Here's a "puzzle" I don't know the answer to offhand: Call two points X, Y' of the plane "equivalent": X ~ X' if they differ by an integer point: X' = X + v for some v in Z^2. Likewise, call any two circles C, C' in the plane "equivalent": C' ~ C if one is a translation of the other by an integer translation: C' = C + w for some w in Z^2. Now let A, B, C be any three distinct points in R^2. Among all possibilities for A, B, C, what is the maximum number of inequivalent circles that pass through 3 points A', B', C' with A' ~ A, B' ~ B, C' ~ C such that no points equivalent to A, B, or C lie in the interior of such a circle ??? —Dan --------- What is the maximum number of circles Unrolling the torus to obtain the plane results in all the points of the form A + (K,L), B + (K,L), C + (K,L) appearing on the plane