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The sensual Apollonian circle packing
Published 23 Aug 2012 in math.NT and math.MG | (1208.4836v3)
Abstract: 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]2, inspired by, and intimately related to, the `sensual quadratic form' of Conway.
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