The sensual Apollonian circle packing
نویسنده
چکیده
The curvatures of the circles in integral Apollonian circle packings, named for Apollonius of Perga (262-190 BC), form an infinite collection of integers whose Diophantine properties have recently seen a surge in interest. Here, we give a new description of Apollonian circle packings built upon the study of the collection of bases of Z[i], inspired by, and intimately related to, the ‘sensual quadratic form’ of Conway.
منابع مشابه
The Apollonian structure of Bianchi groups
We study the orbit of R under the Bianchi group PSL2(OK), where K is an imaginary quadratic field. The orbit SK , called a Schmidt arrangement, is a geometric realisation, as an intricate circle packing, of the arithmetic of K. We define certain natural subgroups whose orbits generalise Apollonian circle packings, and show that SK , considered with orientations, is a disjoint union of all of th...
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