On the Dissection of Rectangles into Right-Angled Isosceles Triangles

Abstract

We consider the problem of dissecting a rectangle or a square into unequal right-angled isosceles triangles. This is regarded as a generalization of the well-known and much-solved problem of dissecting such figures into unequal squares. There is an analogous “electrical” theory but it is based on digraphs instead of graphs and has an appropriate modification of Kirchhoff's first law. The operation of reversing all edges in the digraph is found to be of great help in the construction of “perfect” dissected squares.