This pattern breaks but for a good reason Mosers circle problem

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=YtkIWDE36qU

An apparent pattern that breaks, and the reason behind it. • Summer of math exposition: https://3blue1brown.substack.com/p/so... • Learn more at https://some.3b1b.co/ • Help fund future projects: / 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/a... • Stream the music on Spotify: • https://open.spotify.com/album/1dVyjw... • ------------------ • 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: / 3blue1brown • Reddit: / 3blue1brown • Instagram: / 3blue1brown • Patreon: / 3blue1brown • Facebook: / 3blue1brown

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