Unsolved Problem 26:

Given a simple closed curve in the plane, can we always find four points on this curve that are the vertices of a square?


[Croft 1991]
Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy, Unsolved Problems in Geometry. Springer-Verlag. New York: 1991. Page 51.
Inscribing a Square in a Curve
Each week, for your edification, we publish a well-known unsolved mathematics problem. These postings are intended to inform you of some of the difficult, yet interesting, problems that mathematicians are investigating. We do not suggest that you tackle these problems, since mathematicians have been unsuccessfully working on these problems for many years.

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