19 citations · 36 across the 9 of their papers we have counts for
12 papers · 1 filter
A computer verification of the Kepler conjecture
Thomas C. Hales
The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than . A computer assisted verification confirmed t…
The Honeycomb Problem on the Sphere
Thomas C. Hales
The honeycomb problem on the sphere asks for the perimeter-minimizing partition of the sphere into N equal areas. This article solves the problem when N=12. The unique minimizer is…
Some algorithms arising in the proof of the Kepler conjecture
Thomas C. Hales
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout…
Sphere Packings in 3 Dimensions
Thomas C. Hales
This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original…
The Honeycomb Conjecture
Thomas C. Hales
The classical honeycomb conjecture asserts that any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling. Pappus…
Sphere packings II
Thomas C. Hales
An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decompos…