Let m,n>2 be integers. A regular n-sided polygon region T on a plane contains a regular m-sided polygon region with a side length of 1. Prove that any regular m-sided polygon region S on the plane with side length cosπ/[m,n] can be translated inside T. In other words, there exists a vector α, such that for each point in S, after translating the vector α at that point, it fall into T.
Note: The polygonal area includes both the interior and boundaries. combinatoricscombinatorial geometry2024 CTST