Problem of the Week 1248
Bicycle or Unicycle
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
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.