A while ago we sought these, and it wasn't even Easter. Plot[{Sqrt[-ChebyshevT[4, x]], -Sqrt[-ChebyshevT[4, x]]}, {x, -(1/2) Sqrt[2 + Sqrt[2]], -(1/2) Sqrt[2 - Sqrt[2]]}, AspectRatio -> 3/4] Actually, this is how people remember and draw eggs. Real eggs are more nearly spheroids. The aspect ratio (spare us the obvious synonym) is known to vary, Spherical Egg Discovered in England - Gizmodo <https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CB4QFjAAahUKEwjkj_-jhdTIAhXOW4gKHQCtD6Y&url=http%3A%2F%2Fgizmodo.com%2F5664102%2Fperfectly-round-egg-discovered-in-england&usg=AFQjCNFV9vPERKeDC-2nhF6LOQnYpBOftg&sig2=u5L39_ErLQ9uZALrS7gcBA> , and the hen's egg: factors affecting shell splitting during boiling <https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CB4QFjAAahUKEwii0pib4tPIAhUX_WMKHWS8AEk&url=http%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Fpdf%2F10.1080%2F00071667208415958&usg=AFQjCNEnCwrKC_eGa763tMKYZNHNIIRYJw&sig2=iG0MP9CGLjcwG7NqC5dC9A&bvm=bv.105454873,d.cGc> fails to implicate it as a predictor. --rwg It takes a pretty smooth egg to earn a dentistry diploma.