The Pythagorean theorem can be restated in the following way: the sum of the squares over the sides of a rectangle is equal to the sum of the squares over the diagonals. This point of view allows the author to give an $n$-dimensional generalization of the Pythagorean theorem in the following way: the sum of the squares over the edges of any $n$-dimensional box is equal to the sum of the squares over its diagonals. The elementary proof is of combinatorial character.

Reviewer:

Antonio M. Oller (Zaragoza)