Saturday, August 1, 2009

Bicycles with Square Wheels

I found this picture while I was looking for bikes to illustrate yesterday's post. I also found out about Math Professor Stan Wagen (Macalester College, St Paul, MN) who has actually built two bikes with square wheels that you can ride.

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.

At right, Prof Wagon rides his a bicycle with square wheels; although the "bicycle" pictured is actually a three wheeler. Link The secret is the shape of the road over which the wheels roll.

Watch a video of students riding on the bike:

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.