Pi is approximately 355/113 (pi day short)
This short animation shows the beginning of the creation of the hypocycloid where the ratio between the radii of the two circles is Pi. Because Pi is irrational, the hypocycloid 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 hypocycloid (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 slower version of this video (with not quite 113 revolutions), see • Pi Hypocycloid
If you want to see more hypocycloids, check these:
• Drawing Hypocycloids (synthwave enume...
• Nested Powers of 2 Hypocycloids (synt...
#manim #hypocycloid #spirograph #circle #rollingcircles #irrational #Pi #mathvideo #math #mtbos #animation #iteachmath #mathematics #piday
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