1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:R2->S\{(0,0,1)}
    σ(u,v) = (2u, 2v, u2+v2-1)/1+u2+v2

    Now I wish to find the inverse map:

    σ-1(u,v):S\{(0,0,1)}->R2

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Inverse map
  1. Linear Maps (Replies: 0)

  2. Moment map (Replies: 0)

  3. Real positive mappings (Replies: 0)

Loading...