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 ${\mathbb{C}}^2$.

6 pages

References in corpus (1)

• The discrete square peg problem