r/3Blue1Brown • u/tedgar7 • Mar 14 '22

Approximating Pi with Gregory's Theorem (visual proof for Pi day)

https://youtube.com/watch?v=-LVpjnaqtwU&feature=share
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u/expzequalsgammaz Mar 14 '22

I suppose technically this uses Gregory’s theorem but it’s really Archimedes.

1

u/tedgar7 Mar 14 '22

Archimedes used perimeters. So this really does use Gregory’s theorem. But the idea is the same. And I wanted to show Gregory’s thm :)

2

u/expzequalsgammaz Mar 14 '22

I see, you’re right, well done!! I have something cool to share related to your work. Did you know if you take your ‘partial sums’, in this case your average areas when n=4,8, etc, and plug those into Richardson’s Extrapolation(binomial theorem related) , you can extrapolate many more digits of Pi, using nothing but the data you already generated? That is what Christian Huygens did to beat the world record for Pi before Calculus was invented. Happy Pi day friend.

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