This paradox, usually ascribed to Aristotle but possibly even older, is from an Ancient Greek text, Mechanica, from the 4th century BC.

Aristotle's Wheels
All circles have the same circumference!
Drag the coloured circles and watch the outsides unwind. How can it be that both red lines are the same length?

Use the ratio buttons to change the relative sizes of the circles. The illusion becomes less convincing as the inner circle becomes smaller.

Choose a ratio: Animation:

Click here for an explanation.

It is of course impossible for both wheels to mark out the same length on a single rotation. There are two ways to resolve this paradox:
  1. The inner wheel must slip as it rotates, i.e. it is not a a pure rotation, but is also being dragged along by the rotation of the outer wheel
  2. The inner and outer wheels can be decoupled and thus able to rotate at different speeds. Use the button below to see this happening.


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