Density of Binary Disc Packings: The 9 Compact Packings

Abstract

A disc packing in the plane is compact if its contact graph is a triangulation. There are $9$ values of $r$ such that a compact packing by discs of radii $1$ and $r$ exists. We prove, for each of these $9$ values, that the maximal density over all the packings by discs of radii $1$ and $r$ is reached for a compact packing (we give it as well as its density).

code (SageMath) included in the source archive. arXiv admin note: text overlap with arXiv:1912.02297

References in corpus (4)

• A Simple Proof of Thue's Theorem on Circle Packing
• A densest compact planar packing with two sizes of discs
• A Densest ternary circle packing in the plane
• Compact Packings are not always the Densest

Cited by in corpus (1)

• Compact Packings are not always the Densest