  In 1926, Jarn\'ik introduced the problem of drawing a convex $n$-gon with
vertices having integer coordinates. He constructed such a drawing in the grid
$[1,c\cdot n^{3/2}]^2$ for some constant $c>0$, and showed that this grid size
is optimal up to a constant factor. We consider the analogous problem for
drawing the double circle, and prove that it can be done within the same grid
size. Moreover, we give an O(n)-time algorithm to construct such a point set.
