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: OK, I did. :-) [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 17:44, 31 March 2012 (UTC) |
: OK, I did. :-) [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 17:44, 31 March 2012 (UTC) |
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== So, what about "M. Reeken"? == |
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Now, he or she was "M. Reeken", and I added the "M", which is given in the references. So, "Who Reeken"? Please give the whole name.<br> |
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Just calling someone "Reeken" or "Jordan" or "Jones" or "Schwartz" on first appearace is actually quite rude. If this is a person who wants to be referred to as "M. Reeken", then please give her or him that much. As for the present, we do not know if this was "Marion Reeken", "Michael Reeken", "Michelle Reeken", or "Madison Reeken".<br>[[Special:Contributions/98.67.108.12|98.67.108.12]] ([[User talk:98.67.108.12|talk]]) 16:29, 25 August 2012 (UTC) |
Revision as of 16:29, 25 August 2012
Mathematics Start‑class Mid‑priority | ||||||||||
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Formal proof
I have just clarified the formal proof priority, sorry for doing it anonymously - have not noted I was logged out. JosefUrban (talk) 15:41, 4 January 2009 (UTC)
Illustration
An illustration could really improve the article and give credence to the claim that the concept is intuitive.--Cronholm144 10:14, 25 May 2007 (UTC)
- This has been done.
98.67.108.12 (talk) 16:23, 25 August 2012 (UTC)
Question
Hello, I have a question. A book that I am reading says that "A Jordan curve is an equivalence class of homeomorphisms of I into R2 (or of S1 into R2 in the case of closed curves)." This article defines a Jordan curve as "a simply closed curve."
1. The book I am reading is implying an arbitrary equivalence relation? And what is the purpose of this equivalence class? (I assume that it is just a way of saying 'all the identical homeomorphisms', so that it gets all the same shapes that are represented differently?)
2. This article says that a Jordan curve is a simple closed curve, but I think the definition my book gave says that it doesn't have to be simply closed, though it may, i.e. 'a homeomorphism of S1 in the case of closed curves'. But I know that this article is right, because a Jordan curve is defined identically in Curve.
Sorry for the stupid questions. Great article!
- As for 1, the book certainly refers to some specific equivalence relation. You have to look backwards for a definition of equivalent curves. It is hard to guess what they mean by it without reading it, though one possibility is that curves are equivalent if they differ by a homeomorphic change of parametrization.
- As for 2, note first that a homeomorphism is in this context the same thing as an injective continuous map (because S1 is compact, and R2 is Hausdorff), thus the two definitions agree on what closed curves are Jordan curves. As far as I am aware, allowing Jordan curves to be non-closed is highly unusual. At any rate, the Jordan curve theorem only applies to closed curves. — Emil J. 15:33, 23 September 2008 (UTC)
Applications in collision detection
Hi guys.... I think this article needs to be expanded to encompass one of its most useful applications: 2D collision detection. These sites give a good explanation of what the Jordan Curve Theorem means in a practical sense, and would help explain the concept to the less math-inclined. The strategy: http://tog.acm.org/editors/erich/ptinpoly/ Example implementation: http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html —Preceding unsigned comment added by Oticon6 (talk • contribs) 14:14, 1 April 2009 (UTC)
suggested addition
This paper seems like a nice reference. It has nice pictures in it. I hope one of you experts will include it somehow :)
https://facultystaff.richmond.edu/~wross/PDF/Jordan-revised.pdf — Preceding unsigned comment added by 98.249.0.238 (talk) 00:37, 31 March 2012 (UTC)
- OK, I did. :-) Boris Tsirelson (talk) 17:44, 31 March 2012 (UTC)
So, what about "M. Reeken"?
Now, he or she was "M. Reeken", and I added the "M", which is given in the references. So, "Who Reeken"? Please give the whole name.
Just calling someone "Reeken" or "Jordan" or "Jones" or "Schwartz" on first appearace is actually quite rude. If this is a person who wants to be referred to as "M. Reeken", then please give her or him that much. As for the present, we do not know if this was "Marion Reeken", "Michael Reeken", "Michelle Reeken", or "Madison Reeken".
98.67.108.12 (talk) 16:29, 25 August 2012 (UTC)