id: 06312368
dt: j
an: 2014f.00640
au: Kalajdzievski, Sasho
ti: One Pythagoras for all dimensions.
so: Math. Intell. 36, No. 1, 53 (2014).
py: 2014
pu: Springer US, New York, NY
la: EN
cc: G45
ut: Pythagorean theorem; $n$-dimensional box
ci:
li: doi:10.1007/s00283-013-9425-1
ab: 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.
rv: Antonio M. Oller (Zaragoza)