Compact packings of the plane with two sizes of discs

Abstract

We consider packings of the plane using discs of radius 1 and r. A packing is compact if every disc D is tangent to a sequence of discs D_1, D_2, ..., D_n such that D_i is tangent to D_{i+1}. We prove that there are only nine values of r with r<1 for which such packings are possible. For each of the nine values we describe the possible compact packings.

Latex, 20 pages, 15 postscript figures Only change in second version is to fix some problems with figure borders