An algorithm for generating the sphere coordinates in a threedimensional osculatory packing
Author:
David W. Boyd
Journal:
Math. Comp. 27 (1973), 369377
MSC:
Primary 52A45; Secondary 5204
MathSciNet review:
0338937
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Abstract: This paper develops an efficient algorithm which generates the pentaspherical coordinates of the spheres in an osculatory packing of the threedimensional unit sphere. The algorithm has a treelike 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.
 [1]
David
W. Boyd, On the exponent of an osculatory packing, Canad. J.
Math. 23 (1971), 355–363. MR 0271842
(42 #6723)
 [2]
David
W. Boyd, Improved bounds for the diskpacking constant,
Aequationes Math. 9 (1973), 99–106. MR 0317180
(47 #5728)
 [3]
David
W. Boyd, The osculatory packing of a three dimensional sphere,
Canad. J. Math. 25 (1973), 303–322. MR 0320897
(47 #9430)
 [4]
D.
G. Larman, On the exponent of convergence of a packing of
spheres, Mathematika 13 (1966), 57–59. MR 0202054
(34 #1928)
 [5]
Z.
A. Melzak, On the solidpacking constant for
circles, Math. comp. 23 (1969), 169–172. MR 0244866
(39 #6179), http://dx.doi.org/10.1090/S00255718196902448668
 [6]
F. Soddy, "The bowl of integers and the hexlet," Nature, v. 139, 1937, pp. 7779.
 [1]
 D. W. Boyd, "On the exponent of an osculatory packing," Canad. J. Math., v. 23, 1971, pp. 355363. MR 42 #6723. MR 0271842 (42:6723)
 [2]
 D. W. Boyd, "Improved bounds for the diskpacking 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. 5759. MR 34 #1928. MR 0202054 (34:1928)
 [5]
 Z. A. Melzak, "On the solidpacking constant for circles," Math. Comp., v. 23, 1969, pp. 169172. MR 39 #6179. MR 0244866 (39:6179)
 [6]
 F. Soddy, "The bowl of integers and the hexlet," Nature, v. 139, 1937, pp. 7779.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197303389376
PII:
S 00255718(1973)03389376
Keywords:
Sphere packing,
osculatory packing,
exponent of packing,
algorithm,
computer study
Article copyright:
© Copyright 1973
American Mathematical Society
