Orchard Visibility Problem

A tree is planted at each Lattice Point in a circular orchard which has Center at the Origin and Radius $r$. If the radius of trees exceeds $1/r$ units, one is unable to see out of the orchard in any direction. However, if the Radii of the trees are $<1/\sqrt{r^2+1}$, one can see out at certain Angles.

See also Lattice Point, Orchard-Planting Problem, Visibility

References

Honsberger, R. ``The Orchard Problem.'' Ch. 4 in Mathematical Gems I. Washington, DC: Math. Assoc. Amer., pp. 43-52, 1973.