Sums of distances between points of a sphere

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...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences
Main Author: Glyn Harman
Format: Article
Language:English
Published: Wiley 1982-01-01
Subjects:
geometrical inequalities
extremum problems
irregularities of distribution.
Online Access:http://dx.doi.org/10.1155/S0161171282000647
Description
Summary: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.
ISSN:0161-1712
1687-0425

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