{
  "id": "math/0110209",
  "version": "v1",
  "published": "2001-10-18T23:28:00.000Z",
  "updated": "2001-10-18T23:28:00.000Z",
  "title": "The number of point-splitting circles",
  "authors": [
    "Federico Ardila M"
  ],
  "comment": "12 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let S be a set of 2n+1 points in the plane such that no three are collinear and no four are concyclic. A circle will be called point-splitting if it has 3 points of S on its circumference, n-1 points in its interior and n-1 in its exterior. We show the surprising property that S always has exactly n^2 point- splitting circles, and prove a more general result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-18T23:28:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C99",
      "05A99"
    ],
    "keywords": [
      "point-splitting circles",
      "general result",
      "surprising property",
      "circumference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10209A"
    }
  }
}