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Image of regular m-gon is a regular n-gon

Source: KoMaL A. 711

May 21, 2023
combinatoricscombinatorial geometry

Problem Statement

For which pairs (m,n)(m,n) does there exist an injective function f:R2→R2f:\mathbb{R}^2\to\mathbb{R}^2 under which the image of every regular mm-gon is a regular nn-gon. (Note that m,n≥3m,n\geq 3, and that by a regular NN-gon we mean the union of the boundary segments, not the closed polygonal region.)
Proposed by Sutanay Bhattacharya, Bishnupur, India
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