On a Diophantine equation that generates all integral Apollonian Gaskets
Metric Geometry
2020-08-12 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.2008.04440,
title = {On a Diophantine equation that generates all integral Apollonian Gaskets},
author = {Jerzy Kocik},
journal= {arXiv preprint arXiv:2008.04440},
year = {2020}
}
Comments
18 pages, 14 figures