Two IT faculty members receive international science and engineering visualization award

University of Minnesota mathematics professor Doug Arnold and assistant professor Jonathan Rogness received an honorable mention award in the 2007 International Science and Engineering Visualization Challenge for their video “Möbius Transformations Revealed.” Set to classical music, the video demonstrates the beauty of complex mathematical functions. The video was featured along with the other winning entries in the Sept. 28, 2007 issue of the journal Science.

The competition, sponsored jointly by Science and the National Science Foundation (NSF), highlights exciting visual elements of science and engineering. More than 200 entries were received for the 2007 competition from 34 states and 23 countries representing every continent except Antarctica. The other two winning entries in the noninteractive media category were by a professional science film production company and a 16-person NASA production team.

Möbius transformations are mathematical functions that send each point on such a plane to a corresponding point somewhere else on the plane, either by rotation, translation, inversion, or dilation. It may sound confusing, but after watching the simple and elegant explanation of Möbius transformations created by Arnold and Rogness, everything becomes clear.

The video demonstrates the transformations in two dimensions but then backs away and adds a third—placing a sphere above the plane and shining light through it. As the sphere moves and rotates above the plane, suddenly all the transformations become linked, in a way that conveys visually in minutes what would otherwise take "pages of algebraic manipulations" to explain, Rogness said.

First released on YouTube in June 2007, “Möbius Transformations Revealed” has been watched there by more than 1 million viewers. Download the high resolution video in QuickTime format. Warning: the file is 130 MB.