I want to show that the number $\mu(n)$ of pairs of integers $(x,y)$ with $x^{2}+y^{2}<n$ satisfies $\mu(n)/n \rightarrow \pi $ as $n \rightarrow \infty$
If we consider the lattice $L=\mathbb{Z}<1,0>+\mathbb{Z}<0,1>$ and $X=\lbrace (x,y) \in \mathbb{Z}^{2}|x^{2}+y^{2}<n \rbrace$ from Minkowski's theorm we know that $X\cap L \neq \emptyset $ i want to know that is there any formula for $\mu(n)$? beacuse if we know the formula we can comput the limit.