Discrete & Computational Geometry

, Volume 35, Issue 2, pp 255–267

Compact Packings of the Plane with Two Sizes of Discs


DOI: 10.1007/s00454-005-1172-4

Cite this article as:
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.

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Mathematics, University of Arizona, Tucson, AZ 85721USA

Personalised recommendations