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Homework Help: Inverse map

  1. Sep 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Let S = {(x,y,z) be an element of R3: x2+y2+z2=1} be the unit sphere

    I have a map that takes coordinates from the xy plane to points on the sphere.
    This map is given by:

    σ(u,v) = (2u, 2v, u2+v2-1)/1+u2+v2

    Now I wish to find the inverse map:


    that is, to take points on the sphere onto the xy-plane (the stereographic projection)

    3. The attempt at a solution

    I'm really not quite sure where to start. I understand the logic behind what is asked, but mathematically, I don't quite know!
  2. jcsd
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