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

From the creator

Where's the circle? And how does it relate to where e^(-x^2) comes from?Help fund future projects: https://www.patreon.com/3blue1brown Special thanks to these supporters: https://www.3blue1brown.com/lessons/gaussian-integral#thanks An equally valuable form of support is to simply share the videos. The artwork in this video is by Kurt Bruns, who used Midjourney as part of the process for some pieces. I wrote more about the specifics of that process and my thoughts around it here: https://www.patreon.com/posts/thoughts-on-ai-83881719 Here are several other good posts about the classic Poisson proof vcubingx: https://www.youtube.com/watch?v=9CgOthUUdw4 BriTheMathGuy: https://www.youtube.com/watch?v=S79KPrIm_Gc Dr. Alter's math library: https://idan-alter.github.io/2023/02/20/Gaussian-Integral.html And if you'd like to see many other variations on approaching this integral, take a look at this expository paper from Keith Conrad: https://kconrad.math.uconn.edu/blurbs/analysis/gaussianintegral.pdf 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 -------------

Published 2023-04-02 · Watch on YouTube ↗
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