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A Finite Packing Problem

Published online by Cambridge University Press:  20 November 2018

Norman Oler
Norman Oler*
Affiliation:
McGill University and Columbia University
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The maximum density of packings of a given type into the whole of a Euclidean space is defined to be the limit of the maximum density of such packings into a cube as the edge of the cube goes to infinity.

For E2 in particular, a number of well known results such as those due to A. Thue [1], L. Fejes-Toth [2], and C. A. Rogers [3] yield precise information about packings into the whole space. They are however of limited applicability to problems of finite packing in so-far as each requires some restriction upon the boundary of the configuration.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 2 , May 1961 , pp. 153 - 155
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Thue, A., Uber die dichteste Zusammenstellung von kongruenten Kreisen in einer Ebene, Christiania Vid. Selsk. 1 (1910), 3-9.Google Scholar
2. Fejes-Toth, L., Some packing and covering theorems, Acta Sci. Math. Szeged 12 (1950), 62-67.Google Scholar
3. Rogers, C. A., The closest packing of convex two dimensional domains, Acta Math. 86 (1951), 309-321.10.1007/BF02392671Google Scholar
4. Oler, N., An inequality in the geometry of numbers, Acta Math.,Google Scholar