Fred supplied pictures of ovals of Greg Fee's and Bill Gosper's, which I've added to http://www.tiac.net/~sw/2007/02/Steve_Gray_oval Gack! You'll never pin that avocado on me! That's not equalscale. Try gosper.org/cheapegg.gif . wfl>Correct --- I hadn't meant to imply that the curvature actually went negative --- just that it looked as if it was thinking about it! [Also I cheated, and tried varying Bill's constant coefficients ...] So did I. Interesting problem: Suppose we declare the Moss/Zwolle egg to be Platonically ideal, and seek the "closest" approximation of the form (a+b*cos(t))^2+(c+d*cos(2*t))^2. How do we measure the closeness of two curves? It's not the same as the closeness of two functions, because the curves are parameterized differently. We don't want the answer to change if we simply change the speed with which we trace one of the curves. I'm tempted to resort to a double prodigal(qx,qy). --rwg