Comment by AceJohnny2
8 hours ago
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.
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.
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.
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.