A Survey on the Square Peg Problem
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2014-03-11
SCID: 54.1/stk2j5f9
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Inscribed Square ProblemSquare Peg ProblemToeplitz conjecturecontinuous simple closed curvesplane geometry
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Abstract (AI)
T his is a short survey article on a 103year-old and still open problem in plane geometry, the Square Peg Problem.It is also known as the Inscribed Square Problem and it is due to Otto Toeplitz.Conjecture 1 (Square Peg Problem, [39]).Every continuous simple closed curve in the plane γ : S 1 →
Key Findings
1
The paper surveys the 103-year-old Square Peg Problem, also called the Inscribed Square Problem, originating with Otto Toeplitz.
2
The problem conjectures that every continuous simple closed plane curve contains four points forming the vertices of an inscribed square.
3
The survey addresses an important open question in plane geometry, indicating that the conjecture remains unresolved in its full generality.
Research Object
the Square Peg Problem for continuous simple closed plane curves
Research Subject
the existence of an inscribed square on every continuous simple closed plane curve
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2014-03-11
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