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The Golden Ratio (why it is so irrational) - Numberphile

Numberphile · explainer · Watch on YouTube

Recreational & visual mathPure mathematics

What it is

Numberphile's Ben Sparks shows why the golden ratio is the most irrational number, using seeds, continued fractions and rational approximations. He also explains why plants use it for spacing leaves and seeds.

Why Hacker News recommends it

HN calls it illuminating for explaining why phi is the most irrational number, relevant to hashing, spirals and phyllotaxis.

  • 3 people recommended it
  • 4 different months
  • 2 strong recommendations
  • first 2018, last 2026

What HN commenters said

  1. “This link gets passed around a lot and it's very illuminating”

    Illuminating demonstration that phi is the most irrational number.

    jazzyjackson, 2021-11 · Strong recommendation · in “The Golden Ratio and User-Interface Design”

  2. “but it's a cool video! :)”

    Clear explanation of phi as the most irrational number.

    ttctciyf, 2018-06 · Recommendation · in “Fibonacci Hashing: The Optimization That the World Forgot”

  3. “I remember this being the first time I appreciated the sense in which the phi was the most irrational number”

    Continued fraction derivation showing phi is most irrational.

    glkindlmann, 2026-01 · Recommendation · in “Golden Ratio using an equilateral triangle inscribed in a circle”

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

Topics: golden ratio, continued fractions, phyllotaxis, irrational numbers, fibonacci

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