OVOID

 Other name: ovaloid.

An ovoid is a surface shaped like an egg.
In a general fashion, we can give the following definition: surface of class C1, boundary of a bounded convex subset of space. Then, a closed surface of class C1 all the points of which are elliptic is an ovoid.

To come closer to an egg, we can give the following definition:

 Cylindrical equation:  where  1)  with g positive, C1 on ]a, b[, 2)  concave on [a, b] . Profile of the corresponding egg, curve y²=f(x).

Examples:

 the ellipsoid of revolution (, k being the flattening of the ellipse), opposite with k = 3/4 the Kepler ovoid, the profile of which is a simple folium (, a = 0, b = 1) the ovoid with profile half a double egg (, a = 0, b = 1) the ovoid with profile the oval of the cubical hyperbola with an oval, or Hügelschäffer egg ( , 0 < a < b ), opposite with a = 1, b = 2, k = 3/4 the ovoid with profile the Granville egg (, 0 < a < b) , opposite with a = 4, b = 6, k = 4 the ovoid with profile the Rosillo curve (, b = –a, a < c < d ),  opposite with a = 1, c = 2, d = 3 A. de Quay proposed  for k = 3, r = 4, d = 5 (a  –3,4 ; b  0,5) Simon Cadrin proposed , with a=–1, b=3 ; Cartesian equation of the profile: .

See also the Cartesian ovals, the Ehrhart eggs, the curves of the slider-crank mechanism, the right folia.

For a list of egg-like curves: www.mathematische-basteleien.de/eggcurves.htm