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In Euclidean plane geometry, the equichordal point problem is the question whether a closed planar convex body can have two equichordal points. The problem was originally posed in 1916 by Fujiwara and in 1917 by Wilhelm Blaschke, Hermann Rothe, and Roland Weitzenböck.〔 W. Blaschke, W. Rothe, and R. Weitztenböck. Aufgabe 552. Arch. Math. Phys., 27:82, 1917 〕 A generalization of this problem statement was answered in the negative in 1997 by Marek R. Rychlik. == Problem statement == An equichordal curve is a closed planar curve for which a point in the plane exists such that all chords passing through this point are equal in length. Such a point is called an equichordal point. It is easy to construct equichordal curves with a single equichordal point,〔 particularly when the curves are symmetric; the simplest construction is a circle. It has long only been conjectured that no convex equichordal curve with two equichordal points can exist. More generally, it was asked whether there exists a Jordan curve with two equichordal points and , such that the curve would be star-shaped with respect to each of the two points.〔〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Equichordal point problem」の詳細全文を読む スポンサード リンク
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