Stirling (in 1717) prove that 9 points uniquely define a cubic. McLaurin (in 1720) proved that two cubics intersect in at most nine points. Bezout gets credit for it, due to his incorrect proof which came years later. Around 1750, Euler and Cramer noticed that these seem to contradict, since different cubics are passing through the same nine points. With that set-up, here's my question. Are there some really nice sets of 9 points that have multiple interesting cubics passing through all nine points? In a Mathematica wrapper, here's a set of four cubics that pass through the same 9 points. ContourPlot[{ 41x - 5x^3 == 12y, -41y + 5y^3 == 12x, 365x - 41x^3 == 12y^3, -365y + 41y^3 == 12x^3 }, {x, -4, 4}, {y, -4, 4}, Frame -> False] Cubics in the Triangle Plane http://pagesperso-orange.fr/bernard.gibert/index.html likely has a set of nine triangle centers that leads to a variety of odd cubics, but I haven't figured out a good way to isolate a good case. --Ed