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arXiv · 1910.06645

Further generalizations of the parallelogram law

Antonio M. Oller-Marcén
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Abstract

In recent work by Alessandro Fonda, a generalization of the parallelogram law in any dimension $N\geq 2$ 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 $1\leq k\leq N-1$.

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Antonio M. Oller-Marcén. 2019-10-15. Further generalizations of the parallelogram law. https://arxiv.org/abs/1910.06645

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