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Maximum density space packing with congruent circular cylinders of infinite length
Author(s) -
Bezdek A.,
Kuperberg W.
Publication year - 1990
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300012808
Subject(s) - mathematics , sphere packing , cylinder , plane (geometry) , space (punctuation) , geometry , euclidean space , mathematical analysis , unit (ring theory) , combinatorics , volume (thermodynamics) , physics , philosophy , linguistics , mathematics education , quantum mechanics
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.