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On Packings of Unequal Spheres in Rn

Published online by Cambridge University Press:  20 November 2018

D. G. Larman
D. G. Larman*
Affiliation:
University College London, London, W.C.1, England
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Suppose that a sequence of spheres is packed in order of decreasing diameters into the unit cube In of Rn . In recent work (2), I have shown that for n = 2, there exist positive constants K2, s ( = 0.97) such that the area of has an asymptotic lower bound K2(d(Sm))s . Although the methods used were complicated and possibly only viable in two dimensions, it is intuitively clear that such a result should also be true in higher dimensions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 967 - 969
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Gilbert, E. N., Randomly packed and solidly packed spheres, Can. J. Math. 16 (1964), 286–298.Google Scholar
2. Larman, D. G., An asymptotic bound for the residual area ofa packing of discs, Proc. Cambridge Philos. Soc. 62 (1966), 699–704.Google Scholar
3. Larman, D. G., On the Besicovitch dimension of the residual set of arbitrarily packed disks in the plane, J. London Math. Soc. 18 (1967), 292–302.Google Scholar
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