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Maximum density space packing with congruent circular cylinders of infinite length

Published online by Cambridge University Press:  26 February 2010

A. Bezdek  and
W. Kuperberg
A. Bezdek
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest, P.O.B. 127, H-1364, Hungary.
W. Kuperberg
Affiliation:
Division of Mathematics, F.A.T., Auburn University, Auburn, AL 36849, U.S.A.
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Abstract

We determine what is the maximum possible (by volume) portion of the three-dimensional Euclidean space that can be occupied by a family of non-overlapping congruent circular cylinders of infinite length in both directions. We show that the ratio of that portion to the whole of the space cannot exceed π/√12 and it attains π/√12 when all cylinders are parallel to each other and each of them touches six others. In the terminology of the theory of packings and coverings, we prove that the space packing density of the cylinder equals π/√12, the same as the plane packing density of the circular disk.

Type
Research Article
Information
Mathematika , Volume 37 , Issue 1 , June 1990 , pp. 74 - 80
Copyright
Copyright © University College London 1990

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References

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