An equichordal point is a point for which all the chords of a curve passing through are of the same length. In other words, is an equichordal point if, for every chord of length of the curve , satisfies
(1)
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A function satisfying
(2)
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corresponds to a curve with equichordal point (0, 0) and chord length defined by letting be the polar equation of the half-curve for and then superimposing the polar equation over the same range. The curves illustrated above correspond to polar equations of the form
(3)
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for various values of .
Although it long remained an outstanding problem (the equichordal point problem), it is now known that a planar convex region can not have two equichordal points (Rychlik 1997).