al extension of the 2-d ellipse
. A generic
ellipsoid should not be restricted
to being a surface or solid of rotation
, however. The point
s (x,y,z) which satisfy x2/a2+y2/b2+z2/c2=1
are the outer surface
of a generic ellipsoid center
ed at the origin
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
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
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."