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Indexed under : Mathematics

Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

The square peg problem

The Square Peg Problem (a.k.a. the Inscribed Square Problem and the Toeplitz' Conjecture) is a geometry problem proposed by German mathematician Otto Toeplitz in 1911.

It can be stated as :

β€œDoes every plane simple closed curve contain all four vertices of some square?”

or :

β€œDoes every continuous simple closed curve in the plane Ξ³ : S1 β†’ R2 contains four points that are the vertices of a square?”

or :

β€œDoes every Jordan curve have an inscribed square?”

It remains unsolved.

For technical details see :A survey on the square peg problem, Notices of the American Mathematical Society, 61 (4): 346–352.

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