Letter to J . Lagarias about Integral Apollonian Packings June , 2007 from
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Apollonian Circle Packings: Number Theory II. Spherical and Hyperbolic Packings
Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. In Euclidean space 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. There are infinitely many different integral packings; these were studied in the paper [8]....
متن کامل1047 - 11 - 4 Jeffrey
Jeffrey C. Lagarias* ([email protected]), Dept. of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109-1043. From Apollonian circle packings to Fibonacci numbers. Apollonian circle packings are infinite packings of circles, constructed recursively from a initial configuration of four mutually touching circles by adding circles externally tangent to triples of such circl...
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: 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...
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...
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تاریخ انتشار 2008