But what is a Fourier series? From heat flow to drawing with circles | DE4

Fourier series, from the heat equation epicycles.
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12 minutes of pure Fourier series animations: https://youtu.be/-qgreAUpPwM

Some viewers made apps that create circle animations for your own drawing. Check them out!

Make your own Fourier circle drawings
byu/treeforface in3Blue1Brown

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

The Coding Train

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

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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:

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.

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