Triking Around
Stan Wagon, a mathematician at Macalester College in St. Paul, Minnesota, has built a real tricycle with square wheels, which he rides on a road of inverted catenaries.
Stan Wagon's square-wheeled trike in action.
Wagon first learned about traveling on square wheels when he saw an exhibit at the Exploratorium in San Francisco. The exhibit featured a pair of square wheels joined by an axle riding over an inverted catenary roadbed.
Square wheels on display at the Exploratorium in San Francisco.
Intrigued by the demonstration, Wagon decided to build a square-wheeled bike he could actually ride himself. "As soon as I saw it could be done, I had to do it," he said.
The bike was tricky to build, and Wagon ended up with an unusual kind of tricycle. He also had to construct an inverted catenary surface on which to ride it. Wagon's square-wheeled trike went on display at the Macalester College science center.
"It rides like a normal bike, though steering is difficult," said Wagon. If you turn the square wheels too much, they get out of sync with the inverted catenaries.
Having one front wheel and two back wheels helps make it easier to ride the trike in a straight line. If you had a bicycle instead, you would need to turn the wheel now and then to help keep your balance, and that's hard to do with square wheels on a bumpy road.
For the trike-roadway combination to work, the length of the side of a square wheel also has to match the length of one unit of an inverted catenary road. So if you start with one corner of the square at the beginning of the road, each corner will end up at a point between two catenaries as the wheel rolls along.
At the National Museum of Mathematics in New York City, trikes with square wheels ride on a circular pathway of inverted catenaries.
See also "Riding on Square Wheels."
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