English

Compact packings of the plane with two sizes of discs

Metric Geometry 2008-03-03 v2

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.

Keywords

Cite

@article{arxiv.math/0407145,
  title  = {Compact packings of the plane with two sizes of discs},
  author = {Tom Kennedy},
  journal= {arXiv preprint arXiv:math/0407145},
  year   = {2008}
}

Comments

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