Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



An algorithm for generating the sphere coordinates in a three-dimensional osculatory packing

Author: David W. Boyd
Journal: Math. Comp. 27 (1973), 369-377
MSC: Primary 52A45; Secondary 52-04
MathSciNet review: 0338937
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper develops an efficient algorithm which generates the pentaspherical coordinates of the spheres in an osculatory packing of the three-dimensional unit sphere. The algorithm has a tree-like structure and is easily modified so that, given a prescribed bound, it counts the number of spheres in the packing whose curvatures are less than this bound. The algorithm has been used to produce heuristic estimates of the exponent M of the packing, and these indicate that M is approximately 2.42.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 52A45, 52-04

Retrieve articles in all journals with MSC: 52A45, 52-04

Additional Information

Keywords: Sphere packing, osculatory packing, exponent of packing, algorithm, computer study
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society