Tag Archives: Aristotle’s Wheel Paradox

Aristotle’s Wheel Paradox

Aristotle's Wheel Paradox

Aristotle’s Wheel Paradox A fascinating math paradox.  How can 2 wheels of different diameter both turning one complete revolution travel exactly the same distance??  This puzzle is nicely demonstrated using this wood model.  The Objective is to explain the Paradox. Not everyone agrees that Aristotle invented this little paradox, but everyone agrees that it would be just like him to come up with something like this. The paradox involves two different-sized wheels, one inside another. The two rotate in sync and you can see as you turn the wheels to travel the length of the opening in the puzzle that the etched line on the wheels turns one time, thus the circumference of each wheel has rotated over an equal length.Both wheels use exactly one circumference to trace the same amount of distance – the length of the space in the puzzle. But, 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.That can’t possibly be right…. The smaller radius can’t possibly be equal to the larger one, so what’s going on?To further illustrate the paradox, there is a separate copy of the inner wheel.   We know that when attached to the bigger wheel that it turns one rotation to cover the length of the opening starting at the hash mark.  But now take the small wheel and position it at the same starting point and rotate one revolution…. it does not travel the same distance!   Such a dilemma….  Can you explain it??   Great fun for thinkers!

Are you a person who loves a good mystery? Me too, I also love jigsaw puzzles and you should know the two are now combined to make a mystery lovers life more challenging. These unique puzzles aptly name mystery jigsaw puzzles use the book to spin the tale but to get to the bottom of who dun it the answer lies within the puzzle itself, you cannot solve the mystery without it. There is just one more bit of sleuthing to do the puzzle doesn’t match the jigsaw picture on the box!

Buy Now