Smallest angle among two lines in $n \times n$ grid Given an $n \times n$ grid, what is the minimum angle between any two distinct lines, each going through some grid point $p$ and at least one other grid point?
My guess is the minimum is attained by the line through $(0,0), (n,1)$ and the line through $(0,0), (n,0)$ but how can I show that this is the optimal line pair?

That is not the optimal pair.
Compare the angle between the lines through $(0,0),(4,1)$ and $(0,0),(4,0)$ [about $14^\circ$] with the angle between the lines through $(0,0),(4,3)$ and $(0,0),(3,2)$ [about $3.2^\circ$]. 
