Bicycle or Unicycle Tracks?

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The two wheels of a bicycle typically make separate tracks. One exception is a bike traveling in a straight line. The convoluted path shown in the graphic is an example of a nonstraight track along which a bike travels so that the rear wheel follows exactly in the track made by the front wheel. If

F(t)

is the parametrized curve, then

F(n)=(n,0)

, and the white unit tangent vector at

F(t)

ends at

F(t+1)

. This vector represents the bicycle.