  Let $Z^2$ denote the standard lattice in the plane $R^2$. We prove that given
a finite subset $S\subset R^2$ and $\eps>0$, then for all sufficiently large
dilations $t>0$ there exists a rotation $\rho\colon R^2\to R^2$ around the
origin such that $\dist(\rho(tz),Z^2)<\eps$, for all $z\in S$. The result, in a
larger generality, has been proved in 2006 by Tamar Ziegler (improving earlier
results by Furstenberg, Katznelson, Weiss). The proof presented in the paper is
short and self-contained.

Number Theory;Dynamical Systems