Talk:Witch of Agnesi

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Checklist

Messages to the Future

  • So far, I have no suggestions. I would be nice if someone could make an identical applet that I provided a link to.

References and footnotes

  • Most images were made on my own except for the opening image. Didn't use direct quotes from but summarized cites for the history section in why it's interesting.
  • links are listed at the bottom.

Good writing

  • People are interested because there is such rich history and pride in the person who is know for promoting the curve. "Why It's Interesting" section is a biography on Agnesi and goes into detail her life and the name of the curve.

Quality of prose and page structuring

  • outline steps to construct the witch along with images
  • stress the point of doing every step
  • more mathematical section
  • instructed readers to refer to an image. Images are labeled.

Connections to other mathematical topics The page could link to basic trig but I think it would be a nuisance since I explain cotangent

  • You can turn the word cotangent into the link itself, which I think would be helpful.
  • Proof is included along with images that relate
  • Couldn't find any applications of the equation so instead did a historical section
  • define some geometric terms at the beginning, tried being concise
  • no real use for mouse overs or helper pages
  • Text is in short paragraphs. tried to aim for the 100 or less word limit.
  • Page looks decent in my window and on the computers in the lab.

  • Add more space between your two columns at the beginning. They run very close together in my browser window.
  • Change the image in step 3 to include point D. It was very confusing to have it referenced when it's not on the image. Similarly, change the image in step 4 to include point P.
  • It might be nice to make all of these images a bit bigger. That might mean that you need to just let the steps come in order instead of using the column format

When I don't use the column format the images reach the why it's interesting section. And, the readers would be confused about the images and descriptions being scattered all over the place. I think the colum format is the only way to display the images and phrases.

  • Image 4 needs to be bigger. Maybe edit the image to crop it so that there's less whitespace in the image itself.
  • Instead of saying "All triangles are 180 degrees. " You should specific that the angle measures sum to 180 degrees.
  • "Because they're alternative interior angles" ->In that sentence it's much better to say "they are" instead of "they're"
  • In that same paragraph, break the first half and second half into two paragraph. Each time you describe a single similar triangle, that should be its own paragraph.
  • Try to do something to make this sentence: "In order to derive the Witch it's essential to remember that a is the diameter. " jump out a bit more since it's so important.
  • This sentence: "Notice that point D and E are located on the same y coordiante so instead of saying that D is at \left( \mathrm{i},\mathrm{j} \right) we can say it's at \left( \mathrm{i},\mathrm{y} \right). " should go before your rewritten equation 1
  • Image 5 should move up so a bit so that people can see how you define x, y, i and k.
  • Under your "different Witch" section, you should specific that the equation for the x part doesn't change.
  • I'd suggest reworking how you show that the two forms are equivalent. Reusing a and b so many times is confusing.

Anna, I'm not sure how to address this comment. Is it that you want me to use another variable other than "B"? In that case I could use any letter like "H" for example. However, if that's not the case then I am not sure how I should show that the two expressions are equivalent. I would appreciate some suggestions. Thanks.

  • When you use the pythagorean theorem to created the triangles, don't use a in equation 3 (the first time). Keep all of th equations looking the same by using AB instead of a
  • You have a typo in the fourth line following : "We cross multiply and solve for i. "
  • You are missing a parenthesis in the equation following the line "Substituting the first two expression into the third, we get one expression. "
  • You say, " i = \left ( \frac{xy} {a} \right )^2 " but  i =\frac{xy}{a}  (not squared)

I've addressed all the comments above.

Chris 7.17.11 This is a really interesting topic; I'm delighted you chose to make a Math Images page about it. I love how it connects with the life of Maria Agnesi and that an 18th century female mathematician got recognition associated with it.

My comments are mostly about rewording. I have suggested a few places where sections could actually be removed for brevity and clarity. Nice job, Leah.

Witch of Agnesi

  • The Italian word for witch is strega; "versiera" actually similar to the word "avversiera" in Italian, which means "woman contrary to God." This was interpreted as "witch."

Basic Description

  • Step 3: The line segment AC cannot intersect tangent B because it ends at the circle. Rephrase to note that the segment lies on a line that intersects tangent B at D. You also drew segment EC which you don't talk about in the explanation.
  • Step 4: Your drawing shows that you extended EC to P. It does not show line DP.
  • Step 5: This is the step in which you create DP.
  • Step 6: You might begin this step by saying something like: "To create the Witch of Agnesi, drag point C around the circle. As C changes position..."


  • I've addressed all the comments above and changed the text over the images.
    • Chris 7.21.11 There are still a few changes needed on the diagram steps. Step 2 should not include simply labeling a point C on tangent B. Point C is the point where line AD intersects the tangent line l1. The order should be:
      • Create point D
      • Extend AD to intersect l1. Mark the point of intersection C.
      • Drop a perpendicular line from point C to intersect l2.
      • Make a parallel line to the two tangent lines at D.
      • Where it intersects AB, call the point G. Where it intersects the perpendicular dropped from C, call the point E.

I've changed some of the steps. I had to keep step 2 as it was otherwise the labeling would be off. I would mentioned pt D but then people would wonder why its not named pt C because of the order. .

A More Mathematical Explanation

  • It would be helpful if you could draw actual points for A, B, C, etc. on your images. Also, it would also be nice if the names of the points were the same as in your initial image in the basic description.
  • I'll try to do the images over, but I didn't think it would matter if the basic description labeling was different from the mathematical one. I thought it would be helpful to show that the points can be located anywhere and can be called anything.
    • Chris 7.21.11 I think it is important to be consistent. Readers know that points can get various names.

Yes, I changed the images in the steps so that they are like the ones in the MME section.

*I assume that A is on the x-axis. You might say so explicitly.

  • Paragraph 4 (P4):
    • Sentence 1 (S1) Change "one of the legs" to "leg DE" and add that leg CE is perpendicular to the x-axis.
    • S2: C moves to both the right and left to generate the curve. I would talk about moving D once around the circle. That's easier to understand, I think.
    • Remove S3 and change sentence 4 to "curve formed by the traces E makes while D moves around the circle."


I've addressed all the comments above.

Derivation

  • P1S1: Change "image on the left" to "Image 4."
  • P2S2: The degrees label shows up as a subscript on my computer.
  • P3S2: Change "alternative" to "alternate." Also, change "is the same as" and "Is similar to" to "Is congruent to"
  • P4: You've already stated this is paragraphs 2 and 3, so this paragraph is largely unnecessary. You simply need to add on a last sentence to P3, saying that since the triangles are similar, then their sides are proportional.
  • P5: The last sentence is not needed. Place P6 on the end of P5 since they are directly connected.


I've addressed all the comments above.


  • P7: This paragraph is also not needed. The reader should hopefully be able to figure this out as you progress.


I decided to keep this paragraph because it gives an outline on what's to expect.


  • P9: Change "point D and E" to "points D and E."


I've addressed this comment.


  • An image that corresponds with Eq. 2 would be helpful, showing how the four parts of the proportion correspond to particular distances marked either by one variable or the subtraction of two variables.


I'm creating an image for this.

  • P2 after Eq. 2 You are distributing x on one side but distributing a on the other.
  • Second paragraph from the bottom: Change "Simplify and solve for y" to "Divide each side by y and factor out y from each term."
  • Last paragraph: "Solve for y and you get the Witch in Cartesian form..."


I've addressed all the comments above.


Parametric Derivation

  • Give the image a number.
  • P1: "a little trigonometry"
  • P2S2: "opposite side of a right triangle."
  • P5, Step 2: Add an explanatory sentence: "Factor out the a^2 from both terms in the denominator."


I've addressed all the comments above.


Same Witch, Different Formula

  • Add an "s" to make it "Different Formulas"
  • P1S3: Add an "s" to make it "Other texts"


I've addressed all the comments above.


  • I'm not really sure if this section is necessary. Anyone able to make sense of your article should be able to negotiate the change from diameter being a to radius being a.


I want to keep this section, because it's important to state and show that there is another form to the curve.

General Comments

Overall I think that this is a really good page. Occasionally I thought that the language was a little too colloquial and not technical enough (ie saying that the name 'stuck' in the introduction). Good job, though.

Nordhr 18:31 27 June 2011

*Kate 17:10, 24 June 2011 (UTC):

  • Be consistent about whether you call it the Witch or the witch. I think I like capital-W better, but either one's probably okay.

*I think you should use section headings to separate your derivations and Side Note in the MME

  • I think your general outline for the page is really good, and I like that you used the Why It's Interesting section as an opportunity to talk about Maria Agnesi.
  • I agree- I think the page layout is very good, and your writing is very clear!

Section-Specific Comments

  • At the very very top of the page, you said that the Witch was a cubic curve - it doesn't seem cubic to me, there's no x3 in it…

Leah 15:47, 27 June 2011 (UTC) It's kinda not a cubic curve but I was trying to be descriptive. I'll take this part out. * I agree- is the curve definitely cubic?

  • The intro is good, but i think it could be a little better at hooking in the reader. I like the sentence "It is a cubic curve that is symmetric about the y-axis and approaches an asymptote on the x-axis." I would keep that. But it also think it might be cool to add that "The Witch of Agnesi was originally called la versiera di Agnesi, or "the Curve of Agnesi." The word "curve" is very similar to the word "witch" in Italian, so the name was mistranslated and it stuck." You don't have to add this, I just thought it was SO interesting when I read the why it's interesting section and I had been wondering about the name all along.

Leah 15:47, 27 June 2011 (UTC) Sure thing. I'll add some things to the intro to keep people interested.

Basic Description

Kate 17:10, 24 June 2011 (UTC):

  • I know we were all confused about how to construct the curve at that meeting, but I actually think that what you've got here is a pretty good explanation, if only the text were next to the pictures. It would be much easier to follow if it went:
To construct the Witch geometrically, first draw a circle with diameter a formed from point A and B:
[image of step 1 here]
Draw tangents at A and B. A tangent is a line that touches the curve of the circle just at one point such that the point is the place where the curve and plane will only meet.
[image of step 2 here]
and so on…

Leah 19:56, 24 June 2011 (UTC) Ok, I'll separate the images and place them near the text that corresponds.

*The various location of point P will outline the witch.

First of all, typo, should be "locations" not "location". Second of all, I think it would be clearer to say something more like "As P moves, it will trace out the Witch"

Rebecca 00:37, 27 June 2011 (UTC) Great basic description.. Very clear!

More Mathematical Explanation

Kate 17:10, 24 June 2011 (UTC):

*We again create the curve by having a circle with diameter a drawn tangent to the x-axis with origin at A and connecting to B.

This sentence is confusing. 1) I think you should say that the diameter is perpendicular to the x-axis, not that it's tangent. 2) It's unclear to me whether you're trying to say that A is located at the origin - the point (0,0) - or that A and B are the endpoints of the diameter a.

*The line through points B and C is parallel to the axis

You're talking about C before establishing that C exists, which I don't think is standard math writing. I suggest saying something like "Let there be a point C such that BC is parallel to the x-axis." You do the same thing with points D and E. You might want to check with Gene, but I'm pretty sure when writing about geometric figures, you're supposed to define points before you talk about them. So it's better to say "Let D be the point where AC intersects the circle" than "AC intersects the circle at D".
Leah 20:01, 24 June 2011 (UTC) I think you're right about defining things.

*You say that the curve is traced out by E as it moves, but in Image 3, it's clear that some of the points where E is aren't on the curve - why?

*In order to find the equation of the curve, the triangles formed in the image are important in the derivation.

This sentence doesn't make sense - the two halves of it seem to be parts of different sentences that just happened to get shoved together here.
  • Your label for D is kind of lost in image 4

*Due to alternative interior property

First of all, you're missing a "the", but I think it'd sound better to say "Because they're alternative interior angles, …"

*We prove the two triangles are similar

Which two triangles?

*In your paragraph just before Eq. 1, I think it would be helpful to remind the reader that you proved those two pairs of angles were the same in the paragraph above, and not just say, well these two are both theta.

*I don't think (i,j) and (x,y) are dummy variables in the way I understand that term. Also, I think you should give a little bit more explanation about how you get from the coordinates to the sides of the triangles. And a reminder that a is the diameter would be nice too.

*We now know the x-coordinate of E. - do we? We just solved for i, and I thought i was the x-coordinate of D?? Leah 18:37, 27 June 2011 (UTC) You're right! I guess I put D accidentally.

*You're missing the squared sign on DB in your last equation after the sentence "By Pythagoream Theorem, we will create three equations…"

*It's important to know trigonometric identities, trigonometric functions that have equalities true for any value including variables such as θ

This sentence doesn't make much sense

  • In your last set of displayed equations under the side note:
  • right now, it looks like the two fraction expressions are being multiplied
  • I'm not sure you can substitute y in for a like that - don't you want to use another variable?


xd 18:50, 14 June 2011 (UTC) I realize that the whole derivation uses image 4. but later on you used \triangle ADF \triangle BDG and \triangle BAD, referring to points not in the image. those points are in a different image in basic description. It is good practice to have those points in image 4. Also, your cartesian equation is different from that in wikipedia. has anymore vetted your math?


Leah 15 June (UTC) updated images and added side note on why the there are different ways the witch is presented. Need advice on how I should prove the two ways to represent the witch are the same.

* Rebecca 00:39, 27 June 2011 (UTC) I would consider calling the section "side note" something a little more descriptive. If you do that, then you could hide the section since it isn't essential to understanding the page. It's your call though- you definitely don't NEED to hide it.

Why It's Interesting

Kate 17:29, 24 June 2011 (UTC):

  • She was best known for her contribution in differential calculus, in particular, for her study in the cubic curve: Witch of Agnesi.
I think it would sound better as: "She was best known for her contributions to differential calculus, in particular, for her study of the cubic curve known as the Witch of Agnesi."
  • Run-on sentence: At a young age Agnesi was very involved in academics at the age of nine she could speak Italian, Greek, Latin, Hebrew and French. - "… in academics." should be the end of one sentence and "At the age…" should begin the next sentence.
  • Typo: and deriving mathematical formula.
  • I think you should italicize the name of her textbook.
  • Typo: "…but because she associates with the curve" - should be "because she is associated with the curve"
  • I think you should italicize the Italian words you use in this section.
  • It is ironic that the curve is directed under Agensi. - what do you mean by "directed under"? Do you mean that it's "associated with" her?

*Rebecca 00:45, 27 June 2011 (UTC) I think you mean "despite prejudice she PERSERVERED in mathematics."

  • Very interesting section! I love it. I actually think this section is so interesting that it might be worthwhile to add a teaser to the introductory sentence.
  • Also, I think you should switch the order of your last two paragraphs in this section.

Leah 18:40, 27 June 2011 (UTC) Did Rebecca's suggestions.