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- Title
Irreducible Apollonian Configurations and Packings.
- Authors
Butler, Steve; Graham, Ron; Guettler, Gerhard; Mallows, Colin
- Abstract
An Apollonian configuration of circles is a collection of circles in the plane with disjoint interiors such that the complement of the interiors of the circles consists of curvilinear triangles. One well-studied method of forming an Apollonian configuration is to start with three mutually tangent circles and fill a curvilinear triangle with a new circle, then repeat with each newly created curvilinear triangle. More generally, we can start with three mutually tangent circles and a rule (or rules) for how to fill a curvilinear triangle with circles. In this paper we consider the basic building blocks of these rules, irreducible Apollonian configurations. Our main result is to show how to find a small field that can realize such a configuration and also give a method to relate the bends of the new circles to the bends of the circles forming the curvilinear triangle.
- Subjects
TRIANGLES; IRREDUCIBLE polynomials; PACKING (Mechanical engineering); EULERIAN graphs; INVERSIONS (Geometry)
- Publication
Discrete & Computational Geometry, 2010, Vol 44, Issue 3, p487
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-009-9216-9