{
  "id": "math/9811075",
  "version": "v2",
  "published": "1998-11-11T06:30:35.000Z",
  "updated": "2002-05-20T21:34:59.000Z",
  "title": "Sphere packings III",
  "authors": [
    "Thomas C. Hales"
  ],
  "comment": "22 pages. Fifth in a series beginning with math.MG/9811071",
  "categories": [
    "math.MG"
  ],
  "abstract": "This is the fifth 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 carries out the third step of the program outlined in math.MG/9811073: A proof that if all of the standard regions are triangles or quadrilaterals, then the total score is less than $8 \\pt$ (excluding the case of pentagonal prisms).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-05-20T21:34:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sphere packings",
      "hilberts 18th problem",
      "kepler conjecture",
      "pentagonal prisms",
      "total score"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11075H"
    }
  }
}