A simple sum for simplices

Christian Aebi; Grant Cairns

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arXiv · 2202.05156

A simple sum for simplices

Christian Aebi·Grant Cairns

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Abstract

We give a vector identity for $n+2$ points in $\mathbb R^n$. It follows as a corollary that when $n$ is odd the sum of the signed volumes of the $n$-simplices is zero, and when $n$ is even, the alternating sum of the signed volumes is zero.

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BibTeX RIS

Christian Aebi, Grant Cairns. 2022-02-09. A simple sum for simplices. https://arxiv.org/abs/2202.05156

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