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Sums of distances between points on a sphere — an application of the theory of irregularities of distribution to discrete Geometry

Part of: Real and complex geometry

Published online by Cambridge University Press:  26 February 2010

József Beck
József Beck
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Reáltanoda u.13–15, H–1053 Hungary.
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Extract

This paper is concerned with the solution of the following interesting geometrical problem. For what set of n points on the sphere is the sum of all Euclidean distances between points maximal, and what is the maximum?

Our starting point is the following surprising “invariance principle” due to K. B. Stolarsky: The sum of the distances between points plus the quadratic average of a discrepancy type quantity is constant. Thus the sum of distances is maximized by a well distributed set of points. We now introduce some notation to make the statement more precise.

MSC classification

Secondary: 51M99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 33 - 41
Copyright
Copyright © University College London 1984

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References

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