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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
- 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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