'For any planar polygon with vertices at lattice points the quadratic formula $i(k)=Ak^2 - Bk +C$ gives the number of $k$-points inside the polygon and the quadratic formula $g(k)= Ak^2 + Bk +C$ gives the number of $k$-points in the closed polygon (including the boundary and the interior points), where $A$ is the area of the polygon.'