Compact packings of the plane with two sizes of discs

Tom Kennedy

doi:10.1007/s00454-005-1172-4

Compact packings of the plane with two sizes of discs

Tom Kennedy

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

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 D₁, D₂, ..., 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.

Original language	English (US)
Pages (from-to)	255-267
Number of pages	13
Journal	Discrete and Computational Geometry
Volume	35
Issue number	2
DOIs	https://doi.org/10.1007/s00454-005-1172-4
State	Published - Feb 2006

ASJC Scopus subject areas

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

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10.1007/s00454-005-1172-4

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title = "Compact packings of the plane with two sizes of discs",

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 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.",

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AB - 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.

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Compact packings of the plane with two sizes of discs

Abstract

ASJC Scopus subject areas

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