 
Summary: ON SUM OF DISTANCES ON A SPHERE
Tewodros Amdeberhan
Department of Mathematics, Temple University, Philadelphia PA 19122, USA
tewodros@euclid.math.temple.edu
Abstract. An improved upper bound for the sum of distances between N points on a
unit sphere is presented.
Let P1;:::;PN be points on the unit sphere Sn,1 of the Euclidean space Rn. De ne
the distance
SN;n; = max
X
i j
jPi ,Pjj
where the max is taken over all possibleP1;:::;PN. Thisfunction has been investigated
by several authors 1  5 . Denoting the surface area of Sn,1 by Sn,1 and
cn; = 1
2 Sn,1
Z
Sn,1
jP0 ,Pj P
for any xed point P0, the following are the best known to date estimates for S.
