Infinite fractions and the most irrational number

Pretty good Mathologer video about continued fractions: ▶ this 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.

"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: ▶ this video The video also goes over the details of the pi expansion.

I was going to post this Mathologer video ( ▶ this 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!

Edit: years of searches and minutes after I post this I found ▶ this video 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] link

The golden ratio is the most irrational number: ▶ this video This is why it creates some distinctive patterns when applied to circular/spiral shapes.