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Explore This pattern breaks, but for a good reason | Moser's circle problem with 2,877,536 views, 102,739 likes, and 2,506 comments. Experience the impact of this video content that has captured audience attention.

An apparent pattern that breaks, and the reason behind it. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share the videos. This is 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

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