Watch this fantastic "Circle in Circle" optical illusion machine in action


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Sure it’s a circle. r = sin(theta). You’re going to make your machine out of balls, and then complain that it’s made out of balls?


What, you never saw a trammel of Archimedes before?


This really seems like more of a difference of semantics than illusion. If the gear ratios were changed, the balls wouldn’t move in single straight lines, but they still “technically” wouldn’t be moving in a circle since the individual balls aren’t moving in a constant radius about a fixed point.


I agree, what your mind perceives is a ring of balls rolling inside a larger ring. When you remove the faceplate you are shown that the mechanism is indeed a ring (the smaller gear) rolling inside a larger ring.

The trick to have them describe a straight line is nice though.


an inner circle of white balls appears to be rolling inside the outer circle, but that’s actually not the case at all

No, that is exactly the case. If each ball was individually actuated by a mechanism that moved it back and forth in a straight line, and the balls were all timed to create a circular shape rolling inside the outer ring, then it would be a convincing optical illusion. But the model is literally a wheel inside a wheel, with all the balls connected to the same rigid frame. The explainer video does indeed show an optical illusion, because there is no mechanism connecting the dots outside of our brains.


This is yet another example of what is known as a Tusi Couple. It was first discovered in the 13th century by the Persian astronomer and mathematician Nasir_al-Din_al-Tusi (

Here’s a nice visual -


I like the machine, but “exposing” it to work in the way you suspect is ironic and a bit counter productive.


Yeah, this feels disingenuous to say the balls aren’t moving in a circle, they’re just moving in a circle in a special way. I feel that would be akin to saying a geosynchronous satellite isn’t actually orbiting the Earth, when it is, it’s just doing so in a special way.


Good ol’ “507 movements.” I was hoping they’d have an animated version. No luck, but they do have an alternate version. This one uses the straight line motion in place of gears. Imagine watching the first video while the whole mechanism is rotating to keep the small wheel axle stationary.


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