The Rectangular Peg Problem

2020/05/19 by Joshua Evan Greene, Greene, Joshua Evan, Andrew Lobb +1 · 1 citation
Mathematics · Computer Science · #Mathematics and Applications #Computational Geometry and Mesh Generation #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2005.09193

Abstract

For every smooth Jordan curve γ and rectangle R in the Euclidean plane, we show that there exists a rectangle similar to R whose vertices lie on γ. The proof relies on Shevchishin's theorem that the Klein bottle does not admit a smooth Lagrangian embedding in ℂ².

Cited by

• Inscriptions in non-Euclidean Geometries

Related

• The rectifiable rectangular peg problem
• Generic doubling of rectangular pegs
• On the square peg problem
• The discrete square peg problem
• On the Square Peg Problem and Its Relatives