# Upper bounds on packing density for circular cylinders with high aspect ratio

 Authors: Wöden Kusner Journal: Discrete & Computational Geometry, 524964-978, 2014. Full text: arXiv • DOI

### Abstract:

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 $\pi/\sqrt{12} + 10/t$.

• Section 3, paragraph 2: Define the Dirichlet slice $d_x$ to be the set …
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