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arXiv · 2002.07168

Density of Binary Disc Packings: The 9 Compact Packings

Nicolas Bédaride·Thomas Fernique
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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).

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Nicolas Bédaride, Thomas Fernique. 2020-02-17. Density of Binary Disc Packings: The 9 Compact Packings. https://arxiv.org/abs/2002.07168

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