The Golden Ratio (why it is so irrational) - Numberphile

More links & stuff in full description below ↓↓↓

Note on this video: Ben uses "one over a number" quite often during the video to make a fraction of a turn between 0 and 1, but the same effects apply if you turn more than a complete turn (e.g. sqrt(2) = approximately 1.414... of a turn, i.e. 1 whole turn and 0.414... of a further turn).

NUMBERPHILE

Videos by Brady Haran

[soranuareane]

π = 3 + a bit.

Going to use this in all of my code from now on.

[blacxthornE]

This was one of the best Numberphile videos ever.

[DhulstDirk]

This is the absolute best explanation of the Golden Ratio I have ever seen. Thank you!

[ahobimo]

The idea that numbers can be "more" or "less" irrational kind of blew my mind.

[LMacNeill]

That was mind-blowing, watching that animation run. You could see the whole-number fractions passing as the animation proceeded. It's almost like watching some part of the universe that you can't normally see, but which was somehow exposed by this video. A bit unsettling, yet completely fascinating. I can't quite describe it.

[yeet]

This is perhaps in the absolute TOP3 episodes of numberphile... everything is so great, I've watched it at least 4 times now over the past couple of years since I got into the channel. The content is fascinating, I love this dude, the animations and the music is soooo freaking perfect - even the little snaps when it pauses for a sec' ... just a wonderful peice of art created here

[allison]

"I'll be there in a bit" = "I'll be there in a pi minus 3"

[yamomwasthebomb]

I have heard nearly everything in here before, but I've never seen such a succinct, logical explanation for all of it. This was freaking amazing.

[steveger]

"A BIT is not a mathematical recognized terminology" -
CS major: sweats profusely

[huruey]

That "bad flower" with no rotation is just a legume.

[Joel-coxl]

Hadn't heard of the golden ratio being the "most irrational" number before, that's pretty cool.

[gosugosu]

6:10 also, if you count the number of seeds on one of the 3 spirals starting at the center, then the 7th seed will always line up with one of the 22 spokes - and 22/7 is approximately pi, amazing!

[dalitas]

All of differential calculus is based on "and a bit", It is perfectly ok to use, it just sounds better with Δ, δ, ε

[hliask]

Glad to see that the steward of Gondor is alive and well!

[staculette]

"Gondor has no king, Gondor needs no king." *Boromir*
"Rule of Gondor is mine !" *Denethor*
"So passes Denethor, son of Ecthelion..." *Gandalf*
1:59 "So if I jumped, say, to a tenth of a turn, would you care to predict what you would see ?" *Denethor*

[KimAlexisG]

Wow!!! I already thought I knew a lot about the golden ratio, but I've never thought of one irrational number as being "more irrational than another". The way they calculated phi from that infinite fraction is something I've never seen before and it was absolutely awesome!

[hollyhensler]

I have spent years of academia studying the golden ratio and yet this is the best and clearest explanation I have ever seen on its irrationality! Incredible!

[fraiseld]

Instructions Unclear. Accidentally produced an infinite spin.

[meghanstrudwick]

"Flowers can cancel fractions"
- Ben Sparks, 2018

[aysoodaagh]

This was BEAUTIFUL! You made me fall in love with mathematics. I come and see this video every once in a while to keep being motivated to learn.