Is there a planar convex set having two distinct equichordal points? The problem was first proposed by Fujiwara (1916) and Blaschke et al. (1917), but long defied solution. Rogers went so far as to remark, "If you are interested in studying the problem, my first advice is: 'Don't' " (Croft et al. 1991, p. 9). This advice to the contrary, the problem was recently solved by Rychlik (1996).
Equichordal Point Problem
See also
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References
Blaschke, W.; Rothe, W.; and Weitzenböck, R. "Aufgabe 552." Arch. Math. Phys. 27, 82, 1917.Croft, H. T.; Falconer, K. J.; and Guy, R. K. "The Equichordal Point Problem." §A1 in Unsolved Problems in Geometry. New York: Springer-Verlag, pp. 9-11, 1991.Fujiwara, M. "Über die Mittelkurve zweier geschlossenen konvexen Kurven in Bezug auf einen Punkt." Tôhoku Math. J. 10, 99-103, 1916.Rychlik, M. "The Equichordal Point Problem." Elec. Res. Announcements Amer. Math. Soc. 2, 108-123, 1996.Rychlik, M. "A Complete Solution to the Equichordal Problem of Fujiwara, Blaschke, Rothe, and Weitzenböck." Invent. Math. 129, 141-212, 1997.Wirsing, E. "Zur Analytisität von Doppelspeichkurven." Arch. Math. 9, 300-307, 1958.Referenced on Wolfram|Alpha
Equichordal Point ProblemCite this as:
Weisstein, Eric W. "Equichordal Point Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EquichordalPointProblem.html