The most underappreciated formula | Exploring high-dimensional spheres
On the volumes of higher-dimensional spheresExplore the 3b1b virtual career fair: See https://3b1b.co/talent
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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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3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.
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