1. The problem statement, all variables and given/known data I need to derive the prarametric equation of a certain torus. defined by a unit circle on xz plane with center (a,0) and revolving about z-axis. 2. Relevant equations * I dont know if this is relevent but here is something from wikipedia. Surfaces of revolution give another important class of surfaces that can be easily parametrized. If the graph z = f(x), a ≤ x ≤ b is rotated about the z-axis then the resulting surface has a parametrization r(u,∅)=(ucos∅,usin∅,f(u)). * 3. The attempt at a solution I can derive the parametric equation of unit circle in xz plane which is given by: <sinu+a, cosu> I can also define the locus, (the path formed when constructing the torus, or let us say central circle of the torus), of the centre of the unit circle around Z axis in XY plane as above. if we consider ∅ be the angle of revolution of center of unit circle about z axis, we have <asin∅,acosb>. I have no idea how to connect these two elements. I would be infinitely obliged if someone could explain or provide a link for this. Thank You.