A New Computationally Efficient Method for Spacing n Points on a Sphere

Authors

Jonathan Kogan, Columbia Grammar and Preparatory School, New YorkFollow

Abstract

The problem of equally spacing n points on a sphere is impossible in general, but there are methods that come close to spacing the points equally. The method introduced in this paper uses a spiral that was found using experimental evidence. The resulting spacings are close to theoretical bounds, and the method is computationally efficient for large numbers of points. The method's accuracy ranges from 70% to 86% of the upper bound as n changes.

Author Bio

Jonathan Kogan is currently a high school senior at Columbia Grammar and Preparatory School in New York City. Next Fall, Jonathan will be a student in the University of Pennsylvania’s Jerome Fisher Program in Management and Technology where he will study Computer Science at the engineering school and statistics at Wharton; he also plans to pursue a mathematics minor. Jonathan loves computer science and mathematics and enjoys engaging in all kinds of research projects. In his spare time, Jonathan can be found playing basketball or hanging out with friends.

Faculty Sponsor

Todd Rowland

Recommended Citation

Kogan, Jonathan (2017) "A New Computationally Efficient Method for Spacing n Points on a Sphere," Rose-Hulman Undergraduate Mathematics Journal: Vol. 18: Iss. 2, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss2/5