A generalization of the parallelogram law to higher dimensions

Alessandro Fonda

Abstract


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


Parallelogram law, parallelotope

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DOI: https://doi.org/10.26493/1855-3974.1704.34c

ISSN: 1855-3974

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