Tiling Polygons with Lattice Triangles

Tiling Polygons with Lattice Triangles: "

Abstract 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 coordinates of the
vertices in any tiling are rationals with the possible denominators odd numbers dependent on the cotangents of the angles
in the triangles.

• Content Type Journal Article
• DOI 10.1007/s00454-010-9249-0
• Authors
  
  
  • Steve Butler, University of California, Los Angeles Los Angeles CA USA
  • Fan Chung, University of California, San Diego San Diego CA USA
  • Ron Graham, University of California, San Diego San Diego CA USA
  • Miklós Laczkovich, Eötvös Loránd University Budapest Hungary
  
  

• Journal Discrete and Computational Geometry
• Online ISSN 1432-0444
• Print ISSN 0179-5376

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