{
  "id": "1903.10431",
  "version": "v1",
  "published": "2019-03-25T16:13:37.000Z",
  "updated": "2019-03-25T16:13:37.000Z",
  "title": "Tilings of convex polygons by equilateral triangles of many different sizes",
  "authors": [
    "Christian Richter"
  ],
  "categories": [
    "math.MG"
  ],
  "abstract": "An equilateral triangle cannot be dissected into finitely many mutually incongruent equilateral triangles [Tutte 1948]. Therefore Tuza [Tuza 1991] asked for the largest number $s=s(n)$ such that there is a tiling of an equilateral triangle by $n$ equilateral triangles of $s(n)$ different sizes. We solve that problem completely and consider the analogous questions for dissections of convex $k$-gons into equilateral triangles, $k=4,5,6$. Moreover, we discuss all these questions for the subclass of tilings such that no two tiles are translates of each other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-25T16:13:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C20"
    ],
    "keywords": [
      "convex polygons",
      "mutually incongruent equilateral triangles",
      "largest number",
      "analogous questions",
      "translates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}