Why pi? - The Wallis product for pi, proved geometrically

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 ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown