Mathematical Surfaces

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To most of us, a surface is something we can touch and attribute a shape to--the spherical surface of a ball or the toroidal surface of a doughnut. But there are innumerable surfaces that we cannot touch, or see, or even know of, because they are representations of mathematical functions. Mathematicians have long relied on their own powers of imagination to picture these abstract surfaces. Now, mathematicians such as Richard Palais of the University of California, Irvine, and graphic artists such as Luc Benard are exploiting the magic of computer graphics to recreate these abstract mathematical surfaces in familiar yet intriguing settings.

This illustration presents five well-known mathematical surfaces, rendered as glass objects in a highly realistic "Still Life." To create their chosen surfaces, Benard relied on the computer program 3D-XplorMath, developed by Palais for visualizing many of the most famous mathematical surfaces. He then exported these surfaces into a 3D-rendering program, using it to give the objects a glassy texture and place them on a virtual glass-covered wooden tabletop.

ILLUSTRATION: FIRST PLACE
Still Life: Five Glass Surfaces on a Tabletop
Richard Palais* and Luc Benard
*University of California, Irvine, USA

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