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#quaternions#3drotation#stereographicprojection

Visualizing the 4d numbers Quaternions

3Blue1Brown

8.7M subscribers • 42 videos on Hallway

YouTube
  • Recommended by 6 people: 6 on Hacker News.
  • A classic. People kept recommending it from 2018 to 2023.
  • Presented by Grant Sanderson, creator of 3Blue1Brown

Intermediate. Assumes working knowledge.

5.5M views8 years ago6 recommendations

Graphics and audioComputer scienceRenderingMath for programmers

Grant Sanderson builds visual intuition for quaternions using stereographic projection to explain four-dimensional rotations in three-dimensional space.

How to think about this 4d number system in our 3d space. Part 2: youtu.be/zjMuIxRvygQ Interactive version of these visuals: eater.net/quaternions Help fund future projects: patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: 3b1b.co/quaternion-thanks Quanta article on quaternions: quantamagazine.org/the-strange-numbers-that-birthed-modern-a… The math of Alice in Wonderland: newscientist.com/article/mg20427391-600-alices-adventures-in… Timestamps: - Intro - Linus the linelander - Felix the flatlander - Mapping 4d to 3d - The geometry of quaternion multiplication Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 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: 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: 3b1b.co/subscribe Various social media stuffs: Website: 3blue1brown.com Twitter: twitter.com/3blue1brown Reddit: reddit.com/r/3blue1brown Instagram: instagram.com/3blue1brown_animations/ Patreon: patreon.com/3blue1brown Facebook: facebook.com/3blue1brown

Why it's here

6 people recommend this

What people say. Highly recommended as the best visual explanation of quaternions and how they represent 3D rotations.

Twisolon Hacker News • Recommends

On “Quaternions: the Strange Numbers That Birthed Modern Algebra”

I'm happy to see 3Blue1Brown's most recent video 0 get a mention in this article! He does a great job of explaining quaternions though visual intuition. (I do think simply calling Grant a "math animator" is selling him a bit short. He's a true educator in every sense; animation is just one of the (very effective) learning aides he uses.) 0 link to this video
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mlatuon Hacker News • Recommends

On “Let's remove quaternions from every 3D engine (2018)”

> rotors operate fully in 3D By this, the author means: you can visualize a rotor FULLY in 3D, no extra dimension neccessary. I suspect you never have tried to think about how quaternions work mechanically, I suggest this neat video: link to this video
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huachimingoon Hacker News • Recommends

On “What is the Fourth Dimension? (1884)”

I still remember the first time when I saw videos about non-Euclidian Geometry1 and Higher Dimensions2. I was amazed with such concepts, but I still havent read books about them. They are related somehow with topology3 and curvature (and tangentially, to differential equations). 1 link (5 sided square) 2 link (The road to 4D part 1) link (Carl Sagan's explanation) 3 link (Zach Star's intro) Also, a nice exercise to visualize 4D is to study quaternions and their properties. Vectors are somehow a nice simplification of them, see Maxwell laws. 3blue1brown has a video4. 4 link to this video
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nayukion Hacker News • Recommends

On “The Dirac String Trick (2015)”

The first part of the article about describing sphere rotations with a direction and magnitude has some overlap with quaternion rotations, described and visualized nicely here: link ; link to this video The second part of the article about untangling strings after a 720° turn is also covered in: link ; link ; link ; link
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Jun8on Hacker News • Recommends

On “Quaternions”

3B1B is also informative, especially in explaining why C was not extended using triplets but 4-tuples were needed: link to this video . Here’s a Math SE answer on why: link , here’s a more ELI5 discussion: link . I especially like this very intuitive comment in that thread : link Left as an exercise to reader: prove that no such n-tuples exist for n>4.
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nkriscon Hacker News • Recommends

On “It’s hard to give a good intuitive explanation for the volume of a cone”

I found this video explaining quaternions to actually be a great way to explain (and visualize) higher spatial dimensions: link to this video When you think about the nth dimension as a projection of the n+1th dimension, it begins to make a lot more sense. That doesn’t mean you can necessarily visualize the 4th spatial dimension directly, but you can at least visualize how the 3rd dimension can be a projection of the 4th, just like how we can easily see that the 2nd dimension as a projection of the third.
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peter_d_shermanon Hacker News • Mentions

On “Cool Examples of Shadow Art (2016) [video]”

Perhaps this montage offers a clue about the possible existence of Higher Dimensions in Physics... ...And then again, perhaps not! :-) Related: Professor Leonard Susskind - The World As Hologram: link 3Blue1Brown - Visualizing quaternions (4d numbers) with stereographic projection: link to this video AdS/CFT correspondence link Plato's Cave: link
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