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, occurrence of Pythagorean triples in such gaskets is discussed.
Kocik, Jerzy. "On a Diophantine Equation That Generates All Integral Apollonian Gaskets." (Jan 2012).