Unsolved problem in geometry of whether every simple closed curve in the plane contains four points at the corners of a square
Also known as Toeplitz's conjecture
6 statements · 17% with external sources · numbers in brackets are citations
3 identifiers linking inscribed square problem across the web's reference databases
From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0
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. The general case remains open.