A quantitative version of Tao's result on the Toeplitz Square Peg Problem

Abstract

Building on a result by Tao, we show that a certain type of simple closed curve in the plane given by the union of the graphs of two $1$-Lipschitz functions inscribes a square whose sidelength is bounded from below by a universal constant times the maximum of the difference of the two functions.

25 pages, 9 figures

References in corpus (2)

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