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== The Equichordal Point Problem == == The Equichordal Point Problem ==
A problem in ] that asks wether there exists a curve with two ]. A problem in ] that asks wether there exists a curve with two ].
The problem was originally posed in 1916 by Fujiwara, and solved by ] in 1997. The answer The problem was originally posed in 1916 by Fujiwara<ref name="Fujiwara">M. Fujiwara. Über die Mittelkurve zweier geschlossenen konvexen Curven in
Bezug auf einen Punkt. Tôhoku Math J., 10:99-103, 1916</ref>, and solved by ] in 1996. The answer
in the negative is the subject of ].
in the negative is the subject of ]<ref name="The_Proof">], A complete solution to the equichordal point problem of Fujiwara, Blaschke, Rothe and Weizenböck, ], 1997, Volume 129, Number 1, Pages 141-212.</ref>.
== See also == == See also ==
] ]
] ]
== References ==

{{reflist}}
{{geometry-stub}} {{geometry-stub}}

Revision as of 18:33, 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, and solved by Marek Rychlik in 1996. The answer in the negative is the subject of Rychlik's Theorem.

See also

Rychlik's Theorem Chordal Problem

References

  1. M. Fujiwara. Über die Mittelkurve zweier geschlossenen konvexen Curven in Bezug auf einen Punkt. Tôhoku Math J., 10:99-103, 1916
  2. 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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