Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity. It was one of the winners in the 2007 Science and Engineering Visualization Challenge and was featured along with the other winning entries in the September 28, 2007 issue of journal Science. The video, which was first released on YouTube in June 2007, has been watched there by nearly two million viewers and classified as a “Top Favorite of All Time“ first in the Film & Animation category and later in the Education category. It was selected for inclusion in the MathFilm 2008 DVD, published by Springer.

From this web page you can:

• View the low resolution video on YouTube, or a version with  Portuguese subtitles
• View the medium resolution video in the IMA video library
• Download the high resolution wide-screen narrated video in QuickTime format. Warning: file is 130 MB.
• See some screenshoots (click any of the images below for higher resolution).
• Download some very high resolution renderings:
  2000x1600 px   3840x7800 px   6000x7800 px
• Read an article about the mathematical background (intended for mathematicians).

Möbius Transformations Revealed has been featured in a number of articles and websites, not to mention countless blogs. Some of these are:

Chronicle of Higher Education, 12/18/07 Associated Press, 12/05/07 SIAM News, 12/07 UMNnews, 11/30/07 All Things Considered, Minnesota Public Radio, 11/28/07 MinnPost, 11/27/07 Boing Boing, 11/19/07 Kennislink (in Dutch), 11/17/07 Science News Online, 11/17/07 Science Magazine special feature, 9/28/07 National Geographic, 9/27/07 National Science Foundation press release, 9/27/07

An extract from the video is included in the film Achieving the Unachievable, a documentary about the mathematics in M.C. Escher's art, and images from video were featured in the book Bilder der Mathematik.

Möbius Transformations Revealed was built primarily using POV-Ray with some help from Mathematica. The soundtrack is a performance of "Von fremden Ländern und Menschen" ("Of Foreign Lands and Peoples") from Robert Schumann's Kinderszenen, Op. 15. The pianist is Donald Betts.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.