English

A short proof of the Twelve points theorem

Metric Geometry 2008-08-11 v1 Combinatorics

Abstract

We present a short elementary proof of the following Twelve Points Theorem: Let M be a convex polygon with vertices at the lattice points, containing a single lattice point in its interior. Denote by m (resp. m*) the number of lattice points in the boundary of M (resp. in the boundary of the dual polygon). Then m+m*=12.

Keywords

Cite

@article{arxiv.0808.1217,
  title  = {A short proof of the Twelve points theorem},
  author = {Matija Cencelj and Dušan Repovš and Mikhail Skopenkov},
  journal= {arXiv preprint arXiv:0808.1217},
  year   = {2008}
}

Comments

in English and in Russian, 4 pages, 4 figures