Further generalizations of the parallelogram law
DOI:
https://doi.org/10.11575/cdm.v15i2.69344Abstract
In a recent work of Alessandro Fonda, a generalization of the parallelogram law in any dimension N≥2 was given by considering the ratio of the quadratic mean of the measures of the (N−1)-dimensional diagonals to the quadratic mean of the measures of the faces of a parallelotope. In this paper, we provide a further generalization considering not only (N−1)-dimensional diagonals and faces, but the k-dimensional ones for every 1≤k≤N−1.
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