The unreasonable effectiveness of complex numbers in discrete math

The unreasonable effectiveness of complex numbers in discrete math

A beautiful and out-of-left-field solution to a difficult counting problem
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share the videos.

Artwork by Kurt Burns
Music by Vince Rubinetti

102 Combinatorial problems, by Titu Andreescu and Zuming Feng
https://amzn.to/3wAPoNq

Generatingfunctionology by Herbert Wilf
https://amzn.to/3sPJ8Al

Visualizing the Riemann zeta function

Fourier series

Timestamps
0:00 – Puzzle statement and motivation
4:31 – Simpler example
6:51 – The generating function
11:52 – Evaluation tricks
17:24 – Roots of unity
26:31 – Recap and final trick
30:13 – Takeaways

——————

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:

——————

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

webmaster

Related post