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Infinite fractions and the most irrational number

Mathologer · explainer · Watch on YouTube

Recreational & visual mathPure mathematics

What it is

Mathologer uses continued fractions to show why the golden ratio is the most irrational number, comparing it with root 2, e and pi and pointing to where this shows up in nature.

Why Hacker News recommends it

Recommended as a clear, visual explanation of continued fractions and why phi is hardest to approximate by fractions.

  • 3 people recommended it
  • 3 different months
  • 0 strong recommendations
  • first 2019, last 2026

What HN commenters said

  1. “But its still a really interesting video!”

    Interesting Mathologer video on the most irrational number.

    rrauenza, 2021-10 · Recommendation · in “Where transcendental numbers hide in everyday math”

  2. “The video also goes over the details of the pi expansion.”

    Justifies calling phi most irrational via its continued fraction.

    jerf, 2022-10 · Recommendation · in “The Mystery of 355/113 (2010)”

  3. “Pretty good Mathologer video about continued fractions”

    Good explanation of continued fractions and most irrational number.

    uoaei, 2023-08 · Recommendation · in “Decimal to Fraction”

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

Topics: golden ratio, irrational numbers, continued fractions, mathologer, number theory

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