A lattice point in the plane is a point (a, b) with both coordinates equal to integers. For example, (-1, 2) is a lattice point but (1/2, 3) is not. If D(R) is the disk of radius R and center the origin, count the lattice points inside D(R) and call this number L(R). What is the limit, $\displaystyle \lim_{R \rightarrow \infty} \frac{L(R)}{R^2}$?