The

3-dimensional extension of the

2-d ellipse. A

generic ellipsoid should not be

restricted to being a

surface or solid of rotation, however. The

points (x,y,z) which satisfy

` x`^{2}/_{a}2+y^{2}/_{b}2+z^{2}/_{c}2=1 are the

outer surface of a generic ellipsoid

centered at the

origin with

parameters a, b and c.

The ellipse is

defined to be a

set of points (in the (x,y)

coordinate system) each of whose distances from two fixed points

sums to a

constant. Similarly, the ellipsoid (being an ellipse in any planar section) is a set of points (x,y,z) each of whose distances from two points (no longer fixed;

dependent upon

direction!)

sums to a constant. The two points in any particular direction are on the

edge of an ellipse at the center of the ellipsoid. With this in mind, it can be said that "It takes two

distinct points to

specify a

circle or a

sphere; it takes three distinct points to specify an ellipse; it takes four distinct points to specify an ellipsoid."

*A side note: since the circle is a specific case of the ellipse, Webster's definition could simply state "A solid, all plane sections of which are ellipses."*