Visualizing quaternions (4d numbers) with stereographic projection

How to think about this 4d number system in our 3d space.
Part 2: https://youtu.be/zjMuIxRvygQ
Interactive version of these visuals: https://eater.net/quaternions
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Quanta article on quaternions:
https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/

The math of Alice in Wonderland:
https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/

Timestamps:
0:00 - Intro
4:14 - Linus the linelander
11:03 - Felix the flatlander
17:25 - Mapping 4d to 3d
23:18 - The geometry of quaternion multiplication

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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

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