Tiling Polygons with Lattice Triangles

نویسندگان

  • Steve Butler
  • Fan Chung Graham
  • Ronald L. Graham
  • Miklós Laczkovich
چکیده

Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinate of the vertices in any tiling are rationals with the possible denominators odd numbers dependent on the cotangents of the angles in the triangles.

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عنوان ژورنال:
  • Discrete & Computational Geometry

دوره 44  شماره 

صفحات  -

تاریخ انتشار 2010