24. The wheel and the hub
A wheel rolls along the ground from A to B, making exactly one revolution in the process. Length AB (along the ground) must thus be equal to the circumference of the wheel.
But the wheel’s hub has also made one complete revolution. So length CD must likewise be equal to the circumference of the hub.
Since AB = CD, this proves that both wheel and hub have exactly the same circumference.
This was problem 24 of the ancient Greek work Mechanica, an intriguing discussion of some perplexing mechanical problems, often attributed to Aristotle.