Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T04:22:32.012Z Has data issue: false hasContentIssue false
  • English
  • Français

A Finite Packing Problem

Published online by Cambridge University Press:  20 November 2018

Norman Oler
Norman Oler*
Affiliation:
McGill University and Columbia University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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