2018-04-20

[public] 518K views, 21.4K likes, 207 dislikes audio only

3Blue1Brown

A geometric proof of a famous Wallis product for pi.

Help fund future projects: https://www.patreon.com/3blue1brown

An equally valuable form of support is to simply share some of the videos.

Special thanks to these supporters: http://3b1b.co/wallis-thanks

If you want to dive into the relevant ideas required to make this proof more rigorous, the relevant search term is "dominated convergence".

https://en.wikipedia.org/wiki/Dominated_convergence_theorem

Here's a good blog post on the topic:

https://www.math3ma.com/blog/dominated-convergence-theorem

In the video, I referenced our own blog post expanding on this argument. Unfortunately, it managed to get lost during a website transition.

Another approach to this product by Johan Wästlund:

http://www.math.chalmers.se/~wastlund/monthly.pdf

With more from Donald Knuth building off this idea:

https://apetresc.wordpress.com/2010/12/28/knuths-why-pi-talk-at-stanford-part-1/

Music by Vincent Rubinetti:

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

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