Let f be a real-valued function on the plane such that for every square ABCD in the plane, f(A) + f(B) + f(C) + f(D) = 0.

Prove or disprove that f(P) = 0 for every point P in the plane?

Consider the degraded square where all 4 corners are the point P.

Posted by Steve Herman on 2010-11-16 15:11:03