A short proof of the Twelve points theorem

Details A short proof of the Twelve points theorem A short proof of the Twelve points theorem

2008-08-08

arxiv.org/abs/0808.1217v1

Mathematical Notes 77:1(2005), 108-111

Mathematics

Metric Geometry

in English and in Russian, 4 pages, 4 figures

Scientific paper

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.

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