Thursday Paradox

This ancient paradox, which is brought to us courtesy of Esther Inglis-Arkell at, involves two different-sized wheels, one inside another. The two wheels travel in sync over a certain distance as in this animation below:

The wheel paradox that stumped Aristotle and Galileo

But should the smaller inside wheel rotate over the same distance as the larger external wheel? As Ms Inglis-Arkell states: If you look at the animated gif above, both wheels use their entire circumference to trace the same amount of distance – the red line. Clearly one circumference is smaller than the other. Either that means that the wheels have the same circumference, which they don’t, or that different circumferences “unroll” to the same length, which they can’t.

What is the solution to this puzzle?

About F. E. Guerra-Pujol

When I’m not blogging, I am a business law professor at the University of Central Florida.
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2 Responses to Thursday Paradox

  1. Park Chapman says:

    The outside wheel rotates faster than the inside wheel.

  2. enrique says:

    Good answer, but why would the speed of the rotation have any effect on the distance travelled between two points?

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