Infinite fractions and the most irrational number

Why HN readers recommended it

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

This is a summary from the source dataset, not an endorsement by Hacker News or the video creator.

Video & recommendation details

Creator / channel

Mathologer

Topic

continued fractions

Format

explainer

Level

intro

HN recommenders in dataset

3

HN mentions in dataset

5

Recommendation years in dataset

2019–2026

These counts and years describe the included Hacker News records; they are not YouTube views or the video’s publication date.

From the original HN conversations

Excerpts from the recorded comments. Follow each source for the full comment and surrounding discussion.

• 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!

• "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.

• 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 …