The sum of the distances to certain pointsets on the unit circle

Kenneth Barry Stolarsky

Vol. 59 (1975), No. 1, 241–251

DOI: 10.2140/pjm.1975.59.241

Abstract

Let p₁,⋯,p_n be points on the unit circle U. For p ∈ U define T_λ(p) = ∑ |p−p_i|^λ. The extremal behavior of T_λ(p) is completely described in two cases: (i) 0 ≦ λ ≦ 2 and n = 3 and (ii) 0 ≦ λ < 2n and p₁,⋯,p_n the vertices of a regular n-gon.

Mathematical Subject Classification 2000

Primary: 52A40

Milestones

Received: 19 March 1975

Published: 1 July 1975