, 2017

For which pairs $(m,n)$ does there exist an injective function $\$f\colon \mathbb{R}^2\to\mathbb{R}^2$ under which the image of every regular m$-gon is a regular$n$-gon. (Note that$$m,n\ge$ 3$, and that by a regular$N$-gon we mean the union of the boundary segments, not the closed polygonal region.)