haven't been talking about linkages at all, and now suddenly it's our ultimate goal. Why? What if you put a sentence before it introducing the reader to the challenge (and purpose) of creating such a linkage. (Abram, 7/21)
done (Xingda 7/22)
This sentence is still kinda confusing. If our goal is simply to create a straight line without a straightedge, why do we "need" a linkage? Didn't we just say folding a piece of paper would work. You probably need a full sentence to explain why we are interested in linkages, or you can drop this sentence entirely, and replace it with something like, "This page, however, focuses specifically on the history of making machine parts move in a straight line in engineering contexts" or something like that. (Abram, 7/23)

2. "What is straight.....rarely asked" section points out the fact that the concept of being straight is not easy to articulate we cannot take it for granted. but that is not the whole point of the page. The last sentence of the section know reads "The rest of the page revolves around the discussion of straight line linkage's history and its mathematical explanation." (Xingda 7/15)

Yeah, I get the point, and I think it's a really good one. The problem is just that there are so many ideas: a Cartesian definition of straightness, an "intuitive" definition of straightness (shortest distance), a *caveat* on the "intuitive" definition of straightness, a discussion of how the motion of a beam of light *isn't* straight, and the idea of creasing a paper. (Abram, 7/16)

Some inconsistencies in scope

There are a few places where you either give some information about a topic but not enough for it to actually be useful, or where there is inconsistency in scope: the amount of detail you go into about idea X isn't commensurate with the amount of detail you go into about idea Y. An extreme example of this kind of problem would be if I were to say to you, "Tell me about London. I've never been there", and you responded, "In order to get to the main post office, you have to take the green line of the Tube. The fare is 2 pounds."

  • The reference to "double-action" engines especially, and to replacing a beam with a gear is not enough to actually tell anybody much of anything. Readers are forced to either read the hidden material or live with descriptions and images that don't really have any meaning. Is there a way of choosing a different introductory sentence that is meaningful? For example, "Systems were soon developed for making steam-engines that forced the pivot to move in a straight line, but these brought about new, even larger, mechanical problems. (Click to read more about these systems)?
i think of it this way, the inquisitive readers will want to know what the hell those pictures and terms mean and they will click to learn more, the not so inquisitive and serious readers will overlook that browse through the whole thing anyway and not affect their understanding of the page anyway.
It seems like this approach is, "Confuse the hell out of them! Then they'll be interested!" I think the way things actually tend to work, though, is that if you confuse the hell out of them, they might be intrigued, but they will probably be annoyed. In any case, it seems like a more effective approach is, "Give them a taste of something they *can* understand, and also a sense of why they might want to learn more." (Abram, 7/16)
Having tried this as a teacher, I can't agree strongly enough with Abram. A taste of complicated pictures is good, but it needs to not be overwhelming. Starting off with confusing terms, though, makes most people shut down. Anna (7/16)
addressed (Xingda 7/19)
Looks good. (Abram, 7/21)
  • In the description of image 3, the location of each item on the steam engine is described (e.g. the pump is on the right), EXCEPT for the piston and the beam, which are the only parts of the steam engine that you go on to talk about.
  • Similarly, why describe the purpose of the pump, but not the piston or the beam, when the piston is the thing you will be focusing on? In fact, why describe the purpose of the pump at all, if you're not going to describe the purpose of all the other parts of the engine?
the point is people will tend to think that the engine is only good for pumping and nothing else which is not true. it now reads "Image 3 shows a patent drawing of an early steam engine. It is of the simplest form with a boiler (lower left corner), a cylinder with piston (above the boiler), a beam (on top, pivoted at the middle) and a pump (lower right corner) at the other end. The pump was usually used to extract water from the mines but other devices can also be driven. "
Your change makes sense. Honestly, I had no idea until now that the purpose of the steam engine was *ever* to drive the pump. I thought the pump was just one part of the steam engine used to make it work. (Abram, 7/16)
  • The section on Mr. Prim's reciprocating airpump is confusing. What is a reciprocating airpump? Why do you mention "The slate-lined air cylinders had rubber-flap inlet and exhaust valves and a piston whose periphery was formed by two rows of brush bristles. Prim's machine was driven by a steam engine?" I assume this meant to help explain Image 17, but that is not nearly enough to explain it.
see response to point 1
Two things. First, see my response to your response to point 1. Second, this is a totally separate issue. Point 1 is about a sentence that doesn't make any sense unless the reader clicks on the hidden text. Point 2 is about some confusing stuff that isn't explained *anywhere* on the page. Here the approach seems to be, "Confuse the hell out of them! Then they'll click on external links!" (Abram, 7/16)

(Abram, 7/14)

Small, easy fixes

  • Put the definition of a great circle either in a mouse over or in it's own sentence. You've got too many clauses there. (Anna 6/25)
I don't quite get what you mean. (Xingda 6/28)
Read the sentence out loud, and you might be able to tell that it's kind of awkward. If you put the definition of a great circle in a mouse-over, it may feel much less so. (Abram, 7/16)
  • You've got a couple of places where you say "We intend to..." but you don't explicitly state WHY. Make sure your reader understands the motivation behind what's going on.
There are only two instances that I used "we intend to" and now the issue is addressed (Xingda 6/28)
Looks good to me now. (Abram, 7/16)
  • Drop all references to "I", "My", etc. (Abram, mid-July sometime)

Archived Comments

The purpose of the parameterization section is not clear and/or this section is overkill

You've done a huge amount of work on the algebraic and parametric descriptions of the path traced by P, and congratulations on wading through all that algebra! Well-done. Here are some concerns about this section, however:

  • If the point of this section is to show that P does not move in a straight line, there is a much easier way to achieve this. We discussed an outline of this reasoning at the chalkboard a few weeks ago. I can fill in the details if you would like.
  • In a similar vein, how does the final parametric equation show that P does not move in a vertical line? There's currently no proof included that the nasty equation you end up with can't be simplified to something much nicer, especially given that the equation involves alpha, which is defined in terms of l, which is itself changing. And similarly for the equations for x' and y'.
I think we don't even have to prove that it does not move in straight line. The animation already does that. I think the point of parametrization is to know the position of P. Also, the final parametrization does not involve l at all. It is in terms of \theta, c, d, r and m which are known quantities. (Xingda, 7/7)
  • If the point of the section is something other than demonstrating that P does not move in a straight line, then this section is straying pretty far from the purpose of the page (see also "Amount of Material" discussion below). If you want to include it, it should at least be hidden.
Abram, 6/30
I change the beginning sentence to "We intend to described the path of P so that we could show it does not move in a straight line (which is obvious) and more importantly to pinpoint the position of P using certain parameter we know such as the angle of rotation or one coordinate of point P. This is awfully important in engineering as engineers would like to know that there are no two parts of the machine will collide with each other throughout the motion. " Also, I added some mini introductions to both Algebraic and Parametric section so the train of thought is not broken and the math is not so abrupt. Does that work? (Xingda, 7/7)

This looks great, except for a layout issue that is described in the "layout issues" section. (Abram, 7/14)

Layout Issues

  • Number images and animations. Replace every reference to an image that currently says something like "image to the right" with a reference to the image number. Right now I sometimes truly have no idea what you are referring to. Some of these images may end up getting removed, though (see "Amount of material" discussion below).(Abram, 6/30)
Issue addressed (Xingda, 7/7)
Looks good. (Abram, 7/14)

Small, easy fixes

  • Drop the triple dots meaning "therefore" and "because". The "therefore" dots aren't used very often, and the "because" dots are just about never used, at least in American sources that I've seen (Abram, 6/4).: Issue addressed (Xingda 6/28)
I definitely agree with dropping the dots. (Anna 6/25)
Issue addressed (Xingda 6/28)
Looks good. (Abram, 7/14)

Define engineering terms

The terms "linkage", "member", and "flywheel" are all used, and many readers won't know what they mean. (Abram, 6/30)

Issue addressed. I either used balloon or external link to give definition. (Xingda, 7/7)
Great. The only problem is the mouse-over definition of linkage. As we (very briefly) discussed one meeting, if we only have a sentence or two of text preceding the table of contents, that text is often overlooked, so many readers will never see your mouse-over definition. (Abram, 7/14)
Issue addressed. (Xingda 7/15)
Sorry, how was this addressed? (Abram, 7/16)
I repeated the mouseover definition of linkage again. Is that not good enough? (Xingda, 7/19)
Yeah, that's fine. For some reason it didn't appear as a mouse-over when I was viewing it. The only thing is, now that you've mentioned linkages in "A Question Rarely Asked", the repeat mouse-over should go there instead of at its current location. (Abram, 7/21)
done (Xingda, 7/22)
Looks good. (Abram, 7/23)

Problems with the "imitations" section

Really interesting section, but:

  • The section deserves a heading that explains its purpose
I did not put a heading but it now reads "Another reason we parameterized P is that Watt did not simply used that three bar linkage shown in Image 6 and Image 7. Instead he used something different. To understand that, our knowledge of the parameterizaion of P is crucial. Imitations were a big problems....."
  • It seems like the main point of this section is that the linkage needed to be created in a way that led to *two* quasi-straight line motions, but the first sentence of the paragraph makes it seem like you were mostly going to talk about how Watts tried to trip up would-be imitators.
see above
  • I have absolutely no idea what I should notice in Image 10, nor do I think it has any hope of being useful if you don't tell the reader exactly what they should notice.
Now there is a sentence reads "As shown in Image 10, the original patent illustration, Watt illustrated his simple linkage on a separate diagram on the upper left hand corner but try looking for it on the engine illustration itself. Can you find it at all? That is Watt's secret. This is the equivalent of telling you by using the principle of 1+1 makes 2 you could get 34 x 45; the crucial step in understanding (and to make the engine work smoothly in Watt's case) is avoided."
Ah, this is all much, much clearer now. And really interesting. I would still say you should add a header, because it really is a new idea, and you spend a lot of time on it. (Abram, 7/16)
now it has a header "Watt's Secret" (Xingda 7/19)
Looks good. (Abram, 7/21)
  • "How would we find the parametric equation for point F then?" currently only hides "It is easy enough. Refer to Image 12." (Abram, 7/14)
cannot help it. that is the template
Can't you hide as much or as little as you want? (Abram, 7/16)
No, it shows previews of a few lines only and hides the rest but since in this case there are only a few lines and all of them are math, they show up in preview (Xingda 7/19)
I thought Iris had a way around this problem? (Abram, 7/21)
taken care of long time ago (Xingda 7/22)
Great. (Abram, 7/23)