Meaning of the Mobius transformations video - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T22:37:18Z http://mathoverflow.net/feeds/question/25971 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/25971/meaning-of-the-mobius-transformations-video Meaning of the Mobius transformations video Evgeny Shinder 2010-05-26T05:16:00Z 2010-05-26T13:05:17Z <p>What is this video trying to tell us? <a href="http://www.youtube.com/watch?v=JX3VmDgiFnY" rel="nofollow">http://www.youtube.com/watch?v=JX3VmDgiFnY</a></p> <p>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).</p> http://mathoverflow.net/questions/25971/meaning-of-the-mobius-transformations-video/26014#26014 Answer by AndrĂ© Henriques for Meaning of the Mobius transformations video AndrĂ© Henriques 2010-05-26T13:05:17Z 2010-05-26T13:05:17Z <p>Any M&ouml;bius transformations is a composite of a rotation of <i>S</i><sup>2</sup> (3 degrees of freedom), along with a translation and dilation of &#8477;<sup>2</sup> (3 degrees of freedom), adding up to the six dimensions of the Lie group PSL(2,&#8450;) = group of M&ouml;bius transformations.</p> <p>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.</p>