{
  "id": "math/9811076",
  "version": "v2",
  "published": "1998-11-11T06:34:14.000Z",
  "updated": "2002-05-20T21:39:36.000Z",
  "title": "Sphere packings IV",
  "authors": [
    "Thomas C. Hales"
  ],
  "comment": "53 pages. Sixth in a series beginning with math.MG/9811071",
  "categories": [
    "math.MG"
  ],
  "abstract": "This is the sixth 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 completes part of the fourth step of the program outlined in math.MG/9811073: A proof that if some standard region has more than four sides, then the star scores less than $8 \\pt$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-05-20T21:39:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sphere packings",
      "hilberts 18th problem",
      "paper completes part",
      "oldest problem",
      "discrete geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11076H"
    }
  }
}