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Square-wheeled Bicycle

The square-wheeled bicycle runs smoothly on its specially designed track. 

December 2007

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Two square wheels equal one smooth ride

They may not yet be able to fit a square peg into a round hole, but the 12 students in the Math 489 Mathematics Modeling class have achieved the supposedly impossible—a smooth ride on a square-wheeled bicycle.
The group debuted their engineering phenomenon at the 22nd annual Pi Mu Epsilon undergraduate mathematics conference in November, to a standing ovation.

Terry Jo Leiterman (Mathematics) envisioned the project as a more tangible way of thinking about math. “I wanted to try to create a lab so students had a hands-on way to understand the spirit of mathematics.”

She admits she wasn’t positive the project would work but she soon learned that, despite countless obstacles along the way, her students were closing in on a successful solution. “There were so many opportunities for mistakes,” she said. “That’s how you learn.”
And, after many unsuccessful plans, students began telling her, “We can’t do that.” A turning point occurred, however, when the students realized that the key to the project was not the shape of the wheel, but rather the shape of the track the bicycle would ride on.

“I knew they had to get to that point … to think past the wheel,” Leiterman said. “They had to discover that. It was really an ‘Aha!’ moment.”

Class member Alicia Brinkman ’10 added, “The best part of the project was definitely the final product. Theoretically, the bicycle rides on a road of catenary curves, and to actually see this performed with our bicycle was amazing.”

The task involved pretty advanced mathematics, Leiterman admitted. “The mathematics lies in finding a solution for the road, which involves trigonometry, calculus and differential equations.”

“Although the equation for our road of catenary curves is not something new, we were able to take our hyperbolic cosine equation and use it for something tangible,” Brinkman added.

After all the challenges and about nine weeks of work (both in the lab and outside of class), the students were thrilled with their results and the reception their work has received.

They are now considering submitting their project to the “Guinness Book of World Records,” and the bicycle is generating both local and national media attention.

While the St. Norbert project was not the first square-wheeled vehicle ever designed (a professor at Macalester College in St. Paul, Minn., built a square-wheeled tricycle in the 1990s), Leiterman said it was the first effort achieved completely by students.

“As an instructor, my main goal is to [help students] develop some intuition and build some confidence,” Leiterman said. “I didn’t want to tell them how to do it.”

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