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 $\pi/\sqrt{12}$, 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 languageEnglish
JournalDiscrete & computational geometry
Volume55
Issue number4
DOIs
Publication statusPublished - 2014

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Keywords

  • math.MG
  • 52C17

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