A generalization of the parallelogram law to higher dimensions - Fonda, Alessandro (Ars mathematica contemporanea, 2019)
We propose a generalization of the parallelogram identity in any dimension ?$N≥ 2$?, establishing the ratio of the quadratic mean of the diagonals to the quadratic mean of the faces of a parallelotope. The proof makes use of simple properties of the exterior product of vectors.
Keywords: paralelogramski zakon; paralelotop; parallelogram law; parallelotope