{
  "id": "math/9811071",
  "version": "v2",
  "published": "1998-11-11T06:13:05.000Z",
  "updated": "2002-05-20T20:56:31.000Z",
  "title": "An overview of the Kepler conjecture",
  "authors": [
    "Thomas C. Hales"
  ],
  "comment": "16 pages. First in a series",
  "categories": [
    "math.MG"
  ],
  "abstract": "This is the first in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\\pi/\\sqrt{18}\\approx 0.74048...$. This is the oldest problem in discrete geometry and is an important part of Hilbert's 18th problem. An example of a packing achieving this density is the face-centered cubic packing. This paper has a historical overview and a synopsis of the rest of the series. The other papers in the series are math.MG/9811072, math.MG/9811073, math.MG/9811074, math.MG/9811075, math.MG/9811076, math.MG/9811077, and math.MG/9811078.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-05-20T20:56:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kepler conjecture",
      "hilberts 18th problem",
      "oldest problem",
      "important part",
      "congruent spheres"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11071H"
    }
  }
}