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

Wöden Kusner

Research output: Contribution to journalArticleResearchpeer-review

### 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 $\pi/\sqrt{12} + 10/t$.
Original language English Discrete & computational geometry 55 4 https://doi.org/10.1007/s00454-014-9593-6 Published - 2014

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Circular Cylinder
Circular cylinders
Aspect Ratio
Packing
Aspect ratio
Upper bound
Pi
Circle
Unit

• math.MG
• 52C17

### Cite this

In: Discrete & computational geometry, Vol. 55, No. 4, 2014.

Research output: Contribution to journalArticleResearchpeer-review

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