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Density of binary disc packings: lower and upper bounds (2107.14079v3)
Published 29 Jul 2021 in math.MG and cs.CG
Abstract: We provide, for any $r\in (0,1)$, lower and upper bounds on the maximal density of a packing in the Euclidean plane of discs of radius $1$ and $r$. The lower bounds are mostly folk, but the upper bounds improve the best previously known ones for any $r\in[0.11,0.74]$. For many values of $r$, this gives a fairly good idea of the exact maximum density. In particular, we get new intervals for $r$ which does not allow any packing more dense that the hexagonal packing of equal discs.