content:mathematics:square_peg

# 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 :

"*Does every plane simple closed curve contain all four vertices of some square?" *

or* :*

*"Does every continuous simple closed curve in the plane ฮณ : S ^{1} โ R^{2} contains four points that are the vertices of a square?" *

or* :*

*"Does 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): 346โ352.

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