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Problem of the Week 1248

Bicycle or Unicycle

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Show that a bicycle can travel along an infinite path that starts with the front wheel at the origin in such a way that the rear wheel passes through the origin and, thereafter, travels exactly in the track made by its front wheel. The trivial solution of a straight line path is excluded.

For definiteness, assume that the front wheel of the bike starts at (0, 0) and the rear at (-1, 0).

I am not expecting equations here, but if you make a sketch and send it to me, I can try to evaluate if it is correct.

Source: David Finn, Rose-Hulman Institute of Technology.

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8 September 2017