How are the dots moving? @MathVisualProofs

Uploaded March 2025 | Updated September 2026, 2 weeks ago

This short animation shows a variant of a classic "illusion" created by moving points along a hypocycloid in unison. Can you tell if the dots are moving in a circle or not? This is related to the classical Tusi couple named after Nasir al-Din al-Tusi (en.wikipedia.org/wiki/Tusi_couple).

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Here is a longer form video (and a bit slower) of the same animation: youtu.be/VvX9bMUX-ic

If you want to see more hypocycloids, check these:
youtu.be/gTsdoR2rqwk
youtu.be/DC8JlortDqE
youtu.be/5dwlLH0aqxs
youtu.be/1ctRFgWwg5E

#manim #hypocycloid #spirograph #circle #rollingcircles #irrational #Phi #goldenratio #eulersconstant #e #mathvideo #math #mtbos #animation #iteachmath #mathematics

To learn more about animating with manim, check out:
https://manim.community

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