Two amazing videos about mathematical transformations have been making their way across the Internet via YouTube and Google Video.
The first is Möbius Transformations Revealed (2 minutes, 34 seconds), a video showing a remarkably simple way to view möbius transformations on the complex plane. It was created by Douglas N. Arnold and Jonathan Rogness of the University of Minnesota, Minneapolis and recently won an Honorable Mention for Non-Interactive Media in the 2007 Science and Engineering Visualization Challenge.
The second video, Outside In (21 minutes, 23 seconds), shows sphere eversions [turning the sphere inside-out in a way that does allow the sphere to pass through itself but doesn’t allow sharp corners or tears]. It was created at the now-virtual Geometry Center in Minneapolis under the direction of Silvio Levy, Delle Maxwell and Tamara Munzner and won 9 awards between 1994 and 1998.
More information about Outside In is available here.