Everybody knows that the two circles are of different size. We might even remember the right words to say that they have different circumferences. Heck we might even remember the fact that the circumference is proportional to the radius.

The outside circle is bigger than the inside circle.

But in the video, they both look exactly the same.

What is going on?

The answer, I’m sure you know, is mathematical. Things are not what they seem.

Imagine that you were a student, and your teacher showed you this video. What would your reaction be?

If you were engaged in your work, or if you were engaged in physical work (maybe you’re a bicycle enthusiast), you’d be pretty amazed, I think. Because if this were true, wheels couldn’t work. Of course, if you were not interested in the material, but cared about your grade, you might ask, “Is this on the test?” Or maybe you’d not care at all, and turtle up for a bit. (Yes, I’ll return to the question of engagement at a later date.)

It seems to me that the worst thing a teacher could do now is to reveal the “solution” to the conundrum. To answer the question now would be to kill it. The answer is important, but it’s not important right away. What is necessary is to feel the question. What does the video purport to show? Could I replicate it somehow? Why does this crash my common sense to the ground?

So I won’t answer it today. Maybe tomorrow. Maybe the day after…

Even though I think I know what’s going on here, it is still very puzzling to me! I think I would have to see a physical model in front of me to truly grasp it.

The interesting thing is, as you discovered over at the other forum we both frequent, is that it takes a certain amount of mathematical sophistication to even understand that there is a seeming paradox involved here.

Even though I think I know what’s going on here, it is still very puzzling to me! I think I would have to see a physical model in front of me to truly grasp it.

The interesting thing is, as you discovered over at the other forum we both frequent, is that it takes a certain amount of mathematical sophistication to even understand that there is a seeming paradox involved here.

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