English

The Local-Global Principle for Integral Generalized Apollonian Sphere Packings

Number Theory 2014-01-21 v1

Abstract

Four mutually tangent spheres form two gaps. In each of these, one can inscribe in a unique way four mutually tangent spheres such that each one of these spheres is tangent to exactly three of the original spheres. Repeating the process gives rise to a generalized Apollonian sphere packing. These packings have remarkable properties. One of them is the local to global principle and will be proven in this paper.

Keywords

Cite

@article{arxiv.1401.4789,
  title  = {The Local-Global Principle for Integral Generalized Apollonian Sphere Packings},
  author = {Dimitri Dias},
  journal= {arXiv preprint arXiv:1401.4789},
  year   = {2014}
}