Ivars Peterson's MathTrek
Most mall visitors probably wouldn't expect to find a giant Möbius strip, particularly one disguised as a public bench, sprawled across a courtyard.
A shopping mall known as The Shops at Lake Avenue, just a few blocks from Caltech in Pasadena, Calif., features just such a structure (or is it a sculpture?). Created by conceptual artist and architect Vito Acconci, whose studio is in Brooklyn, N.Y., his "Möbius Bench" resembles a giant rubber band flopped lazily on the ground. Mall visitors can simply look at it or take a seat somewhere along its twisty contours.
The Möbius strip (or band) is a remarkable, one-sided, one-edged surface. You can make a model of a Möbius band by holding one end of a rectangular strip fixed, rotating the opposite end through 180 degrees, then joining together the two ends, leaving a half-twist in the resulting loop.
Acconci created his first Möbius bench in 2001 for an installation in Fukuroi City, Japan. Made from translucent fiberglass, the sculpted bench glows in the dark.
It's actually a three-dimensional Möbius structure. Its cross section is shaped like a "Y," which forms the bench's seat, back, and foot. As it moves through space, the Y turns and rotates and joins itself, producing a wide, twisted loop. A seat on the outside of the loop becomes the back of a seat inside the loop, which becomes the back of a seat outside, which becomes a seat inside, which becomes the foot of seat outside, which becomes the bottom of a seat inside.
The bench functions as furniture, playground equipment, and light source, according to Acconci. As a prototype for Möbius seating, it can be built in different sizes and shapes and made of different materials. In the form of a bench, it serves as outdoor public seating; in the form of a sofa, it becomes private seating in a home.
The Pasadena Möbius bench, installed in 2003, is also made from fiberglass, this time with a silvery blue finish. A fiber optic light strip is mounted all along its edge. The structure covers an area of about 19 feet by 28 feet.
Over the years, the Möbius strip has attracted the attention of a variety of artists, architects, and artisans. Several have created their own versions of Möbius benches, some carved from wood, others fashioned from stone or molded out of bronze.
For more examples of Möbius-strip-inspired structures, see "Möbius at Fermilab," "Möbius in the Playground," "Strolling Down Möbius Lane," and "Sculpting with a Twist."
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