19 Feb
2007
19 Feb
'07
1:52 p.m.
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). The resulting curve has the equation r = cos(theta)^c When c = p/q for integers p,q > 0 with q odd, then the curve is given by the polynomial equation (x^2+y^2)^((q+1)/2) = x^p. E.g., p/q =3/1 gives a reasonable ovoid. Still, "Moss's oval" ( http://mathworld.wolfram.com/MosssEgg.html ) looks to me more like an egg than does the above curve for any values of p and q. --Dan