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Math Trek

A Snowy Twist

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Carving a massive block of packed snow into an elegant sculpture presents all sorts of challenges. It's even tougher when the goal is an intricate mathematical shape with a gravity-defying heart.

Earlier this month, a snow-sculpting team led by mathematician Stan Wagon of Macalester College in St. Paul, Minn., and artist Bathsheba Grossman of Santa Cruz, Calif., endured a demanding schedule and frigid temperatures to create such a form at the 12th annual Breckenridge International Sculpture Championship in Colorado. A "real-time" diary of the event can be found at http://stanwagon.com/snow/breck2002/index.html.

This was the fourth time that Wagon had entered a team in the contest. This year's squad included competition veterans Dan Schwalbe, a software engineer in Hamel, Minn., and John Bruning of Tropel Corp., Rochester, N.Y. Rob Nachtwey, a ski instructor at the Snowbird Resort in Utah, served as team photographer, videographer, and webmaster.

The event represented Grossman's first venture into snow as a carving medium. As an undergraduate student in the late 1980s, she had started out studying mathematics. She found herself drawn to physical representations of geometric abstractions, and she ended up studying art with sculptor Robert Engman at the University of Pennsylvania in Philadelphia.

Nowadays Grossman designs her mathematically inspired sculptures on a computer, using computer-aided design software. She employs rapid-prototyping technology to convert a design into a physical model, built up layer by layer into the full three-dimensional figure. Usually the model is made from wax, resin-impregnated starch, or plastic. To create a metal casting of the sculpture, she typically turns to the ancient lost-wax method, which destroys the model and mold to leave a metal sculpture.

"So the process moves, as it were, backward in time: from virtual idea to hand-finished metal," Grossman says.

A bronze sculpture created by Grossman served as the model for the Minnesota team's Breckenridge snow-sculpting effort. Called Spancel II, the original is only 5 inches tall (see http://www.bathsheba.com/spancel2/).

This sculpture has an intriguing, rarely encountered symmetry, featuring 180-degree rotations around three axes and no reflections. "I can't think of a familiar object that has it," Grossman says.

Initially, Grossman wasn't confident that her sculpture–with its open structure and strongly curved edges and surfaces–could be scaled up and successfully fashioned out of snow. However, her teammates assured her that "snow is very strong."

The final version, which Grossman dubbed A Twist in Time, was 12 feet high. It remained standing even a week after the competition. "Our sculpture here was by far the hardest and riskiest of any," Wagon comments.

"The event was especially exciting for me because. . .I've done very little work at large scales," Grossman says. "Prototyping technology tends to keep me inside an 8-inch box, so it was very liberating and educational to see the design so huge."

This year's championship trophy went to a whimsical sculpture of a bass-playing musician, created by a team from Canada. A Twist in Time earned an honorable mention for "expressive impact" and tied for second in voting by spectators.

Grossman came away with a new appreciation of snow as an artistic medium. "As carving media go, I like it," she says. "It cuts reasonably easily with a sharp shovel, but it gives enough resistance to cut pure curves, unlike soft media such as soap or clay."

While making A Twist in Time, the snow sculptors noticed that Grossman's piece can be viewed as the first two stages of an infinitely nested form–a three-dimensional fractal. Digging deeper into this structure to unveil additional levels of intricacy may be a fruitful avenue of artistic exploration.

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Algebraic Hearts

Here's one possible answer to last week's prime-grid puzzle.

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