There are a number of interesting results related to the tiling of squares. For example, M. Laczkovich has shown that there are exactly three shapes of non-right triangles that tile the square with similar copies, corresponding to angles , , and (Stein and Szabó 1994). In particular, given triangles of shape with no two the same size, tile the square. The best known solution has 8 triangles (Berlekamp 1999).
The total number of squares contained in a grid of unit square is the square pyramidal number