English

Density of Binary Disc Packings: The 9 Compact Packings

Discrete Mathematics 2021-05-04 v3 Metric Geometry

Abstract

A disc packing in the plane is compact if its contact graph is a triangulation. There are 99 values of rr such that a compact packing by discs of radii 11 and rr exists. We prove, for each of these 99 values, that the maximal density over all the packings by discs of radii 11 and rr is reached for a compact packing (we give it as well as its density).

Cite

@article{arxiv.2002.07168,
  title  = {Density of Binary Disc Packings: The 9 Compact Packings},
  author = {Nicolas Bédaride and Thomas Fernique},
  journal= {arXiv preprint arXiv:2002.07168},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T13:44:26.836Z