But what is a Fourier series? From heat flow to circle drawings | DE4

Fourier series, from the heat equation to sines to cycles.
Home page: https://www.3blue1brown.com
Brought to you by you: http://3b1b.co/de4thanks
12 minutes of pure Fourier series animations: https://youtu.be/-qgreAUpPwM

Thanks to [email protected] for the one-line sketch of Fourier via twitter. As it happens, he also has an educational YouTube channel:

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:


The Coding Train


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"


These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim

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.

Music by Vincent Rubinetti.
Download the music on Bandcamp:

Stream the music on Spotify:

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...
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Mathematics three blue one brown 3 blue 1 brown 3b1b 3brown1blue 3 brown 1 blue three brown one blue fourier fourier series
Music Gaming Sport Popular Apple Watch Interesting places How to What is hot Instagram Facebook Tik Tok Twitter Snapchat