{
  "id": "1406.7779",
  "version": "v1",
  "published": "2014-06-27T13:30:28.000Z",
  "updated": "2014-06-27T13:30:28.000Z",
  "title": "Analytical solution of the weighted Fermat-Torricelli problem for tetrahedra: The case of two pairs of equal weights",
  "authors": [
    "Anastasios N. Zachos"
  ],
  "comment": "9 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1406.2947",
  "categories": [
    "math.OC"
  ],
  "abstract": "The weighted Fermat-Torricelli problem for four non-collinear and non-coplanar points in the three dimensional Euclidean Space states that: Given four non-collinear and non-coplanar points A1, A2, A3, A4 and a positive real number (weight) Bi which correspond to each point Ai, for i = 1,2,3,4, find a fifth point such that the sum of the weighted distances to these four points is minimized. We present an analytical solution for the weighted Fermat-Torricelli problem for tetrahedra in the three dimensional Euclidean Space for the case of two pairs of equal weights.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-27T13:30:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted fermat-torricelli problem",
      "equal weights",
      "analytical solution",
      "tetrahedra",
      "dimensional euclidean space states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.7779Z"
    }
  }
}