Tiling of regular polygons with similar right triangles (Q6158196)

A triangle \(T\) tiles a polygon \(A\) if \(A\) can be dissected into finitely many nonoverlapping triangles similar to \(T\). In this paper the authors prove that for every \(n\neq 4\), there is only one right angled triangle that tiles the regular \(n\)-gon. The triangle is very easily described: let \(R_n\) be the regular \(n\)-gon, connecting the center of \(R_n\) with the vertices of \(R_n\) we obtain a dissection of \(R_n\) into \(n\) congruent isoceles triangles. Bisecting each of these triangles into two right angled triangles gives us a dissection of \(R_n\) into \(2n\) congruent right angled triangles. The proof is short and easy to understand and appreciate.