TITLE: Applying analysis to solve a line-of-sight problem
QUESTION [13 upvotes]: This was an optional h.w. problem:
You are at the origin in $\mathbb{Z}\times\mathbb{Z}$. There are trees of a fixed finite radius at each point in $\mathbb{Z}\times\mathbb{Z}$ (other than the origin).
How far can you see?
This was asked in (I think), the context of the Stone-Weierstrass Theorem. So I have been thinking there must be some distance where the diameters of the trees visually converge and you get a polynomial approximation of a visual boundary.
Thanks for your kindness to reply.

REPLY [6 votes]: This the famous Polya Orchard Problem.
The link is to a thorough discussion by Honsberger, marred a little by the fact that it comes from Google Books.  The discussion is quite elementary.
Another detailed discussion can be found here.  Somewhat more machinery is used.
I do not know of a connection with the Stone-Weierstrass Theorem, but that could very well be due to my weaknesses in analysis.