Density of binary disc packings: lower and upper bounds

Abstract

We provide, for any $r\in (0,1)$, lower and upper bounds on the maximal density of a packing in the Euclidean plane of discs of radius $1$ and $r$. The lower bounds are mostly folk, but the upper bounds improve the best previously known ones for any $r\in [0.11,0.74]$. For many values of $r$, this gives a fairly good idea of the exact maximum density. In particular, we get new intervals for $r$ which does not allow any packing more dense that the hexagonal packing of equal discs.

C++ code and sagemath worksheet in ancillary files. Relies on results provided in arXiv:2002.07168

References in corpus (5)

• A Simple Proof of Thue's Theorem on Circle Packing
• Infinite-pressure phase diagram of binary mixtures of (non)additive hard disks
• A densest compact planar packing with two sizes of discs
• A Densest ternary circle packing in the plane
• Maximally Dense Disc Packings on the Plane

Cited by in corpus (1)

• Packing unequal disks in the Euclidean plane