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Comment by AceJohnny2 | Hacker News Reader

Edit: years of searches and minutes after I post this I found https://www.youtube.com/watch?v=CaasbfdJdJg thanks to using "continued fraction" in my search instead of "infinite series" X(

Original: Tangentially, for a few years I've been looking for a Youtube video, I think by Mathologer [1], that explained (geometrically?) how the Golden Ratio was the limit of the continued fraction 1+1/(1+1/(1+1/(...))).

Anyone know what I'm talking about?

I know Mathologer had a conflict with his editor at one point that may have sown chaos on his channel.

[1] https://www.youtube.com/c/Mathologer

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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] https://www.youtube.com/watch?v=sj8Sg8qnjOg

Complete tangent, but, for me, this is where AI shines. I've been able to find things I had been looking for for years. AI is good at understanding something "continued fraction" instead of "infinite series", especially if you provide a bit of context.

Absolutely. In fact my post above originally said "infinite series" instead of "continued fraction", but Googling again, Google AI did mention "continued fraction" in its summary, so I edited my post and tried searching on that which led me to the solution!

100% agree. It’s great if you have a clear sense of what you’re looking for but maybe have muddled the actual terminology. You can find words, concepts, books, movies, etc, that you haven’t remembered the name of for years.

One of the talks I give has this in it. The talk includes Continued Fractions and how they can be used to create approximations. That the way to find 355/113 as an excellent approximation to pi, and other similarly excellent approximations.

I also talk about the Continued Fraction algorithm for factorising integers, which is still one of the fastest methods for numbers in a certain range.

Continued Fractions also give what is, to me, one of the nicest proofs that sqrt(2) is irrational.

Thanks! Do you have a version of that talk published anywhere? I tried searching your YouTube channel [1] for a few things like "golden ratio" "ratio", "irrational"... but didn't find anything.

[1] https://www.youtube.com/@colinwright/

That's not my channel. Alas, my name is fairly common, and there are some proper whackos who publish widely.

I only have one video in my channel ... never really got going, but I keep promising myself I'll start doing more. My channel is here:

https://www.youtube.com/@ColinTheMathmo

I don't have that talk on video, but I can probably sketch the content for you if you're interested, and then give pointers to pages with the details.

How to contact me is in my profile ... I'm happy to write a new thing.

Aw thanks, but I think the Mathologer and Numberphile videos are sufficient for me if you haven't already uploaded yours. I don't want to bother you doing extra work for little return!

I honestly should sketch out the talk anyway. I haven't seen anyone else bring together the proof that sqrt(2) is irrational, and the Continued Fraction method of factoring.

Yeah, maybe I'll hack out a sketch tomorrow, show it to a few people, and get them to tell me what's missing so I can flesh it out.

I owe Chalkdust an article anyway.

Correction! The actual video I was thinking of was this one, also by Mathologer but from 2018:

https://youtu.be/ubHVK71F01M

This one actually has the geometric (rectangle subdivisions) animations I had in mind.

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