Talk:Envelope (mathematics)

message: Interesting, but I can find only one mention of it because "cyclic" (even cyclid/cyclide) is such a common word. take a circle and a curve that does not come into the circle. Take the circles that are centered on the curve and orthogonal to the given circle. The envelope of those circles is the cyclic. 142.177.169.115 19:27, 13 Aug 2004 (UTC)
thread_title: Cyclic

message: It seems to me there is a problem with example 2, the point (u, v) is a solution to the simultaneous equations F=F_t=0 whether the curvature is 0 or not. The only thing that curvature = 0 implies is that the system of equations has a unique solution for the given t. When the curvature is 0, the equations are dependent and there is a line of solutions corresponding to the tangent line. So the solution to the simultaneous equations is really the union of the curve with all tangent lines at points of inflection.  Is there another condition needed to eliminate these extra lines as solutions? Also, if the family is defined by F(x,y,t)=x-t^2 then the solution to F=F_t=0 is x = 0, but this does not satisfy the definition given. In this case the family of curves consists of parallel lines and has no envelope. --RDBury (talk) 06:13, 2 April 2008 (UTC)
thread_title:  Problem with Example 2 or definition 

message: Hello there pma, I hope you're well. Your addition to the envelope article is a very nice piece of mathematics. But I think it might be a bit out of place in the article as it stands. The idea of an envelope is a simple one from differential geometry. When people talk about envelopes they are, by and large, talking about the envelopes of families of smooth submanifolds. Your addition seems very algebraic, and a little out of place. For example: Hölder's inequality? (and in turn Lp-spaces?) It seems to be a very algebraic and topological addition to what was, and ought to be, a differential geometric article.  You obviously know a lot about the topic. Why don't you start another article or at least a new section? I think there's a lot of milage to be had in looking at envelopes from this point of view, but at the moment the example looks right out of place. It had me scratching my head, and I have a PhD in singularity thoery (e.g. discriminants, bifurcations sets, families of functions, etc) and differential geometry. If I was left scratching my head then the interested undergraduate (God help the laymen) would be totally lost. ~~ Dr Dec (Talk)   ~~ 12:50, 10 September 2009 (UTC)
thread_title:  <span class="plainlinks">[http://en.wikipedia.org/w/index.php?title=Envelope_(mathematics)&diff=312939287&oldid=307744747 New example 2]</span> 

message: The new applications section is a nice addition. One of the reasons that envelopes were studies in the past is because they gave singular solutions of differential equations. There are just a couple of things that I think we need to do:
# Give a more concrete introduction, say with ODEs, and maybe give an example.
# Explain how the caustic of reflected parallel light rays relates to differential equations.
Let me know if you'd like me to do either of those. ~~ Dr Dec (Talk)   ~~ 09:02, 21 September 2009 (UTC)
replies: text: Okay, I've added a subsection on ODEs. Any thoughts? ~~ Dr Dec (Talk)   ~~ 10:07, 21 September 2009 (UTC)
replies: text: Caustics would make an easy example to segue into a section on the calculus of variations, that can take up conjugate points and the cut locus.  A good structure might be: (1) odes, (2) caustics, (3) calculus of variations, (4) pdes.  Sławomir Biały (talk) 12:13, 21 September 2009 (UTC)
replies: text: Great minds think alike. I seem to have been busy writing a section on caustic when you made this remark. I would be tempted to keep the DEs together for the sake of continuity. ~~ Dr Dec (Talk)   ~~ 13:16, 21 September 2009 (UTC)
thread_title:  [[Envelope_(mathematics)#Applications|Applications section]] 

message: Honestly, I'm sick of being reverted after good faith attempts to improve the attrocious writing style of this article.  Does anyone here (besides User:Declan Davis) honestly agree that the version of the writing in the definition section is clearer after this revert?  Do other editors here really believe that an enormous profusion of the term "i.e." is the hallmark of good prose style?  I don't wish to get into an edit war over this, already having been told off once before (and then, apparently, given free license to make such copyedits—evidently that has been rescinded).  If there is consensus to make the changes, I would also like to clarify some of the text throughout the article, but I have a feeling that unless I seek such consensus here, Dr. Dec will just continue to revert all of my improvements.  Sławomir Biały (talk) 14:58, 21 September 2009 (UTC)
replies: text: I've changed it twice, and both times left an edit summary to explain my reasoning. After the first change you failed to comment on my edit summary, you just changed it back, without any reasoning. I've left edit summaries and notes on your talk page. You don't seem to have returned the favour. There's no edit war here. In fact the problem would go away if you left notes on my talk page and tried to discuss conflicts, as I have repeatedly done today. This post you have just made is antagonistic. You should have come to my talk page first and explained your reasoning, not just reverted it and then placed a thinly veiled insult on a general talk page. ~~ Dr Dec (Talk)   ~~ 15:05, 21 September 2009 (UTC)
replies: text: I didn't realize that you are the WP:OWNer of the article.  Is there anyone else whose permission I need to ask before making minor copyedits to the article? Sławomir Biały (talk) 15:08, 21 September 2009 (UTC)
replies: text: I have not suggested that I am the owner. As I said on your talk page: "It's becoming very frustrating: we've both spent a lot of time over the last couple of days working on this article. While I take the time to suggest changes to you, and then explain changes, you just undo my work without any warning, let alone explanation. Please be more considerate." And your sarcasm isn't very constructive. If you want to make changes then explain them to people and leave an edit summary. Being frustrated by you going around making changes without any discussion is not claiming ownership; it's simply natural. Wikipedia works much better when editors collaborate. ~~ Dr Dec (Talk)   ~~ 15:21, 21 September 2009 (UTC)

text: I agree with all of these points. I just recommend a multilateral resolution instead of what has been the so far unilateral one. ~~ Dr Dec (Talk)   ~~ 15:25, 21 September 2009 (UTC)
replies: text: Good.  I've tried to clarify the first section, without the term "cut out" that you seem to disagree with (though I would argue that it is quite a standard term throughout mathematics for the locus of an equation). Sławomir Biały (talk) 15:37, 21 September 2009 (UTC)
thread_title:  How to write more clearly 

message: Does this image (used in Timbre#Envelope) fulfill the definition of mathematical envelope? I'm considering adding it as a sample to the article. unsigned comment by 128.138.158.200, 23:47 (UTC), 28 September 2009.
This does not fulfill the definition of a mathematical envelope. As the article clearly states: "In mathematics, an envelope of a family of manifolds (especially a family of curves) is a manifold that is tangent to each member of the family at some point." Your picture is just a single curve, and not a family of curves. The red curve in the picture is tangent to the black curve at some of its points, but that's nothing special: there are uncountably many curves tangent to any given curve, not least the curve itself! ~~ Dr Dec (Talk)   ~~ 22:47, 28 September 2009 (UTC)
replies: text: It's a nice idea, but it's just not what this article is about. You have a single curve, and not a family! and the "envelope" in this sense is just a curve that that bounds the region filled by this one curve. You could write a new article, say Envelope (sound) or something like that and then link to it from this page via a disambiguation. Secondly, please sign your posts by putting ~~~~ at the end of your messages. It'll authomatically be changed into your user details, the time and date so that people know who wrote what and when. ~~ Dr Dec (Talk)   ~~ 09:52, 29 September 2009 (UTC)
replies: text: There is already an article called Envelope detector with most of what you're talking about. It has a red link for Envelope (waves) but it's hard to see why you'd need two articles so maybe a move would be better. Looks like there's some work to be done but it's not my area of expertise.--RDBury (talk) 12:25, 29 September 2009 (UTC)
replies: text: You're right, it's there, right under my nose. Thanks! 128.138.43.211 (talk) 21:59, 1 October 2009 (UTC)
replies: text: Envelope detector should be about the circuits that have envelope (waves) as their output.  But it is not, it is largely about envelope (waves) themselves. SpinningSpark 21:48, 15 May 2010 (UTC)
thread_title:  Possible sample image 

message: The derivation of the condition \partial F/\partial t = 0 seems to be wrong since the point of intersection (x,y) of the curves F(t,x,y)=F(u,x,y)=0 changes with t and u. The limit as u tends to t does not give the partial derivative since that would assume x and y are fixed.  — Preceding unsigned comment added by 193.188.47.48 (talk) 11:01, 16 January 2019 (UTC)
thread_title: Faulty Proof?

message: The astroid should appear symmetrical about the line x = y, but it does not. It would be much better to replace it with a good picture of an astroid.50.205.142.50 (talk) 01:52, 13 May 2020 (UTC)
thread_title:  Bad picture of astroid