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

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

arXiv comment12 pages, 8 figures

References in corpus (2)

• Organizing Principles for Dense Packings of Nonspherical Hard Particles: Not All Shapes Are Created Equal
• Upper bound on the packing density of regular tetrahedra and octahedra

Cited by in corpus (1)

• On the densest packing of polycylinders in any dimension