{
  "id": "math/9811078",
  "version": "v2",
  "published": "1998-11-11T06:55:55.000Z",
  "updated": "2002-06-05T21:25:36.000Z",
  "title": "The Kepler conjecture",
  "authors": [
    "Thomas C. Hales"
  ],
  "comment": "62 pages. Eighth and last in a series beginning with math.MG/9811071. Includes an index of terminology and notation for the entire series. The source package of the first version includes the source code of the software used in the proof. The second version has been completely rewritten",
  "categories": [
    "math.MG"
  ],
  "abstract": "This is the eighth and final paper in a series 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 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": "2002-06-05T21:25:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kepler conjecture",
      "hilberts 18th problem",
      "standard region",
      "final paper",
      "fourth step"
    ],
    "tags": [
      "research tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11078H"
    }
  }
}