If $A=\{z_1,z_2,\dots \}\in {\mathbb{R}}^2$ is an infinite sequence then let$$f(r)=\underset{C}{\max }\left||A\cap C|-\pi r^2\right|,$$where the maximum is taken over all circles $C$ of radius $r$.Is $f(r)$ unbounded for every $A$? How fast does $f(r)$ grow?