{
  "id": "1408.6495",
  "version": "v1",
  "published": "2014-08-27T18:58:42.000Z",
  "updated": "2014-08-27T18:58:42.000Z",
  "title": "An analytical solution of the weighted Fermat-Torricelli problem on the unit sphere",
  "authors": [
    "Anastasios N. Zachos"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.OC"
  ],
  "abstract": "We obtain an analytical solution for the weighted Fermat-Torricelli problem for an equilateral geodesic triangle A_1A_2A_3 which is composed by three equal geodesic arcs (sides) of length Pi/2 for given three positive unequal weights that correspond to the three vertices on a unit sphere. This analytical solution is a generalization of Cockayne's solution given in [4] for three equal weights. Furthermore, by applying the geometric plasticity principle and the spherical cosine law, we derive a necessary condition for the weighted Fermat-Torricelli point in the form of three transcedental equations with respect to the length of the geodesic arcs A_1A_1', A_2A_2'and A_3A_3'to locate the weighted Fermat-Torricelli point A_0 at the interior of a geodesic triangle A_1'A_2'A_3'on a unit sphere with sides less than Pi/2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-27T18:58:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted fermat-torricelli problem",
      "unit sphere",
      "analytical solution",
      "weighted fermat-torricelli point",
      "equal geodesic arcs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.6495Z"
    }
  }
}