<<http://www.sciencenews.org/articles/20040403/mathtrek.asp>>
Riding on Square Wheels Ivars Peterson
A square wheel may be the ultimate flat tire. There's no way it can roll over a flat, smooth road without a sequence of jarring bumps.
Stan Wagon, a mathematician at Macalester College in St. Paul, Minn., 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.
Stan Wagon rides his square-wheeled trike over a special roadway. Courtesy of Stan Wagon
A square wheel can roll smoothly, keeping the axle moving in a straight line and at a constant velocity, if it travels over evenly spaced bumps of just the right shape. This special shape is called an inverted catenary.
Interesting. And maybe useful in some specific cases. But it would probably be quite expensive to build millions of miles of roads with inverted catenary-shaped bumps and to maintain them in that figure, to keep debris, snow, ice, etc., from accumulating in the low points, etc., and even if that was done, only one size of square wheel would work, regardless if one were driving a small car or a motorcycle or a heavily-loaded eighteen-wheeler. I think those difficulties would be enough to cosh the whole idea.
-- Ronn! :)
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