This pattern breaks, but for a good reason | Moser’s circle problem

An apparent pattern that breaks, and the reason behind it. Summer of math exposition: Learn more at Help fund future projects: 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: #manim You can find code for specific videos and projects here: Music by Vincent Rubinetti. Download the music on Bandcamp: Stream the music on Spotify: ------------------ 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: Various social media stuffs: Website: Twitter: Reddit: Instagram: Patreon: Facebook: