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
------------------
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
------------------
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