I wrote: << An interesting family of ovoids (a word I prefer to oval, cuz oval has a deeply ingrained casual meaning) is given by applying the transformation (r,theta) -> (r^c, theta) (c > 1) to the circle r= cos(theta), i.e., with radius = 1/2 and center at (1/2,0).

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The next few lines need correction. They should read: The resulting curve has the equation r = cos(theta)^c, |theta| <= pi/2. When c = p/q for integers p, q > 0 in lowest terms, then the curve is given by the polynomial equation (x^2 + y^2)^(p+q) = x^(2p), x >= 0. --Dan