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Feature

Douglas Arnold

University mathematician Douglas Arnold and colleague Jonathan Rogness have a surprise hit on You Tube.

Show me the Moebius

Video from University mathematicians is a hit--more than a million so far--on YouTube

By Deane Morrison

November 30, 2007; updated December 1, 2007

A video about mathematics making a splash on YouTube? Believe it. "Moebius transformations revealed," a visual journey through the land of 3-D geometry, has just passed the million-hit mark. And no one was more surprised than its makers, University mathematicians Douglas Arnold and Jonathan Rogness. "We thought a few people might see it, and we'd tell our friends," recalls Arnold, who is the director of the University's Institute for Mathematics and Its Applications. Set to the soothing strains of Robert Schumann's "Scenes from Childhood," the video shows the beauty of math by shining a spotlight on a group of mathematical operations called Moebius (yes, he's the guy who invented the one-sided strip) transformations. In such a transformation, a simple rule governs, for example, how points on a plane will be redistributed when the plane is rotated or inverted (turned inside out). "We wanted to show how beautiful mathematics is, and one way to get that across is visually," says Arnold. "It's good for people who aren't good at math. "We were featured [on YouTube] alongside talking cats and people charging their iPods with Gatorade. But I think people like to be challenged intellectually, too." The YouTube idea was born when Arnold attended a lecture on graphics and teaching by Rogness, an assistant professor of mathematics and associate director of the Institute of Technology Center for Educational Programs. Rogness suggested they do a project together, and Arnold suggested a Moebius transformation. They entered their video in the National Science Foundation's annual Science and Engineering Visualization Challenge, where it garnered an honorable mention. And they posted it on YouTube. A previous, more basic Moebius transformation video by Arnold also had attracted the attention of Canadian filmmaker Jean Bergeron. Bergeron used a short clip from the final version in his documentary about renowned Dutch artist Marits Cornelis Escher and Dutch mathematician Hendrik Lenstra. Lenstra used the mathematics related to Moebius transformations to guide him in completing Escher's celebrated drawing "Print Gallery," which features a mysterious blank spot in the middle. The key to finishing the drawing was to find the mathematical formula Escher used to twist and deform the landscape of the picture, then extend the landscape to fill in the blank. Bergeron's 53-minute documentary, "Achieving the Unachievable," received its world premiere at the University November 1, drawing an audience of 700. "Mathematics, when well presented, is something the public will respond to," Arnold says. A high-res, 130-MB version of the video can be downloaded from Arnold's Web site.