Abstract
If S is a given regular d-simplex of edge length a in the d-dimensional Euclidean space \(\mathcal {E}\), then the distances \(t_1\), \(\ldots \), \(t_{d+1}\) of an arbitrary point in \(\mathcal {E}\) to the vertices of S are related by the elegant relation
The purpose of this paper is to prove that this is essentially the only relation that exists among \(t_1,\ldots ,t_{d+1}.\) The proof uses tools from analysis, algebra, and geometry.
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Dedicated to Professor R. G. Swan
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Hajja, M., Hayajneh, M., Nguyen, B. et al. Distances from the Vertices of a Regular Simplex. Results Math 72, 633–648 (2017). https://doi.org/10.1007/s00025-017-0689-1
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DOI: https://doi.org/10.1007/s00025-017-0689-1