1. The problem statement, all variables and given/known data Write the equations of a surface of revolution with axis OZ: A) the Torus obtained by a rotation of a circle x= a + b*sin(u), y= 0, z = b*sin(u) 0 < b < a B) the pseduosphere obtained by the rotation of a tractrix x= a*sin(u), y=0, z= a*(log(tan(u/2) + cos(u)) C) the catenoid obtained by the rotation of the catenary x = a*cosh(u/a) y=0, z= u. 2. Relevant equations Unfortuantly my professor gave the questions from another text, whose 1st chapter covers this material; however, it is not covered in my material (he claims that we should have enough intuition to figure this out, however, I don't seem to have it. But besides that point, I was able to find the following general standard form of parametrization of a surface of revolution on mathworld's website: x(u,v)= phi(v)*cos(u) y(u,v)= phi(v)*sin(u) z(u,v)= psi(v) 3. The attempt at a solution As hinted at above, I don't quite have the background to tackle this problem. At the moment I have written down the standard form, as above; however, I don't know what the functions phi or psi are, nor do I have much of an idea of how to find them, so if there are any ideas of where to go with this. Or I could be looking at this the entirely wrong way. So any help would be appreached so I can get this started. (Oh and the website that I snaged the equation from is as follows: http://mathworld.wolfram.com/SurfaceofRevolution.html) Thanks in advanced for any suggestions on where to get started.