Visualizing quaternions (4d numbers) with stereographic projection

How to think about this 4d number system in our 3d space.
Brought to you by you: http://3b1b.co/quaternion-thanks
Part 2: https://youtu.be/zjMuIxRvygQ
Interactive version of these visuals: http://3imaginary1real.com

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/

------------------

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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

------------------

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: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown