  We introduce a novel discretization of the Monge-Ampere operator,
simultaneously consistent and degenerate elliptic, hence accurate and robust in
applications. These properties are achieved by exploiting the arithmetic
structure of the discrete domain, assumed to be a two dimensional cartesian
grid. The construction of our scheme is simple, but its analysis relies on
original tools seldom encountered in numerical analysis, such as the geometry
of two dimensional lattices, and an arithmetic structure called the
Stern-Brocot tree. Numerical experiments illustrate the method's efficiency.
