![](http://3.bp.blogspot.com/_QIjZXwAi4ag/SnW8ZJpvW2I/AAAAAAAAAao/K60WJHDXMG4/s320/square_wheels.jpg)
In 1960, J. B. Robison found that a bicycle with square wheels could ride down a road, if the road were covered with a nearly parabolic shape. The shape is actually a hyperbolic cosine or catenary, and it is a problem in differential equations to prove that. This link outlines the math.
If the shape of the road is right, then the rider stays level despite the surface.
![](http://4.bp.blogspot.com/_QIjZXwAi4ag/SnRSKI1VoXI/AAAAAAAAAaA/Ck4JrOwFggk/s320/27664.jpeg)
Watch a video of students riding on the bike: http://www.youtube.com/watch?v=LgbWu8zJubo
Stan Wagen posted a demonstration of the solution, on the Wolfram site, and you can watch the video. I was unable to load the Wolfram player to work with the model interactively. Here is a low tech animation.
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