International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1982 / Article

Open Access

Volume 5 |Article ID 650584 | https://doi.org/10.1155/S0161171282000647

Glyn Harman, "Sums of distances between points of a sphere", International Journal of Mathematics and Mathematical Sciences, vol. 5, Article ID 650584, 8 pages, 1982. https://doi.org/10.1155/S0161171282000647

Sums of distances between points of a sphere

Received01 Feb 1982

Abstract

Given N points on a unit sphere in k+1 dimensional Euclidean space, we obtain an upper bound for the sum of all the distances they determine which improves upon earlier work by K. B. Stolarsky when k is even. We use his method, but derive a variant of W. M. Schmidt's results for the discrepancy of spherical caps which is more suited to the present application.

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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