{
  "id": "1911.01397",
  "version": "v1",
  "published": "2019-11-04T18:42:30.000Z",
  "updated": "2019-11-04T18:42:30.000Z",
  "title": "Periodic orbits on a 120-isosceles triangle, 60-rhombus, 60-90-120-kite, and 30-right triangle",
  "authors": [
    "Benjamin Baer",
    "Faheem Gilani",
    "Zhigang Han",
    "Ron humble"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the ball strikes a side of the table as it traverses its trajectory exactly once. In this paper we find and classify the periodic orbits on a billiard table in the shape of a 120-isosceles triangle, a 60-rhombus, a 60-90-120-kite, and a 30-right triangle. In each case, we use the edge tessellation (also known as tiling) of the plane generated by the figure to unfold a periodic orbit into a straight line segment and to derive a formula for its period in terms of the initial angle and initial position.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-04T18:42:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "straight line segment",
      "billiard table",
      "initial angle",
      "piecewise linear path",
      "initial position"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}