The Cartesion equation for a torus takes the form![]()
(if any of
and z are interchanged, a similar, rotated torus will result).
We can obtain a parametric equation by setting
as in the diagram below.

The Cartesian equation becomes
![]()
![]()
Square rooting both sides gives
![]()
Hence![]()
Now recognise that for constant
this equation defines a circle around the
– axis of radius
so set
and![]()