From: Allan Wechsler <acwacw@gmail.com> Either find a circular disk that covers these lattice points and no others, or prove that no such disk exists.
Here is the set. I am abbreviating (x,y) to the two-digit code xy.
01 02 03 04 11 12 13 14 20 21 22 23 24 25 31 32 33 34 35 42 43 44.
--Given a set of points P and another Q in the plane, the question of whether a disk D exists with P inside D but Q outside D, is a linear programming problem, for each point xy we demand a*x*x+b*x*y+a*y*y+c*x+d*y+e > 0 (or <0) and the linear programming will determine whether suitable (a,b,c,d,e) exist. Indeed by replacing the >0 by ">s" and the <0 by "< -s" and maximizing s, you can make the linear program find the "best" such circular disk (if any exist). -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)