
06312368
j
2014f.00640
Kalajdzievski, Sasho
One Pythagoras for all dimensions.
Math. Intell. 36, No. 1, 53 (2014).
2014
Springer US, New York, NY
EN
G45
Pythagorean theorem
$n$dimensional box
doi:10.1007/s0028301394251
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.
Antonio M. Oller (Zaragoza)