Equichordal point problem: Difference between revisions
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There is no <math>C</math> be a [[Jordan curve]] with two [[equichordal points]], with respect to which the curve |
There is no <math>C</math> be a [[Jordan curve]] with two [[equichordal points]], with respect to which the curve |
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<math>C</math> would be [[star-shaped]]. In particular, there is no [[convex]] and [[closed curve]] with two [[equichordal points]]. |
<math>C</math> would be [[star-shaped]]. In particular, there is no [[convex]] and [[closed curve]] with two [[equichordal points]]. |
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=== The Published Proof === |
=== The Published Proof === |
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The proof was published in the hard to read article <ref name="The_Proof">[[Marek R. Rychlik]], A complete solution to the equichordal point problem of Fujiwara, Blaschke, Rothe and Weizenböck, [[Inventiones Mathematicae]], 1997, Volume 129, Number 1, Pages 141-212.</ref> |
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[[Marek R. Rychlik]], |
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A complete solution to the equichordal point problem of Fujiwara, Blaschke, Rothe and Weizenböck, |
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[[Inventiones Mathematicae]], 1997, Volume 129, Number 1, Pages 141-212 |
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1996, pages 108-123]</ref>, but it only hints atthe ideas used in the proof. |
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=== A research announcement (on-line, free) === |
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== References == |
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: ''Note: This paper is easy to read as compared to the article cited above, but it only hints at |
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{{reflist}} |
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the ideas used in the proof. |
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[[Marek Rychlik]], |
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The Equichordal Point Problem, |
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1996, pages 108-123] |
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Revision as of 05:22, 25 November 2010
The theorem solves the Equichordal Point Problem of Fujiwara, originally posed in 1916. The problem was rediscovered in 1917 by Wilhelm Blaschke, Rothe and Weizenböck.
The Theorem
There is no be a Jordan curve with two equichordal points, with respect to which the curve would be star-shaped. In particular, there is no convex and closed curve with two equichordal points.
The Published Proof
The proof was published in the hard to read article [1] There is also easy to read research announcement [2], but it only hints atthe ideas used in the proof.
References
- ^ Marek R. Rychlik, A complete solution to the equichordal point problem of Fujiwara, Blaschke, Rothe and Weizenböck, Inventiones Mathematicae, 1997, Volume 129, Number 1, Pages 141-212.
- ^ [http://www.mpim-bonn.mpg.de/era-mirror/1996-03-002/1996-03-002.html Marek Rychlik, The Equichordal Point Problem, Electronic Research Announcements of the AMS, 1996, pages 108-123]