Sink or Float Materials Bundle! $48.50!
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MatheMUSEments Square Wheel
By Ivars Peterson

Riding around on a flat tire is no fun. It feels really bumpy. But a square wheel may be the ultimate flat tire. There's no way it can roll over a flat, smooth road without jolting the rider again and again.

Stan Wagon, a mathematician at Macalester College in St. Paul, Minnesota, has a bicycle with square wheels. It's a weird contraption, but he can ride it perfectly smoothly. His secret is the shape of the road over which the wheels roll.

A square wheel can roll smoothly if it travels over evenly spaced bumps of just the right shape. That special shape is called an inverted catenary. A catenary is the curve formed by a chain or rope hanging loosely between two supports.
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