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.

A generalization of the parallelogram law to higher dimensions

Fonda, Alessandro
2019-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2939586
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