# The absurd circle division pattern (updated) | Moser’s circle problem

From 3Blue1Brown.

An apparent pattern that breaks, and the reason behind it.
Summer of math exposition: https://3blue1brown.substack.com/p/some3-begins
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
15:55 – SoME3

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)

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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/

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