Tilings of Parallelograms with Similar Right Triangles
We say that a triangle tiles the polygon if can be decomposed into finitely many non-overlapping triangles similar to . A tiling is called regular if there are two angles of the triangles, say and , such that at each vertex of the tiling the number of triangles having as a vertex and having angle at is the same as the number of triangles having angle at . Otherwise the tiling is called irregular. Let be a parallelogram with acute angle . In this paper we prove that if the parallelogram is tiled with similar triangles of angles , then or , and if the tiling is regular, then only the first case can occur.
parallelogram right triangle regular and irregular tiling