2023-07-02

[public] 265K views, 83.4K likes, dislikes audio only

3Blue1Brown

An apparent pattern that breaks, and the reason behind it.

Summer of math exposition: https://3blue1brown.substack.com/p/some3-begins

Learn more at https://some.3b1b.co/

Help fund future projects: https://www.patreon.com/3blue1brown

An equally valuable form of support is to simply share the videos.

For the long-time viewers among you, if this sounds familiar, it's because it's a remake of one of the earliest videos on the channel. It's such a wonderful problem, and the audio/pacing in earlier videos was really suboptimal, so I wanted to freshen it up a little here.

Timestamps

0:00 - The pattern

2:20 - Counting chords

4:03 - Counting intersection points

6:20 - Euler's characteristic formula

11:30 - Connection with Pascal's triangle

15:10 - Reflections

Correction at 8:56 - The number of the regions should of course be (1, 2, 3, 4, 5), instead of (0,1,2,3,5)

Thanks to these viewers for their contributions to translations

Arabic: mouhsiiin

French: Jonhfing

Hebrew: Omer Tuchfeld

Hungarian: Fabó Bence

Russian: fedor

Spanish: Paweł Cesar Sanjuan Szklarz

Thai: @korakot

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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:

https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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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