  In 1976, P. R. Scott characterized the Ehrhart polynomials of convex integral
polygons. We study the same question for Ehrhart polynomials and
quasi-polynomials of *non*-integral convex polygons. Turning to the case in
which the Ehrhart quasi-polynomial has nontrivial quasi-period, we determine
the possible minimal periods of the coefficient functions of the Ehrhart
quasi-polynomial of a rational polygon.
