The discrete square peg problem

Abstract

The square peg problem asks whether every Jordan curve in the plane has four points which form a square. The problem has been resolved (positively) for various classes of curves, but remains open in full generality. We present two new direct proofs for the case of piecewise linear curves.

Cited by in corpus (7)

• Any cyclic quadrilateral can be inscribed in any closed convex smooth curve
• Inscribing a regular octahedron into polytopes
• The Rectangular Peg Problem
• On the number of inscribed squares of a simple closed curve in the plane
• Square-like quadrilaterals inscribed in embedded space curves
• Fulton-MacPherson compactification, cyclohedra, and the polygonal pegs problem
• The algebraic square peg problem