Why π is in the normal distribution (beyond integral tricks)

Where’s the circle? And how does it relate to where e^(-x^2) comes from? Help fund future projects: Special thanks to these supporters: #thanks An equally valuable form of support is to simply share the videos. The artwork in this video is by Kurt Bruns, aided by Midjourney Here are several other good posts about the classic Poisson proof vcubingx: BriTheMathGuy: Dr. Alter’s math library: And if you’d like to see many other variations on approaching this integral, take a look at this expository paper from Keith Conrad: Correction: 13:46 - The denominator should read 2πσ^2 Timestamps: 0:00 - The statistician’s friend 3:44 - The classic proof 12:47 - The Herschel-Maxwell derivation 21:55 - Reflecting back on the proof 23:50 - A bonus problem Thanks to these viewers for their contributions to translations French: Jeremy Senn, Laurent Joubert German: dreivmeister, lprecord, mathiashaebich Hebrew: David Bar-On, Omer Tuchfeld Hindi: prateekbansal97 Spanish: Joel Tovar Turkish: kilobravo3 ------------------ These animations are largely made using a custom python library, manim. See the FAQ comments here: #manim You can find code for specific videos and projects here: Music by Vincent Rubinetti. Download the music on Bandcamp: Stream the music on Spotify: ------------------ 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: Various social media stuffs: Website: Twitter: Reddit: Instagram: Patreon: Facebook: