On a Diophantine equation that generates all integral Apollonian Gaskets
arXiv:2008.04440 · doi:10.5402/2012/348618
Abstract
A remarkably simple Diophantine quadratic equation is known to generate all Apollonian integral gaskets (disk packings). A new derivation of this formula is presented here based on inversive geometry. Also occurrences of Pythagorean triples in such gaskets is discussed.
18 pages, 14 figures