Mathematika

Research Article

Maximum density space packing with congruent circular cylinders of infinite length

A. Bezdeka1 and W. Kuperberga2

a1 Mathematical Institute of the Hungarian Academy of Sciences, Budapest, P.O.B. 127, H-1364, Hungary.

a2 Division of Mathematics, F.A.T., Auburn University, Auburn, AL 36849, U.S.A.

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.

(Received July 03 1989)