Snow Moebius Strip: Doing the Twist

Contact Sharon Tang-Quan at [email protected]





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The next time you enter a snow-sculpting contest, you may want to consult a mathematician for help. A team including a UC Berkeley computer engineer entered the International Snow Sculpture Championships in Breckenridge, Colorado. This year the team took on the challenge of creating a knotted Moebius strip-and then splitting that band along its whole length.

Carlo H. Séquin, a UC Berkeley electrical engineering and computer science professor, created the team's design based on a triply twisted Moebius strip. Such a Moebius strip is constructed by joining the two ends of a rectangular piece of paper, after rotating one end by 540 degrees. Séquin created three-dimensional scale models of the structure on a rapid prototyping machine in Etcheverry Hall to help the snow carvers visualize this complicated geometry.

For the past seven years, "Team Minnesota" has been headed by Stan Wagon, a professor at Macalester College in Minnesota. The team has typically chosen mathematical schemes for its entries. This year, Team Minnesota consisted of Séquin, Wagon, John Sullivan of the Technical University of Berlin, Dan Schwalbe of Minneapolis and Richard Seeley of Silverthorne, Colorado.

The 2005 theme originated from the realm of knot theory.

"The roots and inspiration for my design go back to an encounter with sculptor Keizo Ushio from Japan, who carved a split torus at the 1999 Art+Mathematics conference," Séquin said. "Since then, I have constructed ever more complex split tori, Mobius bands, and knots," he said.

The team abandoned the basic three-fold symmetry of the triply twisted band in order to make a more dramatic-looking sculpture and to make the best possible use of the provided snow blocks, which measured several feet tall. Special attention was spent on raising the three lobes of the Moebius band to different heights for a more artistic sculpture.

"Since the original ribbon has an odd number of half-twists and thus is single sided, the splitting operation will not actually divide the knot into two parts, but will just produce a single strand of twice the length of the original ribbon-thus the name of the sculpture: ‘Knot Divided,'" he said.

The snow carvers were allowed four and a half days to carve their creations. Within the first three days of the competition, the team experienced unseasonably warm weather, with a strong sun and temperatures climbing into the 40 degree range. The team's major concern was the structural stability of the large, leaning arched lobes.

"To reduce weight at the top, we slightly tapered down the cross section towards the top," Séquin said. "To increase support, we let the bottom of the lobes touch at a couple of points, and we did not split the original band into two strands all the way down to the platform on which the sculpture rested," he said.

The dropping temperatures on the fourth day allowed the structure to stand in place for the judging and public viewing. At the end of the contest, judges awarded the winning prize to a sculpture of the shell of a nautilus. The nautilus was also created using mathematical planning.

Séquin's involvement comes as a lifelong interest in geometry and topology. He has actively collaborated with some sculptors for 11 years now, which he says has enabled him to combine his mathematical and artistic interests.

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