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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 C^{1},
boundary of a bounded convex subset of space. Then, a closed surface of
class C^{1} 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, C^{1} 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 slidercrank mechanism, the right folia.
For a list of egglike curves: www.mathematischebasteleien.de/eggcurves.htm
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© Robert FERRÉOL 2017