منابع مشابه
The Norm in Taxicab Geometry
In this paper, we will define the inner-product and the norm in taxicab geometry and then we will discuss this inner-product geometrically.
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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...
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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...
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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...
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In the last decade tremendous effort has been put in the study of the Apollonian circle packings. Given the great variety of mathematics it exhibits, this topic has attracted experts from different fields: number theory, homogeneous dynamics, expander graphs, group theory, to name a few. The principle investigator (PI) contributed to this program in his PhD studies. The scenery along the way fo...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2020
ISSN: 0035-7596
DOI: 10.1216/rmj.2020.50.25