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

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jazzyjackson · 2022-04 · Strong recommendation

a mind-rewiring video by numberphile concerning the golden ratio [0] made sense of all the spiral overlay art: yes, plants use it because it is an optimal solution for minimizing overlap when sprouting leaves during growth, maximizing spatial coverage but also, as a number that is least able to be approximated by rational, erm, ratios - it is a pattern that most closely approximates random patterns. So more than any other spiral, a fibonacci spiral has the highest likelihood of overlapping random points in 2D space... (and fibonacci series converges on the golden ratio because they are equivelent expressions of the continued fraction 1+(1/(1+(1/(1+(1/(1+(1/... [0] [VIDEO]

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jazzyjackson · 2021-11 · Strong recommendation

Golden ratio is not arbitrary, it solves the problem: How to make sure nothing lines up. This link gets passed around a lot and it's very illuminating, demonstrating that the golden ratio is objectively "the most irrational number": [VIDEO]

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glkindlmann · 2026-01 · Recommendation

I learned about this not from Mathologer, but Numberphile [1]. The second half of the video is the continued fraction derivation. I remember this being the first time I appreciated the sense in which the phi was the most irrational number, which otherwise seemed like just a click-bait-y idea. But you've found an earlier (9 years ago vs 7) Mathologer video on the same topic. [1] [VIDEO]

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