Möbius transformations revealed is a neat a short video by Douglas Arnold and Jonathan Rogness, and it's shared under a creative commons Attribution-Noncommercial-Share Alike 3.0 license. It depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity.

The video was a winner in the 2007 Science and Engineering Visualization Challenge. The video (bellow) it's also available on the site to download in high resolution (130 MB). It was built primarily using POV-Ray and Mathematica, and the soundtrack (from Schumann's Kinderscenen, Op. 15, I) is performed by Donald Betts and distributed by Musopen.