Skip to main content

Maximum density space packing with congruent circular cylinders of infinite length

  • A. Bezdek (a1) and W. Kuperberg (a2)

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.

Hide All
1.Bezdek A. and Kuperberg W.. Placing and moving spheres in the gaps of a cylinder packing. Elemente der Mathematik. To appear.
2.Tóth L. Fejes. Regular Figures (Pergamon Press, Oxford, 1964).
3.Kuperberg K.. A nonparallel cylinder packing with positive density (1988) (pre-print).
4.Thue A.. Über die dichteste Zusammenstellung von kongruenten Kreisen in der Ebene. Christiania Vid. Selsk. Skr., 1 (1910), 39.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 15 *
Loading metrics...

Abstract views

Total abstract views: 162 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th November 2017. This data will be updated every 24 hours.