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arXiv · 1309.6996

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

Wöden Kusner
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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 $π/\sqrt{12}$, 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 $π/\sqrt{12} + 10/t$.

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Wöden Kusner. 2013-09-26. Upper bounds on packing density for circular cylinders with high aspect ratio. https://doi.org/10.1007/s00454-014-9593-6

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