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
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: 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
------------------
These animations are largely made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
https://github.com/3b1b/videos/
Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
------------------
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: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown