1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Mapping a cylinder onto a sphere

  1. Feb 8, 2012 #1
    1. The problem statement, all variables and given/known data
    How might I show that the map (in cylindrical polar coordinates) given by [itex]f:(1,\phi,z)\to(\sqrt{1-z^2},\phi,z)[/itex] does not change the area?

    2. Relevant equations

    3. The attempt at a solution
    I can see this is like having a sphere in a cylinder and we shine "light" on the cylinder orthogonal to its axis inwards towards its axis so that the image falls on the unit sphere housed inside. A hint to the problem is given to be that the area of the spherical disc of spherical radius [itex]r[/itex] is [itex]2\pi(1-\cos r)[/itex].
  2. jcsd
  3. Feb 9, 2012 #2
    Don't worry, I have solved it, thanks for reading though.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook