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Sphere packing in R3

Published online by Cambridge University Press:  26 February 2010

J. H. Lindsey II
J. H. Lindsey II
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
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Extract

The following theorem shows that when packing unit spheres in a large box the spheres occupy at most about 0.7784 of the volume of the box. This improves Rogers' bound [2], which is approximately 0.7796. In the most efficient known packing the ratio is about 0.7405. The box in the theorem could be any bounded solid. Then the (l + 2)(m + 2)(n + 2) becomes the volume of a larger solid all of whose boundary points are at least one unit away from the original solid. At the start of the proof the even larger box could be replaced with a large ball concentric with and radius five units larger than some ball containing the original solid.

Type
Research Article
Information
Mathematika , Volume 33 , Issue 1 , June 1986 , pp. 137 - 147
Copyright
Copyright © University College London 1986

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References

1.Blichfeldt, H. F.. The minimum value of quadratic forms, and the closest packing of spheres. Math. Ann., 101 (1929), 605–608.CrossRefGoogle Scholar
2.Rogers, C. A.. Packing and Covering (Cambridge University Press, Cambridge, 1964).Google Scholar
3.Rogers, C. A.. The packing of equal spheres. Proc. Lond. Math. Soc., 8 (1958), 609–620.CrossRefGoogle Scholar
4.Sloane, N. J. A.. The packing of spheres. Scientific American, 250 (Jan. 1984), 116–125.CrossRefGoogle Scholar