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A Swift Introduction to Geometric Algebra

sudgylacmoe · explainer · Watch on YouTube

Pure mathematicsRecreational & visual math

What it is

An animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.

Why Hacker News recommends it

HN calls it the best video on geometric algebra, one that makes the subject click in about 40 minutes.

  • 7 people recommended it
  • 7 different months
  • 4 strong recommendations
  • first 2020, last 2024

What HN commenters said

  1. “I highly recommend the video”

    Made geometric algebra click in about 40 minutes

    canjobear, 2020-11 · Strong recommendation · in “Geometric Algebra (2012)”

  2. “has the best video by far on Geometric Algebra (imho)”

    Considered the best video on geometric algebra

    strainer, 2021-10 · Strong recommendation · in “A few of the best math explainers from this summer [video]”

  3. “If you want an inspiring (imho) overview of the power of geometric algebra, I thoroughly enjoyed the video”

    Inspiring overview of the power of geometric algebra

    kilovoltaire, 2022-04 · Strong recommendation · in “Exponentially Better Rotations”

  4. “Here are 2 45mn videos you'll not regret”

    Shows quaternions as simple multivectors in geometric algebra

    BenoitP, 2024-07 · Strong recommendation · in “Quaternions in Signal and Image Processing”

  5. “Some of the perceived complexity of complex numbers and quaternions seems to stem from not knowing the bigger picture.”

    Gives the bigger picture behind quaternions and complex numbers

    skaskaska, 2023-10 · Recommendation · in “Exploring Quaternions (2018)”

  6. “Primer on the topic”

    Primer on geometric algebra with eye-opening physics connections

    user070223, 2024-08 · Recommendation · in “Poor Foundations in Geometric Algebra”

  7. “You're in for a nice trip, the concept is called Geometric Algebra”

    Introduces geometric algebra, which generalizes cross products

    mtizim, 2024-12 · Recommendation · in “A visual proof that a^2 – b^2 = (a + b)(a – b)”

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

Topics: geometric algebra, multivectors, quaternions, rotations, math visualization

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