Paraboloid

Paraboloid is a solid figure in which parabolic sections can be cut. If a parabola be rotated about its axis, it will give the paraboloid ofrevolution, the sections at right angles to the axis being circles. Should these sections be ellipses instead of circles, we have the elliptic paraboloid. A more complicated surface is the hyperbolic paraboloid, the sections in planes parallel to two pairs of axes being parabolae, and those in the plane containing the third pair of axes being hyperbolae. The surface so obtained is saddle-shaped, and extends to infinity in the direction of each of its axes. Although so curiously curved, it is possible to draw straight lines upon it; hence it is called a ruled surface, and may be constructed by suitably arranging a number of stretched strings.