Math Research Project

Finding the optimal distribution of points around a unit sphere

by Gavin Yancey

I’ve been interested in learning how angles interact with each other in higher dimensions. If I have a polyhedron with known faces, how do I figure out the angles between the faces? At the beginning of last year in an independent math study course, I decided I wanted to work on three dimensional angles. After some time, I eventually narrowed down my topic to how to arrange a certain number of points on a sphere such that the minimum central angle between any two of the points is maximized. In other words, they are all as far apart from each other as possible.
Currently, I’m approaching the problem with two strategies: mathematical and computational. For the mathematical approach, I’ve written the problem as a constrained minimization, and have been working on simplifying and then solving it. For the computational approach, I’ve been writing a program to empirically solve the problem by placing random points on a sphere, then repeatedly moving them away from each other by a decreasing amount.