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Spherical distributions of $ N$ points with maximal distance sums are well spaced


Author: Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 48 (1975), 203-206
MSC: Primary 52A40
DOI: https://doi.org/10.1090/S0002-9939-1975-0365363-X
MathSciNet review: 0365363
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Abstract: It is shown that if $ N$ points are placed on the unit sphere in Euclidean $ 3$-space so that the sum of the distances which they determine is maximal, then the distance between any two points is at least $ 2/3N$. Results for sums of $ \lambda $th powers of distances are also given.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0365363-X
Article copyright: © Copyright 1975 American Mathematical Society

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