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The Torus
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In geometry, a torus (pl. tori) is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle, which does not touch the circle. A torus can be defined parametrically by:
where u, v are in the interval [0, 2π], R is the distance from the center of the tube to the center of the torus,
r is the radius of the tube.An equation in Cartesian coordinates for a torus radially symmetric about the z-axis is 
and clearing the square root produces a quartic:
The surface area and interior volume of this torus are given by
