Fourier series, from the heat equation epicycles. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/de4thanks 12 minutes of pure Fourier series animations: https://www.youtube.com/watch?v=-qgreAUpPwM Some viewers made apps that create circle animations for your own drawing. Check them out! https://www.reddit.com/r/3Blue1Brown/comments/cvpdn7/make_your_own_fourier_circle_drawings/ https://isaacvr.github.io/coding/fourier_transform/ Thanks to Stuart@Biocinematics for the one-line sketch of Fourier via twitter. As it happens, he also has an educational YouTube channel: https://www.youtube.com/channel/UCKOiJd9YCbv7LeL2LFOGiLQ Small correction: at 9:33, all the exponents should have a pi^2 in them. If you're looking for more Fourier Series content online, including code to play with to create this kind of animation yourself, check out these posts: Mathologer https://www.youtube.com/watch?v=qS4H6PEcCCA The Coding Train https://www.youtube.com/watch?v=Mm2eYfj0SgA Jezmoon http://www.jezzamon.com/fourier/index.html For those of you into pure math looking to really dig into the analysis behind this topic, you might want to take a look at Stein Shakarchi's book "Fourier Analysis: An Introduction" Timestamps: 0:00 - Drawing with circles 2:10 - The heat equation 6:25 - Interpreting infinite function sums 9:52 - Trig in the complex plane 14:11 - Summing complex exponentials 22:11 - Example: The step function 23:54 - Conclusion Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ These animations are largely made using a custom open-source 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. 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