### 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 |
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Journal | Discrete & computational geometry |

Volume | 55 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 |

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### Keywords

- math.MG
- 52C17