2020/02/17 by Nicolas Bédaride, Thomas Fernique, Bédaride, Nicolas +1
Computer Science · Mathematics · #52C15 #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2002.07168
openalex publication_date 2020/02/17 · openalex created_date 2020/06/19 · openalex updated_date 2026/07/28
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).