====== 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 γ : S<sup>1</sup> → R<sup>2</sup> 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 :[[https://www.ams.org/journals/notices/201404/rnoti-p346.pdf|A survey on the square peg problem]], {{:oa_padlock_grn.png?16}} //Notices of the American Mathematical Society//, 61 (4): 346–352.