One can study an Apollonian circle packing (ACP) from many different angles. Such packings are certainly of interest in classical geometry. But ACP's encode fascinating information of an entirely different flavor: an infinite family of so-called integer ACP's encodes beautiful and mysterious number theoretic properties. The Apollonian gasket was first described by Gottfried Leibniz in the 17th century, and is a curved precursor of the 20th-century Sierpiński triangle. The Apollonian gasket also has deep connections to other fields of mathematics; for example, it is the limit set of Kleinian groups; and see also the Circle packing theorem.
Geometry of the Apollonian Circle Packings Weiru Chen, Mo Jiao, Calvin Kessler, Amita Malik, Xin Zhang Introduction The fine structures of Apollonian gaskets are encoded by local spatial statistics. In this article, we report our empirical results on some of such statistics, namely, pair correlation, nearest neighbor spacing and electrostatic ...
2014 allegro 34tga