Equichordal Point Problem: Difference between revisions
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A problem in [[convex geometry]] that asks wether there exists a curve with two [[equichordal points]]. |
A problem in [[convex geometry]] that asks wether there exists a curve with two [[equichordal points]]. |
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The problem was originally posed in 1916 by Fujiwara<ref name="Fujiwara">M. Fujiwara. Über die Mittelkurve zweier geschlossenen konvexen Curven in |
The problem was originally posed in 1916 by Fujiwara<ref name="Fujiwara">M. Fujiwara. Über die Mittelkurve zweier geschlossenen konvexen Curven in |
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Bezug auf einen Punkt. Tôhoku Math J., 10:99-103, 1916</ref>, and solved by [[Marek Rychlik]] in 1996. The answer |
Bezug auf einen Punkt. Tôhoku Math J., 10:99-103, 1916</ref>, and solved by [[Marek Rychlik]] in 1996<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>. The answer |
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in the negative is the subject of [[Rychlik's Theorem]] |
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in the negative is the subject of [[Rychlik's Theorem]]<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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== See also == |
== See also == |
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# [[Rychlik's Theorem]] |
# [[Rychlik's Theorem]] |
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Revision as of 18:43, 25 November 2010
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The Equichordal Point Problem
A problem in convex geometry that asks wether there exists a curve with two equichordal points. The problem was originally posed in 1916 by Fujiwara[1], and solved by Marek Rychlik in 1996[2]. The answer in the negative is the subject of Rychlik's Theorem
See also
References
- ^ M. Fujiwara. Über die Mittelkurve zweier geschlossenen konvexen Curven in Bezug auf einen Punkt. Tôhoku Math J., 10:99-103, 1916
- ^ 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
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