Ex: Prove for all eps exists K such that for all k>K, for all finite P in gen pos in the plane and q point we can partition P into k groups evenly such that for all but at most an eps fraction of the triples i,j,h, if we take a triangle with vertices from i,j.h, then either all or none such triangles contain q.
Ex: Prove that the energy of a finer partition is smaller. (Hint: \sum_i (a_i-x)^2 attains its min at x=average(a_i))