Aristotle's Wheel

Strategies and Hints

  1. The problem appears to prove that the two circles have the same circumference. However, this cannot be true because one circle is larger than the other.

  2. No, in 1 second point C would travel a distance less than the length AB.

  3. No, the circumference of the smaller disk must be less than the length AB.

Solution

Although AB equals the circumference of the larger disk, CD is not the circumference of the smaller disk. The confusion stems from the different circumferences of the circles and the distance the points travel as the wheel rolls from left to right.