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
DOI: https://doi.org/10.1090/S0025-5718-1973-0338937-6
MathSciNet review: 0338937
Full-text PDF Free Access

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?)

  • [1] D. W. Boyd, "On the exponent of an osculatory packing," Canad. J. Math., v. 23, 1971, pp. 355-363. MR 42 #6723. MR 0271842 (42:6723)
  • [2] D. W. Boyd, "Improved bounds for the disk-packing constant," Aequationes Math. (To appear.) MR 0317180 (47:5728)
  • [3] D. W. Boyd, "The osculatory packing of a three dimensional sphere," Canad. J. Math. (To appear.) MR 0320897 (47:9430)
  • [4] D. G. Larman, "On the exponent of convergence of a packing of spheres," Mathematika, v. 13, 1966, pp. 57-59. MR 34 #1928. MR 0202054 (34:1928)
  • [5] Z. A. Melzak, "On the solid-packing constant for circles," Math. Comp., v. 23, 1969, pp. 169-172. MR 39 #6179. MR 0244866 (39:6179)
  • [6] F. Soddy, "The bowl of integers and the hexlet," Nature, v. 139, 1937, pp. 77-79.

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

DOI: https://doi.org/10.1090/S0025-5718-1973-0338937-6
Keywords: Sphere packing, osculatory packing, exponent of packing, algorithm, computer study
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society