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 ... https://www.youtube.com/watch?v=cy8r7WSuT1I

How to think about this 4d number system in our 3d space. Brought to you by you: http://3b1b.co/quaternion-thanks Interact with these visuals: http://3imaginary1real.com Quanta article on quaternions: https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/ The math of Alice in Wonderland: https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/ ... https://www.youtube.com/watch?v=d4EgbgTm0Bg

Another view on the quadratic formula. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/thanks ------------------ Music by Vincent Rubinetti. 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 If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 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_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown ... https://www.youtube.com/watch?v=MHXO86wKeDY

A visual explanation of what the chain rule and product rule are, and why they are true. Full series: http://3b1b.co/calculus Brought to you by you: http://3b1b.co/eoc4-thanks And by Brilliant: https://brilliant.org/3b1b Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ ... https://www.youtube.com/watch?v=YG15m2VwSjA