Last modified: Monday, April 28, 2003
Minimal surfaces appeal to architects and sculptors, IUB mathematician finds
NOTE: Matthias Weber's minimal surfaces can be viewed at http://www.indiana.edu/~minimal/gallery/index.html. For more information, contact Weber at 812-855-8724 or firstname.lastname@example.org.
BLOOMINGTON, Ind. -- It's happened enough times that it no longer surprises Matthias Weber, an assistant professor of mathematics at Indiana University Bloomington.
A sculptor sends him a photograph of a recent creation, and Weber determines that the sculpture's shape corresponds closely to a minimal surface. Weber can even produce the mathematical equation that will generate an image of the minimal surface on a computer. But the sculptor has little knowledge of mathematics.
How can this happen? The answer may lie in what all minimal surfaces have in common.
"A minimal surface is formed when the pressure on both sides of a surface is the same," Weber explained. "'For example, when you dip a bent coat hanger into soapy water, the soap bubble that forms on the hanger is a minimal surface." These soap bubbles can have various shapes, depending on the shape of the coat hanger, but in every case the bubble is trying to minimize surface tension, he said.
"This equilibrium condition seems to attract some artists," he said, even when the shape involved is much more complex than a soap bubble. "These artists sculpt near-minimal surfaces without realizing it."
Weber also hears from architects who have seen computerized illustrations of his minimal surfaces and are intrigued by the possibility of adapting them to structures, both interior and exterior. He has exchanged virtual three-dimensional models of minimal surfaces with some architects and is exploring ways to collaborate with them. Minimal surfaces are extremely stable as physical objects, he pointed out, and this can be an advantage in many kinds of structures.
Calendars are another possible use for his work, highlighting the aesthetic qualities of minimal surfaces.
These aesthetic qualities are on vivid display in Weber's two computer galleries of minimal surfaces. The "Old Gallery" (http://www.indiana.edu/~minimal/gallery/index/index.html) is the more deliberately artistic, with minimal-surface objects set in imaginary landscapes.
"The images in the Old Gallery are not intended as illustrations of mathematical facts," he said. "They more than fulfill their purpose if non-specialists see them and can feel some of the intriguing enchantment that a mathematician feels when exploring the mathematical objects."
In the "New Gallery" (http://www.indiana.edu/~minimal/gallery/index/catalog.html), which is more mathematically accurate, he said he tries to use aesthetically pleasing textures to emphasize the three-dimensional nature of the minimal surfaces.