{
  "id": "math/0509292",
  "version": "v7",
  "published": "2005-09-13T20:05:57.000Z",
  "updated": "2007-04-01T20:19:26.000Z",
  "title": "Periodic Orbits of Billiards on an Equilateral Triangle",
  "authors": [
    "Andrew M. Baxter",
    "Ron Umble"
  ],
  "comment": "Version 7: Minor edits made, some figures redrawn, Table 1 moved from appendix to body of text.",
  "categories": [
    "math.DS",
    "math.CO"
  ],
  "abstract": "We give a complete solution of the following problem: Find, classify and count the (classes of) periodic orbits on an equilateral triangle. We prove that Fagnano's period 3 orbit is the only periodic orbit with odd period. A periodic orbit is either prime or some d-fold iterate thereof. We count prime and iterate periodic orbits of period $2n$ via a bijection with a certain partition of $n$, then count only prime orbits using the prime factorization of $n$.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2007-04-01T20:19:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E15",
      "05A15",
      "05A17",
      "51F15"
    ],
    "keywords": [
      "equilateral triangle",
      "d-fold iterate thereof",
      "iterate periodic orbits",
      "fagnanos period",
      "complete solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9292B"
    }
  }
}