\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2014f.00640}
\itemau{Kalajdzievski, Sasho}
\itemti{One Pythagoras for all dimensions.}
\itemso{Math. Intell. 36, No. 1, 53 (2014).}
\itemab
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.
\itemrv{Antonio M. Oller (Zaragoza)}
\itemcc{G45}
\itemut{Pythagorean theorem; $n$-dimensional box}
\itemli{doi:10.1007/s00283-013-9425-1}
\end