Parametric Equations of a Torus
The Cartesion equation for a torus takes the form
(if any ofand z are interchanged, a similar, rotated torus will result).
We can obtain a parametric equation by settingas in the diagram below.
The Cartesian equation becomes
Square rooting both sides gives
Now recognise that for constantthis equation defines a circle around the– axis of radiusso setand