Yes, you’ve read it right! Mathematician Stan Wagon has proven something impossible or even crazy to be the opposite.
In mid 1900’s he was intrigued by an exhibit in the Exploratorium in San Francisco. It was a pair of square wheels joined by an axle traveling over a bumpy roadbed. His curiosity led him to investigating the relationship between the shapes of wheels and the roads over which they roll.
“As soon as I learned it could be done, I had to do it,” Stan said. The result was an interestingly rideable square-shaped bicycle!
The secret is in the surface the square wheels are travelling on. They can smoothly roll and keep the axles moving in a straight line if they are rolling over bumps that are evenly spaced and of the right shape. This shape is referred to as an inverted catenary. It is the curve depicting a chain or a rope hanging loosely between two supports. When it is turned upside down, you get an inverted catenary.
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Here’s a video clip on how a weird square-wheeled bicycle can actually give you a smooth ride!