elipsoid
An ellipsoid, sometimes spelled elipsoid, is a smooth, closed quadric surface that generalizes a sphere to three unequal axes. In its standard form, it consists of all points (x, y, z) satisfying x^2/a^2 + y^2/b^2 + z^2/c^2 = 1, where a, b, and c > 0 are the semi-axes along the coordinate directions. The center is at the origin; translating or rotating yields a general ellipsoid.
The ellipsoid is convex and symmetric about its three principal axes. The lengths of its principal diameters
Volume and surface area: The volume is V = 4/3 π a b c. The surface area does not
Special cases: If a = b = c, the ellipsoid reduces to a sphere. If two axes are equal,
Applications: Ellipsoids model many physical and geometric shapes. In geodesy, the Earth is approximated by an