{
  "id": "1406.2947",
  "version": "v2",
  "published": "2014-06-11T16:05:30.000Z",
  "updated": "2014-06-12T03:51:06.000Z",
  "title": "Analytical solution of the weighted Fermat-Torricelli problem for convex quadrilaterals in the Euclidean plane: The case of two pairs of equal weights",
  "authors": [
    "Anastasios N. Zachos"
  ],
  "comment": "13 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "The weighted Fermat-Torricelli problem for four non-collinear points in R^2 states that: Given four non-collinear points A_1, A_2, A_3,A_4 and a positive real number (weight) B_i which correspond to each point A_i, for i = 1, 2, 3, 4, find a fifth point such that the sum of the weighted distances to these four points is min- imized. We present an analytical solution for the weighted Fermat-Torricelli problem for convex quadrilaterals in R2 for the following two cases: (a) B_1 = B_2 and B_3 = B_4, for B1 > B4 and (b) B_1 = B_3 and B_2 = B_4.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-12T03:51:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E12",
      "52A10",
      "51E10"
    ],
    "keywords": [
      "weighted fermat-torricelli problem",
      "convex quadrilaterals",
      "analytical solution",
      "euclidean plane",
      "equal weights"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.2947Z"
    }
  }
}