College of LAS « Illinois

Mathematics

Putting Math into Pictures

Conveying complex mathematical idea with 3D images.

If a picture is worth a thousand words, then the 3D images by LAS mathematician George Francis speak volumes. Shown here as a series of "still lives," these images are usually viewed as animations in one of U of I's virtual reality environments. With the aid of high-powered computers, the images morph from one surface into another shape while seemingly suspended in space. Anyone wearing special "3D glasses" may explore the surfaces from the top, bottom, front, back, or even from the inside out.

Admired for their beauty, these images were first created in 1992 to demonstrate the value of visualizations, especially animations, in conveying complex mathematical ideas. Illustrations of any sort are generally frowned upon by most mathematicians because of their potential to mislead, which is why images of any sort were absent from college-level math textbooks until the 1950s. But Francis's images, here dubbed illiSnail, are winning converts because of their ability to show abstract processes. "Imagine trying to grasp how a gymnast performs a back flip from words or even a photograph," says Francis. "Every step in the process is important to understanding the entire movement, and process is what these animations capture."

October 2003