Maximum density space packing with congruent circular cylinders of infinite length
作者:
A. Bezdek,
W. Kuperberg,
期刊:
Mathematika
(WILEY Available online 1990)
卷期:
Volume 37,
issue 1
页码: 74-80
ISSN:0025-5793
年代: 1990
DOI:10.1112/S0025579300012808
出版商: London Mathematical Society
数据来源: WILEY
摘要:
AbstractWe 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.
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