Geodesic
A generalization of the parallelogram law to higher dimensions
Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 411-417.

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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.
DOI : 10.26493/1855-3974.1704.34c
Keywords: Parallelogram law, parallelotope 
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Alessandro Fonda. A generalization of the parallelogram law to higher dimensions. Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 411-417. doi : 10.26493/1855-3974.1704.34c. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1704.34c/

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