Compact packings of the plane with two sizes of discs

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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 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.

Original languageEnglish (US)
Pages (from-to)255-267
Number of pages13
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - Feb 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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