This article arose in looking for a 3-dimensional equivalent of the theorem of Pythagoras. One approach is to consider the diagonal of a rectangular box. Another approach, which is explored in this article is to focus on an equation where the sum of two integer cubes is equal to the sum of two other integer cubes. Geometrical diagrams involving isosceles triangles are developed to represent such equations.

Reviewer:

Ramesh Kapadia (London)