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Visualizing the 4d numbers Quaternions

3Blue1Brown · explainer · Watch on YouTube

Recreational & visual mathPure mathematics

What it is

3Blue1Brown builds visual intuition for quaternions, showing how to think about this four-dimensional number system using stereographic projection and rotations in 3D space. It is part one of a two-part series with an interactive companion site.

Why Hacker News recommends it

HN commenters recommend it as the best visual explanation of quaternions and a good way to visualize higher dimensions.

  • 6 people recommended it
  • 6 different months
  • 1 strong recommendations
  • first 2018, last 2023

What HN commenters said

  1. “He does a great job of explaining quaternions though visual intuition.”

    Visual intuition for quaternions

    Twisol, 2018-09 · Strong recommendation · in “Quaternions: the Strange Numbers That Birthed Modern Algebra”

  2. “I suggest this neat video”

    Neat mechanical explanation of how quaternions work

    mlatu, 2020-01 · Recommendation · in “Let's remove quaternions from every 3D engine (2018)”

  3. “a nice exercise to visualize 4D is to study quaternions and their properties.”

    Visualizing 4D via quaternions

    huachimingo, 2021-05 · Recommendation · in “What is the Fourth Dimension? (1884)”

  4. “described and visualized nicely here”

    Nicely visualized quaternion rotations

    nayuki, 2021-08 · Recommendation · in “The Dirac String Trick (2015)”

  5. “3B1B is also informative, especially in explaining why C was not extended using triplets but 4-tuples were needed”

    Explains why 4-tuples were needed rather than triplets

    Jun8, 2021-12 · Recommendation · in “Quaternions”

  6. “I found this video explaining quaternions to actually be a great way to explain (and visualize) higher spatial dimensions”

    Great way to explain and visualize higher spatial dimensions

    nkrisc, 2023-07 · Recommendation · in “It’s hard to give a good intuitive explanation for the volume of a cone”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: quaternions, 4d, 3d rotation, stereographic projection, visualization

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