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e^(iπ) in 3.14 minutes, using dynamics | DE5

3Blue1Brown · explainer · Watch on YouTube

Recreational & visual mathPure mathematics

What it is

A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.

Why Hacker News recommends it

HN commenters point to it as a quick, visual way to understand Euler's identity.

  • 4 people recommended it
  • 4 different months
  • 1 strong recommendations
  • first 2020, last 2021

What HN commenters said

  1. “3Blue1Brown: Amazing math visualizations”

    Great first 3Blue1Brown video on how e^pi*i works.

    davidwf, 2021-01 · Strong recommendation · in “Ask HN: What YouTube channels do you subscribe to?”

  2. “is a nice compliment to this post.”

    Short visual explanation of Euler's identity.

    dgritsko, 2020-05 · Recommendation · in “Why is e^(pi I) = -1?”

  3. “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)”

  4. “This video [1] kinda helps, although it glosses over the critical fact”

    Builds intuition for Euler's identity, though glosses over rotation by i.

    adrusi, 2021-06 · Recommendation · in “Show HN: Kalk, A calculator with math syntax, complex numbers”

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, complex numbers, calculus, math visualization, 3blue1brown

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