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Inscribed square problem

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The inscribed square problem, also known as the square peg problem or the Toeplitz' conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some square? This is true if the curve is convex or piecewise smooth and in other special cases. The problem was proposed by Otto Toeplitz in 1911. Some early positive results were obtained by Arnold Emch and Lev Schnirelmann. As of 2022, the general case remains open.

Inscribed square problem - Wikipedia Jump to content From Wikipedia, the free encyclopedia Unsolved problem about inscribing a square in a Jordan curve Unsolved problem in mathematics Does every Jordan curve have an inscribed square? More unsolved problems in mathematics Example: The black dashed curve goes through all corners of several blue squares. The inscribed square problem , also known as the square peg problem or the Toeplitz conjecture , is an unsolved question in geometry : Does every plane simple closed curve contain all four vertices of some square ? This is true if the curve is co

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