Irregular Tilings of Regular Polygons with Similar Triangles

Abstract We say that a triangle T tiles polygon A , if can be dissected into finitely many nonoverlapping triangles similar to . show $$N>42$$ N > 42 then there are at most three nonsimilar such the angles of rational multiples $$\pi $$ π and regular N -gon. tiling is called regular, pieces have two angles, $$\alpha α $$\beta β each vertex number same as Otherwise irregular. It known for every infinitely tile regularly. $$N>10$$ 10 -gon irregularly only Therefore,