How would you write (z-1)^2 = x^2 + ...

How would you write (z-1)^2 = x^2 + y^2 in the form R(u,v)?


  Plot3D[1+Sqrt[x^2+y^2],{x,-2,2},{y,-2,2}];

Spherical Coordinates do quite nicely here.

x=x(u,v)=a cos u sin v
y=y(u,v)=a sin u sin v
z=z(u,v)=a cos v
u from 0 to 2Pi
v from 0 to Pi

I hope you can see this is (cos u sin v, sin u sin v, 1+sin v).


  ParametricPlot3D[{Cos[u] Sin[v], Sin[u] Sin[v], 1+Sin[v]},{u,0,2 Pi},{v,0,Pi}];