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arXiv · 1810.02231

Compact packings of the plane with three sizes of discs

Thomas Fernique·Amir Hashemi·Olga Sizova
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Abstract

A compact packing is a set of non-overlapping discs where all the holes between discs are curvilinear triangles. There is only one compact packing by discs of size $1$. There are exactly $9$ values of $r$ which allow a compact packing by discs of sizes $1$ and $r$. We prove here that there are exactly $164$ pairs $(r,s)$ allowing a compact packing by discs of sizes $1$, $r$ and $s$.

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Thomas Fernique, Amir Hashemi, Olga Sizova. 2020-02-08. Compact packings of the plane with three sizes of discs. https://doi.org/10.1007/s00454-019-00166-y

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