On a Detail in Hales's "Dense Sphere Packings: A Blueprint for Formal Proofs"
Metric Geometry
2017-12-12 v1
Abstract
In "Dense Sphere Packings: A Blueprint for Formal Proofs" Hales proves that for every packing of unit spheres, the density in a ball of radius is at most for some constant . When tends to infinity, this gives a proof to the famous Kepler conjecture. As formulated by Hales, depends on the packing. We follow the proofs of Hales to calculate a constant independent of the sphere packing that exists as mentioned in "A Formal Proof of the Kepler Conjecture" by Hales et al..
Cite
@article{arxiv.1712.03568,
title = {On a Detail in Hales's "Dense Sphere Packings: A Blueprint for Formal Proofs"},
author = {Nadja Scharf},
journal= {arXiv preprint arXiv:1712.03568},
year = {2017}
}