October 20, 2010

Martin Gardner’s Möbius Surprise

A prolific writer on a wide variety of topics, Martin Gardner died earlier this year. On Oct. 21, 2010, on what would have been his 96th birthday, groups all over the world will gather to celebrate Martin's work and continue his pursuit of a playful approach to mathematics, magic, science, art, literature, and much more.

I was reminded again of Martin's generosity and of his delight in surprises when I recently came across a letter  that he had written to me about 10 years ago, when I was pursuing some investigations into Möbius strips as the basis of artworks.

In replying to my query, Martin remarked that he had, by coincidence, just completed an article about Möbius strips for a children's science magazine.  He noted that the article contained nothing that hadn't been in his Scientific American column on the subject in December 1968. "Except for the following," he added, and he had drawn a diagram (below) to illustrate the construction.

Martin concluded with the following instructions: "Trisect the twisted band, then bisect the untwisted one, and open up for a big surprise!"

Of course, he didn't reveal what the surprise was, so I had to try it for myself.

Initial configuration, with one twisted band and one untwisted band, made from a cross-shaped sheet of paper.

Tangled configuration after cutting.

Final configuration, revealing a small Möbius strip interlocked with a rectangular loop.

As Martin had suggested, the result was a delightful surprise.

Photos by I. Peterson

October 12, 2010

Möbius in Toronto

A glistening, sinuous shape at the other end of a courtyard caught my eye as I was walking down Yonge Street during a recent visit to Toronto. I had to take a closer look.

The sculpture sits in the Anne Johnston Courtyard, between two high-rise towers (named Quantum and Quantum 2) at 2181 and 2191 Yonge Street, in Toronto, Canada.

About 8 feet tall, the stainless-steel sculpture forms a giant, twisted band that stretches skyward in a wide, stiff loop. I quickly confirmed that the band does, indeed, have the one edge and one side characteristic of a Möbius strip.

I later discovered that the sculpture, created by Toronto artist Lilly Otasevic, is titled Möbius. Her own description of the sculpture acknowledges its mathematical roots and notes the Möbius strip's present-day ubiquity as the underlying form of the three-arrow recycling symbol.

Otasevic says that her sculpture represents "transformation and timeless continuity of natural processes," symbolizing balance and "our unity with nature." Many of her other artworks have also been inspired by nature and natural processes, especially the interplay between light and shadow and interrelationships between organic and inorganic matter, as seen in crystals, Fibonacci spirals, cellular structures, and elsewhere.

Otasevic joins a growing number of artists who have found inspiration in the wonderful mathematical discovery of August Ferdinand Möbius, a list that includes Max Bill, Charles Perry, and others.

Photos by I. Peterson