{
  "id": "1810.10089",
  "version": "v1",
  "published": "2018-10-23T21:02:42.000Z",
  "updated": "2018-10-23T21:02:42.000Z",
  "title": "An Upper Bound for Lebesgue's Covering Problem",
  "authors": [
    "Philip Gibbs"
  ],
  "comment": "21 pages",
  "categories": [
    "math.MG"
  ],
  "abstract": "A covering problem posed by Henri Lebesgue in 1914 seeks to find the convex shape of smallest area that contains a subset congruent to any point set of unit diameter in the Euclidean plane. Methods used previously to construct such a covering can be refined and extended to provide an improved upper bound for the optimal area. An upper bound of 0.8440935944 is found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-23T21:02:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "upper bound",
      "lebesgues covering problem",
      "henri lebesgue",
      "optimal area",
      "unit diameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}