Visualizing quaternions (4d numbers) with stereographic projection

How to think about this 4d number system in our 3d space. Part 2: Interactive version of these visuals: Help fund future projects: An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: Quanta article on quaternions: The math of Alice in Wonderland: 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 ------------------ 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: ------------------ 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: Various social media stuffs: Website: Twitter: Reddit: Instagram: Patreon: Facebook: