I Remezed the epicyclic, b i t 3 i t 4 i t z = ---- + e + c e + d e i t e and polar i t 2 2 r = e ((cos(2 t) + b) + (c cos(t) + d) ) approximations to Moss's egg, minimaxing (very nearly) the signed distance measured (somewhat arbitrarily) along the ray from the center of its semicircular arc. This proved difficult and surprising, due to a chicken-and-egg conundrum that does not occur with polynomial and rational Remez: To get started, you need an approximate set of turning points good enough for the equal-ripple equations to have a real solution, which in turn must be good enough to have as many turning points as degrees of freedom. Then, when I finally got enough ripples, both iterations developed an *extra* ripple for which there is no parameter to control. Then you have to guess which ripple to leave unconstrained (disrupting the alternating sign pattern of your equations), and hope it winds up smaller than the ones you minimaxed. I only eyeballed the turning points instead of computing them, and I didn't try every possible omission pattern, but for the epicyclic, b = 0.17108, c = - 0.03844, d = - 0.0484, with six ripples of .02 and a seventh of .008. (Slightly < 2% of the egg minor axis.) (The other three degrees of freedom are translation, scale, and ripple height.) For the polar, b = 3.83214, c = 1.41969, d = 5.42912, (vs my original 3,1, and 5), with six ripples of 3% and a seventh of 2%. Now the surprise: There is a better (2.5%) minimax, without the seventh ripple!: b = 5.40849, c = 1.81059, d = 6.07139 . I would have bet against the possibility of multiple solutions, and strongly against the superiority of fewer ripples. But all three are aesthetically competitive with Moss's egg, using only three buggerfactors. --rwg MONASTERIAL ANAL-EROTISM AMELIORANTS