The Equichordal Point Problem
Marek Ryszard Rychlik · 1996
. If C is a Jordan curve on the plane and P, Q # C, then the segment PQ is called a chord of the curve C. A point inside the curve is called equichordal if every two chords through this point have the same length. Fujiwara in 1916 and independently Blaschke, Rothe and Weitzenbock in 1917 asked whether there exists a curve with two distinct equichordal points O 1 and O 2 . This problem has been fully solved in the negative by the author of this announcement just recently. The proof (published elsewhere) reduces the question to that of existence of heteroclinic connections for multi-valued, algebraic mappings. In the current paper we outline the methods used in the course of the proof, discuss their further applications and formulate new...