Tiling of regular polygons with similar right triangles

TL;DR

This paper proves a unique tiling property for regular polygons with similar right triangles, showing that for each polygon (except the square), there is exactly one such triangle that can tile it.

Contribution

It establishes a complete classification of right triangles capable of tiling regular polygons, except for the case of the square.

Findings

Unique right triangle tilings for all regular polygons except the square

Proof of the exclusivity of these tilings

Complete characterization of tiling possibilities

Abstract

We prove that for every $N\ne 4$ there is only one right triangle that tiles the regular $N$-gon.