Unexpected applications and a beautiful proof.
Looking for a new career? Check out https://3b1b.co/talent
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An equally valuable form of support is to simply share the videos.
Home page: https://www.3blue1brown.com

Credits:
Senia Sheydvasser: Co-writing and sphere deformation animations
Paul Dancstep: Those lovely fluffy sphere animations 
Vince Rubinetti: Music

Timestamps:
0:00 - To comb a hairy ball
1:24 - Applications
8:46 - The puzzle of one null point
12:12 - The proof outline
16:41 - Defining orientation
21:44 - Why inside-out is impossible
25:59 - 3b1b Talent
27:44 - Final food for thought

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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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Website: https://www.3blue1brown.com

The Hairy Ball Theorem