17,443 views since Nov 26, 2023

Fourier series, from the heat equation epicycles.
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12 minutes of pure Fourier series animations:    • Pure Fourier series animation montage  

Some viewers made apps that create circle animations for your own drawing. Check them out!
  / make_your_own_fourier_circle_drawings  
https://isaacvr.github.io/coding/four...

Thanks to Stuart@Biocinematics for the one-line sketch of Fourier via twitter. As it happens, he also has an educational YouTube channel:
   / @biocinematics  

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
   • Epicycles, complex Fourier series and...  

The Coding Train
   • Coding Challenge 125: Fourier Series  

Jezmoon
http://www.jezzamon.com/fourier/index...

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


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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/a...

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...

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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