Near minimum energy distributions on the sphere using Voronoi cells

Abstract

In this thesis we investigate the use of Voronoi cells to estimate a minimum energy configuration on the sphere. We introduce the notion of a Voronoi cell and give examples of its uses in various areas of mathematics. We consider the icosahedral decomposition of the sphere and apply a minimal energy configuration on the planar equilateral triangle to obtain spherical coordinates of a near minimal energy configuration on the sphere.

Date of Award	2011
Original language	American English
Awarding Institution	Eastern Illinois University
Supervisor	Patrick Coulton (Supervisor)