Compact packings of the plane with two sizes of discs

Details Compact packings of the plane with two sizes of discs Compact packings of the plane with two sizes of discs

2004-07-08

arxiv.org/abs/math/0407145v2

Discrete and Computational Geometry 35 (2006), 255-267

Mathematics

Metric Geometry

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

Scientific paper

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.

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