Golden Ratio using an equilateral triangle inscribed in a circle

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

If you like this sort of thing, there's a game where you can solve these kinds of proofs: https://www.euclidea.xyz/en/game/packs/Alpha

I once wondered what happens when you take x away from x squared, and let that equal 1.

I sat down and worked it out. What do you know golden ratio.

Oh and this other number, -0.618. Anyone know what it's good for?

Recently read through The Power of Limits and deepened my appreciation for the golden ratio. https://www.shambhala.com/the-power-of-limits-1203.html

That is neat, I did not know this method of constructing a gold ratio. Once you have a golden ration it's easy to construct a pentagon (with straight-edge and compass).

I always like the equlateral triangle with the top half removed to for a rombus, the shape is used in the mosaic virus. now I understand my attraction to it, thanks!

not related directly, but there is a ui library that uses golden ratio for spacing. https://www.chainlift.io/liftkit

Thanks! I didn't know this one either.

> Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation

Are we really upvoting this on HN? Truly the end times have come.