{
  "id": "1711.04504",
  "version": "v1",
  "published": "2017-11-13T10:31:02.000Z",
  "updated": "2017-11-13T10:31:02.000Z",
  "title": "Tilings with noncongruent triangles",
  "authors": [
    "Andrey Kupavskii",
    "János Pach",
    "Gábor Tardos"
  ],
  "categories": [
    "math.CO",
    "cs.DM",
    "math.MG"
  ],
  "abstract": "We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that no convex polygon with more than three sides can be tiled with finitely many triangles such that no pair of them share a full side.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-13T10:31:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex polygon",
      "equal perimeter",
      "full side",
      "pairwise noncongruent triangles",
      "equal area"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}