The Rectangular Peg Problem
Abstract
For every smooth Jordan curve $\gamma$ and rectangle $R$ in the Euclidean plane, we show that there exists a rectangle similar to $R$ whose vertices lie on $\gamma$. The proof relies on Shevchishin's theorem that the Klein bottle does not admit a smooth Lagrangian embedding in $\mathbb{C}^2$.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.09193
 Bibcode:
 2020arXiv200509193G
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Metric Geometry;
 Mathematics  Symplectic Geometry
 EPrint:
 6 pages