A visual trick to compute the sum of two normally-distributed variables. 3b1b mailing list: https://3blue1brown.substack.com/ Help fund future projects: https://www.patreon.com/3blue1brown For the technically curious who want to go deeper, here's a proof of the central limit theorem using Moment generating functions: https://www.cs.toronto.edu/~yuvalf/CLT.pdf And here's a nice discussion of methods using entropy: https://mathoverflow.net/questions/182752/central-limit-theorem-via-maximal-entropy Relevant previous videos Central limit theorem https://youtu.be/zeJD6dqJ5lo Why π is there, and the Herschel-Maxwell derivation https://youtu.be/cy8r7WSuT1I Convolutions and adding random variables https://youtu.be/IaSGqQa5O-M Time stamps 0:00 - Recap on where we are 2:10 - What direct calculation would look like 3:38 - The visual trick 8:27 - How this fits into the Central Limit Theorem 12:30 - Mailing list ------------------ 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=d_qvLDhkg00

Euler's formula intuition from relating velocities to positions. Home page: https://www.3blue1brown.com Yeah yeah, the runtime is 4:08, but it's 3.14 minutes to the conclusion. Not familiar with the calculus referenced in this video? Try taking a look at this one: https://youtu.be/m2MIpDrF7Es Another perspective on this formula, from Mathologer: https://youtu.be/-dhHrg-KbJ0 ... https://www.youtube.com/watch?v=v0YEaeIClKY

Video with the solution: https://youtu.be/as7Gkm7Y7h4 3b1b on a meta-puzzle: https://youtu.be/wTJI_WuZSwE This comes from a collaboration I did with Stand-up Maths, where on his channel we covered the solution, and here on 3blue1brown we analyze a meta-puzzle. Editing from long-form to short by Dawid Kołodziej This comes from a collaboration I did with Stand-up Maths, where on his channel we covered the solution, and here on 3blue1brown we analyze a meta-puzzle. Editing from long-form to short by Dawid Kołodziej ... https://www.youtube.com/watch?v=NQFIU5Exjuo

Experiments with toy SIR models Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/sir-thanks Simulations by Harry Stevens at the Washington Post: https://www.washingtonpost.com/graphics/2020/world/corona-simulator/ Simulations by Kevin Simler at Melting Asphalt: https://meltingasphalt.com/interactive/outbreak/ Excellent visualization of each country's current growth from Minutephysics and Aatish Bhatia: https://www.youtube.com/watch?v=54XLXg4fYsc If you want to hear a mathematician/epidemiologist's summary of COVID-19, I found this MSRI talk very worthwhile: https://youtu.be/MZ957qhzcjI Marcel Salathé on Contact Tracing: https://twitter.com/marcelsalathe/status/1242430736944201730 ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim The source code for this video is visible here: https://github.com/3b1b/manim/blob/shaders/from_3b1b/active/sir.py If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Opening music: Candlepower by Chris Zabriskie is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/) Source: http://chriszabriskie.com/divider/ Artist: http://chriszabriskie.com/ Other 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=gxAaO2rsdIs