{
  "id": "0710.0708",
  "version": "v1",
  "published": "2007-10-03T03:45:27.000Z",
  "updated": "2007-10-03T03:45:27.000Z",
  "title": "A characterization of all equilateral triangles in \\Bbb Z^3",
  "authors": [
    "Ray Chandler",
    "Eugen J. Ionascu"
  ],
  "comment": "8 pages, 3 figures, continuation of previous work",
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper is a continuation of previous work of the authors. We extend one of the theorems that gave a way to construct equilateral triangles whose vertices have integer coordinates to the general situation. An approximate extrapolation formula for the sequence ET(n) of all equilateral triangles with vertices in $\\{0,1,2,...,n\\}^3$ (A 102698) is given and the asymptotic behavior of this sequence is analyzed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-03T03:45:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A67"
    ],
    "keywords": [
      "characterization",
      "construct equilateral triangles",
      "approximate extrapolation formula",
      "asymptotic behavior",
      "general situation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.0708C"
    }
  }
}