The most underappreciated formula | Exploring high-dimensional spheres

  Open with LBRY

On the volumes of higher-dimensional spheres
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Home page: https://www.3blue1brown.com

Thanks to UC Santa Cruz for letting me film there, and special thanks to
Pedro Morales-Almazan for arranging everything.

My video on Numberphile with a fun application of this problem: https://youtu.be/6_yU9eJ0NxA

Timestamps:
0:00 - Introduction
1:01 - Random puzzle
6:16 - Outside the box
14:35 - Setting up the volume grid
21:14 - Why 4πr^2
25:21 - Archimedes in higher dimensions
36:17 - The general formula
40:40 - 1/2 factorial
44:58 - Why 5D spheres are the biggest
50:16 - Concentration at the surface
54:27 - A unit-free interpretation
57:50 - 3b1b Talent
59:13 - Explaining the intro animation

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These animations are largely made using a custom Python library, manim. See the FAQ comments here:
https://3b1b.co/faq#manim

Music by Vincent Rubinetti.
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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https://www.youtube.com/watch?v=fsLh-NYhOoU