Corrigendum to “Apollonian Circle Packings and Prime Curvatures”
نویسندگان
چکیده
منابع مشابه
Apollonian Circle Packings
Figure 1: An Apollonian Circle Packing Apollonius’s Theorem states that given three mutually tangent circles, there are exactly two circles which are tangent to all three. Apollonian circle packings are produced by repeating the construction of mutually tangent circles to fill all remaining spaces. A remarkable consequence of Descartes’ Theorem is if the initial four tangent circles have integr...
متن کاملApollonian Circle Packings
Circle packings are a particularly elegant and simple way to construct quite complicated and elaborate sets in the plane. One systematically constructs a countable family of tangent circles whose radii tend to zero. Although there are many problems in understanding all of the individual values of their radii, there is a particularly simple asymptotic formula for the radii of the circles, origin...
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
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: 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]....
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2013
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-013-0025-y