# Talk:Envelope

### From Math Images

Smaurer1 14:18, 10 June 2012 (EDT)

Peng,

I've read through your latest version. This is going to be a beautiful page. For most of it, I just think it needs copyediting (that is, small corrections to English and consistent use of italic). I have made *some* of the copyedits I saw; compare the current version of the page with your last version using the history, to identify the sort of changes I made. Then I suggest you get the other students on your team to make further copyedits.

Three general issues that we should probably discuss with the whole summer group:

- highlighting of words being defined (use boldface, I think)
- minus signs in math expressions written without the <math>....</math> environment. Dont use "-"; use &ndash (followed by a semicolon but I didn't put a semicolon here because that makes the dash actually appear, as now:
*x – y*). - Should curve names (astroid, ellipse, circle) be capitalized? You do, but generally they are not. However, the capitalization calls attention to them, which may be appropriate here.

The one part of the page that needs more work is your revised material on a More Mathematical Explanation. You don't have it quite right. I will meet in person with you to discuss it, and a few other things.

Interesting observation: The parabola envelope of the firework is just a vertical displacement of the parabola formed by fragments that shoot out exactly horizontally.

Hi Peng, I've been playing with those gifs you were having trouble with because of their size. The first I could put in a thumbnail with no problem, but I did have the glitch you were talking about with the second. You can just put that one in a frame, which allows you to do all the regular formatting other than resizing. Here's the syntax I used for the gifs; you can do other things with the specs, and it should still work:

-Diana (10:16, 6/4/12)

Hi Peng,

The latest incarnation of this page looks great. I especially like the explanations of key terms that you added in hidden sections. I only have a few suggestions:

- When the "Click to show the mechanism behind this" sections under the Asteroid with ellipses section and the Deltoid section are hidden, there's a box underneath them. Did you mean to have that there? It's strange looking; I suggest taking it out.
- I definitely see what you mean about adding a less mathematical explanation of those two envelopes (the Asteroid with ellipses and the Deltoid) being redundant. But these sections are a bit weird when the mathematical explanations are hidden. I think these two small changes would make the page flow better for people who choose not to open those sections:
- Place the hidden section below the gif, rather than above, so that there isn't so much space between the animation and the non-mathematical bit.
- Add just
*one*sentence to the non-mathematical parts of each of these sections. For example, "...asteroid: using**a family of ellipses**. We see below that as*C*varies, these ellipses sweep the area of that figure." And "...one of the most beautiful envelopes out of it. Here we can see that as the point*M*anchoring the Wallace-Simson line moves around the circle, that line sweeps a Deltoid." If you just add brief sentences saying something about the gif -- they don't have to be these -- the sections won't seem to just stop in the middle as they do now.

- Under the more mathematical section in "Resolving the second problem: the boundary condition," your explanation of the implicit function theorem is long enough that the reader loses track of the fact that you had indicated you were going to prove the boundary condition. I don't think you need to take it out or hide it, but it would be good to make it very clear to the reader that you are constructing a proof here, first by saying something like, "We will now prove this condition using
**the implicit function theorem**," instead of, "This condition is easy to prove using**the implicit function theorem**." Then as you move from the examples in figures 6-3 and 6-4 into the general case of an envelope, make it explicit that this is what you are doing; that you're returning to the main body of your proof. - In the "Why It's Interesting" section, under "Applications in Microeconomics: the Envelope Theorem," the beginning of your second paragraph: "To answer these questions..." no longer makes sense, because you have a new sentence between this paragraph and the questions you're referring to from the previous paragraph; you'll need to re-phrase this. I'd use, "To analyze all these curves at once..."

Very good job overall! I really love this page. -Diana 15:19, 18 June 2012 (EDT)