A densest compact planar packing with two sizes of discs

Abstract

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.

Latex, 21 pages, 2 postscript figures