{
  "id": "1107.1077",
  "version": "v1",
  "published": "2011-07-06T09:51:00.000Z",
  "updated": "2011-07-06T09:51:00.000Z",
  "title": "Unit Distances in Three Dimensions",
  "authors": [
    "Haim Kaplan",
    "Jiri Matousek",
    "Zuzana Safernova",
    "Micha Sharir"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the number of unit distances determined by n points in R^3 is O(n^{3/2}), slightly improving the bound of Clarkson et al. established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [arXiv:1011.4105]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [arXiv:1104.4987].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-06T09:51:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C10"
    ],
    "keywords": [
      "dimensions",
      "polynomial partitioning technique",
      "draft stage",
      "similar proof",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.1077K"
    }
  }
}