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Some Lower Bounds for Density of Multiple Packing

Published online by Cambridge University Press:  20 November 2018

W.J. Blundon
W.J. Blundon*
Affiliation:
Memorial University of Newfoundland
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A system of circles is said to form a k-fold packing of the plane if every point of the plane is an interior point of at most k circles. In this paper we consider only lattice packings, that is, we suppose that the centers of the circles form a lattice. We further restrict our consideration to circles of equal radius. Without loss of generality, the circles may have unit radius.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 4 , December 1964 , pp. 565 - 572
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Blundon, W. J., Multiple packing of circles in the plane, J. London Math. Soc. 38(1963), 176–182.CrossRefGoogle Scholar
2. Blundon, W.J., Note on a paper of Heppes, Acta Math. Acad. Sci. Hung. 14(1963), 317.CrossRefGoogle Scholar
3. Fejes Tóth, L., Neuere Ergebnisse in der diskreten Geometrie, Elemente der Math. 15(1960), 25–36.Google Scholar
4. Heppes., A., Mehrfache gitterfőrmige Kreislagerungen inder Ebene, Acta Math. Acad. Sci. Hung. 10(1959), 141–148.CrossRefGoogle Scholar