ePIc ePIcycloid PI approximation visual @MathVisualProofs

Uploaded March 2025 | Updated September 2026, 2 weeks ago

This short animation shows the beginning of the creation of the epicycloid where the ratio between the radii of the two circles is Pi. To begin with, we show how close the 22/7 approximation is - the epicycloid almost closes up. However, because Pi is irrational, the epicycloid will never close, so we end after 113 revolutions. As a byproduct, it appears that the curve almost closes up, and there are total of 355 intersection points between the circle and the epicycloid (spikes). This means this visual shows that Pi is roughly 355/113, which is one of the best simple approximations of the circle constant.

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To see a hypocycloid version of this, check out:
youtube.com/shorts/qWuLcrzwV8I
or
youtu.be/5dwlLH0aqxs

If you want to see more epicycloids, check this video:
youtu.be/BwzZCU1DQak

#manim #epicycloid #spirograph #circle #rollingcircles #irrational #Pi #mathvideo #math #mtbos #animation #iteachmath #mathematics #piday

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

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