A short proof of the Twelve points theorem

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.

in English and in Russian, 4 pages, 4 figures