Mapping a cylinder onto a sphere

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Homework Statement


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?


Homework Equations





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].
 

Answers and Replies

  • #2
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Don't worry, I have solved it, thanks for reading though.
 

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