%0 Journal Article
%T Upper bounds on packing density for circular cylinders with high aspect ratio
%A W£żden Kusner
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s00454-014-9593-6
%X In the early 1990s, A. Bezdek and W. Kuperberg used a relatively simple argument to show a surprising result: The maximum packing density of circular cylinders of infinite length in $\mathbb{R}^3$ is exactly $\pi/\sqrt{12}$, the planar packing density of the circle. This paper modifies their method to prove a bound on the packing density of finite length circular cylinders. In fact, the maximum packing density for unit radius cylinders of length $t$ in $\mathbb{R}^3$ is bounded above by $\pi/\sqrt{12} + 10/t$.
%U http://arxiv.org/abs/1309.6996v1