Any cyclic quadrilateral can be inscribed in any closed convex smooth curve

Abstract

We prove that any cyclic quadrilateral can be inscribed in any closed convex $C^1$-curve. The smoothness condition is not required if the quadrilateral is a rectangle.

6 pages, 10 figures

References in corpus (3)

• Quadrilaterals inscribed in convex curves
• The discrete square peg problem
• Inscribing a regular crosspolytope

Cited by in corpus (7)

• Quadrilaterals inscribed in convex curves
• Configuration Spaces, Multijet Transversality, and the Square-Peg Problem
• Fun Problems in Geometry and Beyond
• Families of similar simplices inscribed in most smoothly embedded spheres
• Square-like quadrilaterals inscribed in embedded space curves
• Rectangle Coincidences and Sweepouts
• A quantitative version of Tao's result on the Toeplitz Square Peg Problem