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:
1 view
213
150
2 months ago 00:01:40 1
How To Make A CPU
2 months ago 00:05:58 1
Frederic Chopin Fantaisie Impromptu in C sharp minor, Op 66
2 months ago 00:01:52 1
Pattern Practice #1 | ESL | EFL | What do you like to do? | ELF Learning
2 months ago 00:46:11 1
Leather Draco Nightmare Briefcase DIY
2 months ago 00:01:00 1
Handmade blanket
2 months ago 00:19:56 1
Crochet. Ear warmer headband. Single crochet stitch/ Вязание крючком. Повязка. Столбик без накида
2 months ago 00:31:32 1
No one has ever knitted this model this easily before. crochet stitch
2 months ago 00:10:00 1
Bossa Nova (Ride Cymbal) - Drum Groove
2 months ago 06:06:06 1
SACRAL CHAKRA Healing Music | LET GO Negative Emotions | IMPROVE Sexual Health | Chakra Meditation
2 months ago 00:02:33 1
✋ No YouTuber has introduced to you the uses of this hole. Please watch the following sewing tips