Compact Packings of the Plane with Two Sizes of Discs
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- Kennedy, T. Discrete Comput Geom (2006) 35: 255. doi:10.1007/s00454-005-1172-4
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 D1, D2, ..., Dn such that Di is tangent to Di+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.