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Infinite fractions and the most irrational number

Mathologer · 658.5K views · 2016-07-30 · 13:29

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Overview

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.

On Hacker News

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

Recommended by 3 HN people across 3 months · HN mentions 2019–2026

Topics

Recreational & visual mathPure mathematics
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golden ratioirrational numberscontinued fractionsmathologernumber theory

What people said

uoaei · 2023-08 · Recommendation

Pretty good Mathologer video about continued fractions: [VIDEO] One neat trivium I like to quiz the mathematically-minded on is: what number is the most irrational , i.e., toward which number do rational approximations converge the slowest ? The answer can be determined from continued fractions and is discussed in the video near the end.

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jerf · 2022-10 · Recommendation

"same with golden ratio (repeating 1s)" Mathologer has a good video in which he uses this to justify calling the golden ratio the "most irrational" number because of this expansion: [VIDEO] The video also goes over the details of the pi expansion.

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rrauenza · 2021-10 · Recommendation

I was going to post this Mathologer video ( [VIDEO] ) based on e being "the most irrational number" -- but I misremembered. It's the golden ratio, phi. But its still a really interesting video!

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Sources

Video by Mathologer, played through YouTube.

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