论文信息 - SUMS OF DISTANCES BETWEEN POINTS ON A SPHERE, n

SUMS OF DISTANCES BETWEEN POINTS ON A SPHERE, n

Given N points on a unit sphere in Euclidean m space, m 5:2, 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=i5 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.

K. Stolarsky | Kenneth B. Stolarsky

[1] I. J. Schoenberg. On Certain Metric Spaces Arising From Euclidean Spaces by a Change of Metric and Their Imbedding in Hilbert Space , 1937 .

[2] Glyn Harman,et al. Sums of distances between points of a sphere , 1982 .

[3] W. Schmidt. Irregularities of distribution , 1968 .

[4] G. Björck,et al. Distributions of positive mass, which maximize a certain generalized energy integral , 1956 .

[5] Günter Sperling. Lösung einer elementargeometrischen Frage von FEJES TÒTH , 1960 .

[6] L. Fejes Tóth,et al. On the sum of distances determined by a pointset , 1956 .

[7] E. Hille,et al. Some geometric extremal problems , 1966, Journal of the Australian Mathematical Society.