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A densest compact planar packing with two sizes of discs

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arxiv math/0412418 v1 pith:3N5RUXSW submitted 2004-12-21 math.MG

Tom Kennedy This is my paper · ORCID
classification math.MG
keywords compactdiscspackingpackingsadmitsconsiderdensestdensity
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We consider packings of the plane using discs of radius 1 and r=0.545151... . The value of r admits compact packings in which each hole in the packing is formed by three discs which are tangent to each other. We prove that the largest density possible is that of the compact packing shown in figure 1.

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Cited by 1 Pith paper

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  1. On Dense Tetrahedra in Binary Sphere Packings

    math.MG 2025-05 conditional novelty 6.0 of 10

    A computer-assisted geometric proof shows that packings of spheres of radii 1 and sqrt(2)-1 have density at most about 0.812542, slightly improving the previous best bound of 0.813.

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