That's Not How the Golden Ratio Works

⬣ LINKS ⬣

⬣ ABOUT ⬣
There’s much to admire about the Golden Ratio, but its significance is largely overblown. In this video, we separate some of the facts from the fiction, while analysing Darren Aronofsky’s “Pi”.

⬣ TIMESTAMPS ⬣
00:00 - Intro
02:57 - What is the Golden Ratio?
04:53 - The Fibonacci Sequence and the Golden Ratio
10:54 - Nature and Diophantine Approximation
15:14 - Hurwitz’s Inequality
21:20 - Numerology and Gematria
26:09 - Is Pi Good?
29:02 - Verdict

⬣ INVESTIGATORS ⬣
Nothing for you here. Sorry!

⬣ SEE ALSO ⬣
Numberphile video featuring Ben Sparks:

Astrology Future Eye

Assassinations Foretold in Moby Dick! by Brendan McKay

⬣ REFERENCES ⬣
G. H. Hardy, E. M. Wright: “An Introduction to the Theory of Numbers” Fourth Edition. Oxford University Press (1960).

⬣ CREDITS ⬣
Music by Danijel Zambo, Tobias Voigt, and Apex Music.

Pi (film) footage (C) Protozoa Pictures, Artisan Entertainment, Summit Entertainment.

Requiem for a Dream footage (C) Thousand Words, Protozoa Pictures, Artisan Entertainment, Summit Entertainment.

IMAGES
Gears
Monty Hall
Golden Spiral
Sacred Creation
Jeeves
8 Mile poster (C) Universal Pictures
Mona Lisa
Parthenon
Archimedean Spiral
Euler Spiral
Spiral: From the Book of Saw (C) Universal Pictures
Logarithmic Spiral
Sunflower
Parthenon with Golden Rectangle
Pinecone
Pineapple
Adolf Hurwitz
Nautilus Shell
Milky Way
Hurricane Katrina

[AnotherRoof]

⬣ *CORRECTIONS, CLARIFICATIONS, AND COMMON COMMENTS* ⬣
1. 2:29 I say this graph looks like the Riemann-Zeta function. It isn't! This is a graph of the Gamma function. This is why I dropped analysis in favour of algebra...
2. 8:37 the table showing bone lengths: the index metacarpal should be 490.7, giving a ratio of 1.721. Still not the golden ratio!
3. 18:29 line four there is a q^2 denominator when it should just be a q. The funny thing about this is that one of my patrons caught the mistake in an early draft -- I fixed the q on the line above but forgot to fix this one! >_<
4. 19:19 I'm using "size" to refer to "absolute value" here, and then I misspeak, saying: "...so this whole thing is an integer which has size less than 1 [...] so it must be 0; that's the only integer less than 1." I meant to say "that's the only integer with *size* less than 1." Clearly, if n is an integer with |n|<1 then n=0, and that's what I meant!
5. I mispronounce "gematria" throughout the video. It is said with a hard g as in "girl" -- my apologies, don't know how this one slipped through!

[jasonmp]

Also, Pi is essentially a student film, the kind of indie film that no longer sees mainstream breakout. It cost $130k to make. They weren’t going around paying mathematics consultants.

[evansherburn]

The golden ratio isn’t a number, it unlocks tusk act 4

[j.xn]

Finally someone said it. I'm an artist and I'm dead tired of seeing people disregard others work for not fitting into some ratio or formula, as if a beautiful composition actually relies on pseudo science and not every other choice in the frame or composition.

[MassiveDestructionSP]

Bah! Next you're gonna tell me that I can't use a horse to channel the Golden Ratio into my nails.

[Kram]

ViHart has also covered how plants are doing golden ratios - as have many before and after her. But her exploration goes one step further: It also shows how they actually are able to do this. Like, how does a plant actually measure the golden angle?
And the answer is that it kinda doesn't. It involves the following of chemical gradients in a way that just so happens to *usually* (but due to inherent randomness actually not quite always!) causes the tightly fitting spiral patterns we see in sunflowers, pine cones, and some (but far from all) plants' leaf growth patterns.

[opensocietyenjoyer]

"golden ratio is when spiral" is what 99% of the public take away from 99% of "golden ratio" videos

[ciaranheikeclark]

I enjoyed the beautiful sunflower joke :)

[erikziak]

0:10 As a mechanical engineer, I feel physical pain when seeing images like that, especially if all the wheels are the same size and the shape of the tooth is what it is. Ouch!

[stjernis]

Blackboard fills itself in and even animates a bit, 3b1b style. Nice touches.

[GeoPuff]

Hey, just wanted to say that your video quality has noticeably improved over time, and this was one of my favorite ones so far! From the sunflower joke, to the misleading the audience to prove your point, I just love all the different ways your videos keep me engaged. This is one of my favorite channels!

[FeeshUnofficial]

The only ones who know how to apply the golden ratio properly are the Zeppeli family and Johnny Joestar

[brandontylerburt]

The woo surrounding the Golden Ratio often seems to act as a thought-stopper for many people—that is, people will memorize the "fact" that it's got something to do with the chambered nautilus and the Fibonacci sequence and beauty ... and then they'll lose any desire to find out what it actually is or anything more about it. And now we're all doomed to hear somebody expounding at length on how the Golden Spiral is just everywhere, man, at least once a year at a party, so transported by an unoriginal idea they don't notice our eyes glazing over as we nod politely and try to summon the desired level of feigned astonishment. Nothing travels at the speed of stupidity, so I don't think this video will be enough to stamp it out. But thank you very much for a well-conceived and nicely presented explanation.

[rtg_onefourtwoeightfiveseven]

19:19 Clarification for the confused (like I was): when Roof says "it's the only integer (with size) less than 1", he means "...with absolute value less than 1", which is relevant because the original quantity was less than 1 when wrapped in an absolute value.

[publiconions]

Love the Numberphile shout-out... Ben is the best and that is one of his best episodes

[pyrotas]

I am a Physicist. And about this dephinite subject there are countless examples of disinformation and bad science communication. This on the other hand is probably the most lucid and most directly explained content out there. This channel is criminally under-rated!

[popcorn]

12:00 the way you casually do by hand what most of us did with Python or Mathematica … is what I’m here for! So refreshing!

[_devotio_]

I can't believe gyro zeppeli lied to me

[aldasundimer]

This is one of my favorite movies and i was also obsessed with it in my early twenties. I even made an electronic song where I used samples from the movie. I think the statements about pi being found everywhere in nature is opposed by the speech of Saul where he states that this is basically numerology. For me the movie is more about the urge of human to understand life in it's whole, to find the ultimate truth and the inability to achieve this through science.

[CiaoRooster]

The Pi expansion is also wrong on the math club banner for Pi Day in Drew Barrymore’s “Never Been Kissed.” I think they strayed after 3.1415 or there about, super early.
Spotted it in theaters. Drove me crazy.