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Sums of distances between points on a sphere. II


Author: Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 41 (1973), 575-582
MSC: Primary 52A40
DOI: https://doi.org/10.1090/S0002-9939-1973-0333995-9
MathSciNet review: 0333995
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Abstract: Given $ N$ points on a unit sphere in Euclidean $ m$ space, $ m \geqq 2$, we show that the sum of all distances which they determine plus their discrepancy is a constant. As applications we obtain (i) an upper bound for the sum of the distances which for $ m \geqq 5$ is smaller than any previously known and (ii) the existence of $ N$ point distributions with small discrepancy. We make use of W. M. Schmidt's work on the discrepancy of spherical caps.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0333995-9
Article copyright: © Copyright 1973 American Mathematical Society

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