Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group
نویسندگان
چکیده
منابع مشابه
Apollonian Circle Packings : Geometry and Group Theory
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)×(center) is an integer vector. This series of papers explain such...
متن کاملApollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)×(center) is an integer vector. This series of papers explain such...
متن کاملApollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings
A Descartes configuration is a set of four mutually tangent circles in the Riemann sphere, having disjoint interiors. Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. Part I shoewed there is a natural group action on Desc...
متن کاملApollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions
This paper gives n-dimensional analogues of the Apollonian circle packings in parts I and II. Those papers considered circle packings described in terms of their Descartes configurations, which are sets of four mutually touching circles. They studied packings that had integrality properties in terms of the curvatures and centers of the circles. Here we consider collections of n-dimensional Desc...
متن کاملApollonian Circle Packings: Number Theory
Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. It is possible for every circle in such a packing to have integer radius of curvature, and we call such a packing an integral Apollonian circle packing. This paper studies number-theoretic properties of the set of integer curvatures appearing in such packings. Ea...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2005
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-005-1196-9