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 | References | Similar Articles | Additional Information
Abstract: Given points on a unit sphere in Euclidean
space,
, 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
is smaller than any previously known and (ii) the existence of
point distributions with small discrepancy. We make use of W. M. Schmidt's work on the discrepancy of spherical caps.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1973-0333995-9
Article copyright:
© Copyright 1973
American Mathematical Society