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Euler's formula with introductory group theory

3Blue1Brown · explainer · Watch on YouTube

Recreational & visual mathPure mathematics

What it is

3Blue1Brown builds intuition for Euler's formula, e^(pi i) = -1, using the core ideas of group theory. It treats exponentiation geometrically as rotation and scaling instead of repeated multiplication.

Why Hacker News recommends it

Recommended as a mind-opening, visual explanation of why Euler's formula is true.

  • 3 people recommended it
  • 3 different months
  • 1 strong recommendations
  • first 2017, last 2024

What HN commenters said

  1. “check out the one he did on Euler's formula[1]. Blew my mind.”

    Mind-blowing explanation of Euler's formula

    BucketSort, 2017-04 · Strong recommendation · in “Miniatures: Mathematical and Algorithmic Applications of Linear Algebra [pdf]”

  2. “3blue1brown explains it better than I could”

    Geometric understanding of e to the pi i

    kortex, 2020-12 · Recommendation · in “Alternative notation for exponents, logs and roots? (2011)”

  3. “This is a really nice explanation”

    Nice explanation connecting Euler's formula to group theory

    moefh, 2024-07 · Recommendation · in “What makes e natural? (2004)”

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

Topics: euler's formula, group theory, complex numbers, exponentiation, 3blue1brown

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