{
  "id": "2004.01034",
  "version": "v1",
  "published": "2020-04-01T12:57:29.000Z",
  "updated": "2020-04-01T12:57:29.000Z",
  "title": "Incongruent equipartitions of the plane into quadrangles of equal perimeter",
  "authors": [
    "Dirk Frettlöh",
    "Christian Richter"
  ],
  "comment": "19 pages, 9 figures. arXiv admin note: text overlap with arXiv:1905.08144",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "Motivated by a question of R.\\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex quadrangles of the same area and the same perimeter. As a byproduct we obtain vertex-to-vertex dissections of the plane by mutually incongruent triangles of unit area that are arbitrarily close to the periodic vertex-to-vertex tiling by equilateral triangles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-01T12:57:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C20"
    ],
    "keywords": [
      "equal perimeter",
      "incongruent equipartitions",
      "mutually incongruent convex quadrangles",
      "euclidean plane",
      "equilateral triangles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}