The rectangular peg problem


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 the theorem of Shevchishin and Nemirovski that the Klein bottle does not admit a smooth Lagrangian embedding in $\mathbb{C}^2$.


Joshua Evan Greene

Department of Mathematics, Boston College, USA

Andrew Lobb

Mathematical Sciences, Durham University, UK