What is this video trying to tell us?
<http://www.youtube.com/watch?v=JX3VmDgiFnY>


The statement that fractional linear transformations correspond to rotations of the sphere under the stereographic projection is wrong (since for example some fractional linear transformations have only one fixed point, which is impossible for the rotation).



Meaning of the Mobius transformations video
Any Möbius transformations is a composite of a rotation of *S*2 (3 degrees of freedom), along with a translation and dilation of ℝ2 (3 degrees of freedom), adding up to the six dimensions of the Lie group PSL(2,ℂ) = group of Möbius transformations.


In the video, the translations are depicted by letting the sphere move left and right on the surface of the plane, while the dilations are depicted by lifting the sphere in the third dimension.


