The Golden Ratio: Is It Myth or Math?
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The golden ratio. Some say it’s the most mythical number in the universe. Others say it underlies everything from nature’s patterns to beauty in art and design. But, like, what is it? And does the myth of the golden ratio hold up to its mathematical reality? Let’s find out
References: sites.google.com/view/golden-...
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Just trying to think rationally about irrational things… Leave a comment and let me know what you thought of the video! I'm on Instagram @DrJoeHanson & @okaytobesmart
Awesome video👍I learned about this at school and I actually listened 😱
Good marketing strategy by attracting the annoying jojo gaefans here... Garbage anime toxic fanbase but good marketing ... If it was intentional that is... If it wasn't then yeah excuse the jojo fans they don't represent the anime community.
Thank you for this ep
at 8:34 3/1 = 1?
Please pronounce the Ts in the word pattern, there are no Ds in it.
How to make Fibonacci soup? You need : 1. Yesterdays soup 2. Day before yesterdays soup
And then to make Fibonacci soup for tomorrow you have to take today's soup and yesterday's soup. But wait... how can you use yesterday's soup if you already used it for today's soup?
This is so funny why is no one liking this
@@MariOmor1true lol
@@MariOmor1 make a new soup and mix it with that soup?
@@MariOmor1 you dont wanna know
Funny Valentine has been real quiet since this has dropped
"I'll do anything for my country"
@@Agilku117 "DIRTY DEEDS DONE DIRT CHEAP!"
@@ousamadearu5960 Filthy Acts Done at An Unreasonable Price
@@yunarukami14 dimes for crimes.
@@Agilku117 My heart and actions are utterly unclouded! They are all those of "justice"!
What’s neat about plants growing with the golden angle between their leaves or other parts is that they don’t have to be at the golden angle at the start. Leaves can adjust over time to maximize sunlight, settling into the golden ratio rather than forming it automatically.
yes@@TheUnitAce
which is why it should have been mentioned that at least one of the most blatnatly obvious mechanisms for this is phototropism instead of some magnetism mechanism that was mentioned.
They follow a natural mathematical sequence that gets marginally closer and closer to the golden ratio over time. The sequence can become infinity close to the golden ratio, but it will never BE the golden ratio.
Mixing logic with relativism. Nice.
The paper leaf part was so amazing. Genuinely creative way of explaining science
never expected the video to take that turn
Gyro and Johnny taking notes, then airdropping em to Gappy as we speak
True
Do gappy get spin tho
@@britinc1984 yes it turns out that snw bubbles are spinning
@@semag2090 mp1pp0
Glad to know I wasn't the only one thinking about this
Him: Golden Ratio My brain: You mean Golden Spin?
That's what it's all about
That's what it's all about
Johnny! This is how you spin spin okay?
Ein deutscher jojo fan???
Jojo fans are now everywhere lmao
In Stell Ball Run(jojo part 7) they achieve the perfect rotation, by spinning steel balls(as well as nails) in the golden ratio, which when done perfectly will never stop spinning. Probably not possible irl, but still felt the need to share since i couldnt find any jojo refrences.
Thanks for the explanation, I was wondering why everyone was bringing up JJBA.. though, the more I learn about it the more I feel like that show just does everything and anything lol
@@yeetbigly5827 EVERYTHING happens in jojo
Thanks for explaining this in depth! One of my past art teachers seemed to obsess over the golden ratio, telling us to look for it in art, and most of the time when they pointed it out in works, I just couldn't see it or things didn't seem to line up perfectly, like the shell you mentioned. I've been wondering about it ever since, and finally, I have clarity!
I felt the same way. I was looking at and was so confused what I was missing, it felt like the curve and squares were just drawn onto random parts of buildings and art, guess I was right
It honestly feels likr they just nitpick spots that fit their argument. Sometimes they just out it into a spot with open air nothing to back it up.
Golden Ratio for art is BS. The actual necessary aspect is the concept of leading the eye around the canvas to retain attention and not lead the eye off the canvas elsewhere (unless that is the entire point of the work, which is another story). A lot of composition 'advice' regarding ratios and placement of content on a page is an attempt to "dumb down" or "simplify" everything into easily repeatable formulas, sort of like templates. Good for mass-produced and soul-less works, but not where/what you want to start off with if you are actually working with proper ideas/concepts that you want to convey
@@gaerekxenoscause plants actually use the golden ratio for maximum energy efficiency, do you think we might also should follow a ratio? Or are you saying that if we try to follow that ratio, we’ll never come close, so be natural in things?
I had a similar experience. Some people--educated people--just try to shoehorn this Fibonacci business into everything, like every significant ancient structure ever built.
What if you wanted to learn about the golden ratio, but then gyro said: _lesson 5_
Why did you have to remind me of lesson 5, I gonna cry
Arigato Gyro
@@Handleisn_tAvailable ?
CHUMIMIIIIIN!
Tusk act 4!
damn. jojo got so popular that humans made the golden ratio in real life
Luv u ani lr gito
As a human i can comfirm this
As a confirm i can human this
a confirm as this can I human.
as a jojo fan on part 7 i can confirm this
Love how you integrate comedy to get your lessons easier to digest... wasn't really sure what the Golden Number was all about, now it' s clear!
using this for my project on golden ratios phi number 1:48 irrational numbers 2:06 euclid's findings 2:54 golden triangle 4:12 golden spiral 5:03 fibonacci 6:28
"Gyro, does this man know that technique?" "I don't know Johnny. I don't know."
There it is!
I was hoping for a JoJo reference
@@jullehemmi9812 I refuse
I saw the title of this video. Clicked on it just to find a Jojo comment. I'm not disappointed.
* Infinitely rotates refresh button so you cant watch *
The fact that his name is Joe just makes this even more Canon to JJBA
I knew I'd find a jojo ref here
So I wasn't the only one who started watching this for jjba
Joe joe bizarre adventure
@@Amuneh yes
it took me less than 2 seconds to find a jojo reference
All I can hear is Gyro Zeppeli singing PIZZA MOTZARELLA
Irrational numbers and ancient greeks bothered me until I realized what you mentioned in passing early in your video- "ratio" which requires two components. So it's not about the dividing of one into the other for a quotient but it is to consider the relationship itself which creates the geometric result. Geometry literally means "earth meausre'. It was decades ago now that I began to conceive of Phi as a geometric function and what fun I've had. The ancient architectures become clearer when you look through that lens. Great video and thank you for pushing through the myth a bit.
This is spinning my head because it's too bizzare
I see what you did there
IS THAT A JOJO REFERENCE
Finally, a good f**ing comment
lmao those references
OK but I DO want to watch that golden ratio documentary that was mentioned in the pre roll ad. The host looked a lot like Joe, weird.
Hey doc please reply!
**chews carrot** 🥕 ehhh......what's up doc?
The force uses the golden ratio.
Especially if it uses that intro 😂
You are like the elon musk of youtubers
A 5 to 6 proportion has an aesthetic quality for oil paintings I have preferred over the GR. Though for a long sided rectangle the GR is pristine. The GR enables much and is wondrous for designing a house, as it just makes everything seem to work quite easily. The GR really is an amazing phenomenon.
One number to rule them all!
I did pick the golden rectangle in the beginning, but only because I knew the "right" answer would be credit card shaped, so I looked for the most credit card looking rectangle... it didnt "feel" more special than the others. Everyone knows that the perfect rectangle shape is the one used for the A-series of paper sizes anyway, ie any rectangle with a ratio of 1:root 2
“This is the Golden Spiral” The comment section: *SPEEEEEEEN*
Nyo-ho!
CHUMIMINN!!!
Lesson 5
Doj~~~~~~~~yannnn
ORA ORA!!!
I just found the word golden ratio in my maths textbook and I googled it and saw this vid so I clicked on it and now I feel like I'm in a cult or something.
We aren't a cult, we are a "family."
@@abeestosruinsageneration3725 lol vin diesel memes?
family is more inportant than family
@@TheWanderstar I'm an uncultured swine and I don't know what you are talking about. Now go ahead and find the golden ratio in a cup of tea, please.
Math. Not even once.
I love the fact that Derek paid tribute to Bolyai by mentionning him, even though he wasn't recognized as the cornerstone of the non-Euclidian geometry. We should appreciate people for who they are and thank them for doing their best.
φ + didn't ask + golden ratio
When steel ball run finally got dropped, prepare yourselves to see golden ratio everywhere.
And yes that's gonna be a Ten years to wait for
Yea 8-10 years later
@@naipsiefilderussatser4067 nah Id say 5 years at most since stone ocean is gonna release soon
@@joyconbulb3743 I mean horses are a pain to animate
@@funkydong5315 True but they could easily get some people who animated like attack on titan on board since they would be use to it. It would still take long but not no 10 years like some people are saying.
Can we have more of Joe doing parodies of History Channel
Sure! Sometimes it just has to be done
🖐️🤨🖐️ A L I E N S
Finally a comment not made by a mainstream sheep.
That would be awesome.
Basically thing that some ppl think proves god actually is yet another evidence for evolution. Time always wins.
I use PHI in my art cause it makes things just look nice. I just like rules based starting points for creative endeavours and PHi is one of my go to rules.
Subject I've been curious about for a while now. Thanks for making it easy to learn
Thanks I needed to learn this, I'm in a horse race and a friend showed me the power this holds and I'm kinds struggling to get the hang of it
Don't worry, you would master it soon enough when you meet the president
I somehow misread that as "I'm a horse" and imagined you as the horse in the race... Idk, I guess I blame the creepy pineapple thing at the end of the video for kinda making my imagination run wild :P lol And also, good luck ! :)
@@joeykitty8678 🤣🤣🤣
There is nothing about this to "get the hang of". It is horse hockey. Bet your friend has lost shitloads of money at horse race betting
For the unbased, jojo
Listen Joe, here goes our 5th and last lesson: The shortest route was a detour. It was the detour that was our shortest path!
Arigatou, Luiz
Chumimin!
ORAORAORAORAORAORAORAORAORAORAORA
@@urangames457 okay this is getting cringe
@@SidewaysTrueno tell that to Tusk whose line i quoted
Saying its the elon musk of numbers is a statement that did not age well
I don't think that I could have learned this any way else besides the way this video did, it was brilliant, super fun and as a plus I got a little smarter
This video is gonna blow up after Jojo part 7 is animated
facts. that's why I'm here loll
Yep
Can you elaborate?
lol
joj
I can’t believe that opening sequence lasted 30 seconds haha. Joe is surprisingly funny
I found Uncle Carl to be funnier
Lol yeah, he had so much fun filming it, he had to show it again at the end! 😂
It could have been an intro of History Channel's Ancient Aliens 🤣 Mystery, Conspiracy, lunacy 🤣
Actually 32 seconds, which is almost 34. Aha! a Fibonacci number! Could that be coincidence??
The ONLY WAY too save lives is to STOP doing {WAR IS MURDER} so Corporations can put a "McDonalds" or Star Bucks or whatever.... For if you allow {G4S] and their U.N. Troops of the USA Common Wealth “BLUE EYES” FLAGS too REPLACE all (World Military) as is the case right now, then these HUNGER GAME of [WAR GAMES] Qballs~ /_\ will never end......., and FREE MASON Lodge Members will keep (murdering) +=+ our nonmason Parents, and our nonmason “Children” in their MADE FOR TV WARS as Entertainment: on this side of FLAT EARTH... ugetube.com/watch/a-i-is-making-it-easier-to-kill-you-here-s-how-nyt_TLsMEGwojEBZ8pN.html The Rag Tag Rebellion "of and for" OUR WORLD REPUBLIC CONSTITUTION Coalition... The Society of nonmason~ #TheCrewRRR [///|||\\\] johnnyexodices.wordpress.com 🎱 Send Crpyto to: @Exodice on #Coinbase, so I can get a Global Citizens PASS PORT to say What Up!!! too all these INTERNATIONALIST!!!
Fantastic, open mided and realistic account of the hype of Golden Ratio. Well done.
I wonder why gravity causes the spiral of galaxys to be the same as these plants
This was a really great video! I'm so glad I stayed until the end!
Him : Did you pick this one? Me : No I didn't- Him : *Because this is the most aestheticly pleasing rectangle* Me : oh ok sorry 👀
i picked the one directly left to the phi one haha
Correct
Same lol
"The world is a messy place" - Looking around my home: wow, how did he know
👁️👄👁️
how did he know? Phi !!
@@deheerschappij Oh no, I thought I had a chance to better myself. Damn universe
Golden ratio baby!
thats why we have cancer , so we thank God for our not-messy bodies ,, if there was no cancer in people we would think our bodies are messy . this youtuber is clearly using science to tell us things are messy so we dont study it , but when we know that things are well designed we will try to discover more ,, and everything scientist came to discover have seen the beauty of its design , and that if it moves a little bet from what its designed it get destructed.
Stephen Wolfram of Mathematica has discussed this quite a bit: how the universe can start from such simple computation. I think what's really appealing here is that this is an interesting, seeming complicated number, and natural phenomenon that comes from very simple rules.
I love your channel, often learn a lot. Wonderful film. Thank you!
I thought I would only watch it’s okay to be smart in school but now I’m using it to understand how a manga character works
i see you are a man of culture
Read the maga
not me who didn't know what a golden Ratio is until I read part 7 :')
wait why
@@flamingaish jojo reference
Lesson 5 Johnny : the shortest route is the detour
You're making my head spin.
Arigato gyro
Shortest time-wise or distance-wise?
Rest well Gyro
Three after the pinned our breed is strong
loved the content but enjoyed your delivery more... first time I've seen your channel... I'll be watching more
Great breakdown~ there is one thing however that you're missing ~ which is why our brains actually like spirals (and not just our brains, apparently, octopedes and pufferfish build spiral-like sandcastles to attract females) ~ which has to do with the way our primary visual cortex maps to our retina (which is, in essence, logarithmic) which means that spirals actually produce symmetric self-reinforcing waves of stimulation inside our V1 cortex.
"Spin your nails in the golden ratio!... then you should have the ability to harness the power of infinity"
_To infinity and beyond!_
Tusku acto 2
D4c!!
You mean the infinity stones?
nature is a JOJOOO REFERENCE
I love PBS and never touched one of the math videos until now. This guy right here is the proof to "you don't hate math/are bad at math, you just got taught the wrong way".
Learning math takes hard work and patience. A bad teacher can make it harder, but nothing makes up for hard work and patience.
I mean, I wouldn't say you really learn anything about math here. It's a good, concise explanation of the golden ratio that debunks some myths about it, but the math is used is very simple, and I say that as someone who hates math.
Fundamentally you're not learning mathematics per se here. You're not gonna be able to understand most maths any better I gave up on maths of my own will because it was sucking up too much time, that's literally what everyone does to anything they don't like. The only reason anyone is bad at anything is non engagement
Everyone has the same building blocks in their brain and can all learn math to the same degree, it boils down to if your interested or not.
@@gyozakeynsianism and that is the truth
I'm having a hard time finding out if this is a history lesson or a maths one. Very cool!
Just love this...even this old brain is understanding your talk xxx
"Our brain loves patterns, for example if we remember the position of a mouth, nose and eyes we later see faces everywhere" Amogus
Get out of my head
S I L E N C E
Aaahhhhhhhh ahhhhhhhhh,get out of my head, get out of my head, get out of my head, get out of my head, get out of my head, get out of my head, get out of my head, get out of my head, get out of my head, get out of my head, get out of my head, get out of my head, grabs a 12 gauge shotgun, ends it all (like a boss)😎
📮
Disgusting. Vile. Bring back tradition, reject modernity. Amogus shall fall, and Illuminati shall rise once more!
Interesting how the only thing I knew about the golden rectangle before watching this video was Steel Ball Run's infinite spin
me too and tbh I never heard of Golden Rectangle until I read part7 I am not even joking I thought it was a manga thing and it didn't exist in real life :')
Same
Same
when i finished jjba sbr i never thought that there is such a beautiful process behind golden ratio.
I think we just have a compulsive need to fit a chaotic world into a rigid structure. We often unknowingly attempt make sense of things that can’t make sense nature. Like images in a cloud.
The Fibonacci sequence and the golden ratio are a power couple.
Like DIO & PUCCI
love wins
like obanai and mitsuri
They are the Clintons of math
They are the Truth of the universe
You've scrolled down enough to find my comment Well done Here are some tips: 1: If you have the will, then do it. 2: Work those muscles. 3: Believe in the spin. 4: Pay your respects. Spin your bullets in the golden ratio. 5: The shortest route is the detour. It is the detour that will be your shortest path.
Arigato, History Egg.
How do i overcome addiction
@@kratomleaf8937 self-control
@@kratomleaf8937 spin
THANK YOU GYRO
Will this teach me to shoot my fingernails
You need a stand to shoot but if you know these your shoot will be real accurate and powerful
That intro hit me so hard, i was expecting the line: 'the golden ratio strikes back!'
"Ape brain like pretty pattern" - Joe
And THAT's the true monkey puzzle!
i broke the funny number likes
@@liamjedi5341 no.
I lik preti pattn :3
Where banana ❌ Where pretty pattern ✅
I love how the comment section just evolved into jojo. Everything is related to jojo nowadays
everything is golden ratio everything is jojo reference golden ratio is jojo reference
@@jtg7496 yes
everything is a jojo reference
Everything is a jojo siwa reference because things exist in the show and things exist out of the show
@@Stickman_Productions why does this make me physically recoil?
This is the best PBS channel I feel confident in saying that after 2 videos
You explain things really well
Literally anything: **exists** JoJo fans: "It's free real estate."
I think you fortnite because they steal *EVERYTHING*
I agree man, I'm tired of anime fans screaming in my ear.
it's the golden anime
I mean this is true cuz this is free real estate
@@dragonic_ragecore lol, you'll never get rid of us
ADMIT IT ! ADMIT THAT STEEL BALL RUN IS YOUR FAV PART
still havent read it, im gonna get the first 3 volumes in cristmas!!!
me when i falled off my horse because golden ratio is actually not everywhere in nature
stone ocean is mine
Yes
Hell yeah
I had a design problem for the compression of a rubber part and a metal shell length … in a since of frustration I applied the golden ratio to the design dimension …. DESIGN WAS VERY SUCCESSFUL !!!!
As a youngster in college, my math prof of my analytic geometry course was amazed to run into me in the library on my way to check out D. W. Thompson's 'On Growth and Form'. It's a true classic; if this kind of thing interests you, it's still my first recommendation.
I love how this video became jojo fanbase gathering spot.
gyro is the only reason I clicked on the video
@@loturzelrestaurant gaming
@@officialgaming9203 Yes? The user 'Gaming', will 'help'? Yes?
@@officialgaming9203 Gaming will kick some 'Karens', if he knows that term? Battle some Sexists and kick them off YT? Which would be quite cool?
@@loturzelrestaurant gaming
thirty-five minutes ago, this was posted already seven thousand views im so glad im not the only one learning for fun
Amazing work behind this video, thank you!
One doesn't always know all the history of something before it gets named. That's especially true in mathematics where the same thing can be discovered independently. For example, what we call the Pythagorean theorem was known over a thousand years before Pythagoras in Old Babylonia, and known in both India and China about the time Pythagoras lived. It wasn't well known until recently that the Fibonacci sequence appeared in other places before Leonardo Pisano Fibonacci (1170-1250) included his rabbit problem in his arithmetic book, Liber Abaci, in 1202. About 50 years earlier Hemachandra (1089-1173) counted the number of ways a line of poetry can be composed of short syllables of length 1 and long syllables of length 2. A line of length 1 can only be a short syllable; one of length 2 either two shorts or 1 long; etc. The same sequence 1, 2, 3, 5, 8, ... results. Apparently Gopala had studied these numbers in about 1135, other Indian mathematicians as early as the 7th century, and perhaps even Pingala, the author of the Chandaḥśāstra, centuries before that.
TIL why “irrational numbers” are called “irrational.” I always thought it was a strange name but it makes a lot more sense now that I know it comes from “ratio.”
kzhead.info/sun/d62rprFpnpWkg40/bejne.html Golden ratio More detailed explanation
Aloha. I thought this channel's comment-section/s, if any place, would have smarteristic and smarttastic people. So i wanted to ask your opinion of a Project of mine, trying to help youtube help itself - getting it to become less of what can only be described as 'Messy' without wanting to use hard swearing... P0rn, Racism, Sexism, Scam, Spam-Bots, P0rn-Spam-Bots and much more. Oh, and of course the new Kid in Town: The Covid-Denier/Mask-Hater. All of them are non-subtle (some more than others) and therefore easy to find. I used the reportbutton as it was originally intended; not as Cancel-Culture but to help. Just this week, i got 1 Covid-Denier-Channel (yes, the entire thing, not just 1 video) and 2 Open Racists (Users, not KZheadrs) removed. And this feels good. No, its not a 'Wonder-Miracle-Solution!!', but who needs that? Do you need that? Yet, i feel confident about this enough to ask: Wanna join the Fun? The helping? Both? Sorry for the long comment and sorry there is no Miracle-Hyper-Super-Solution, but hey, its cost-free and totally-your-own-time-schedule, as well as just plain fun, so i hope such Package is good enough for you. Smart is in this channel's name, after all, so i hope you at least consider helping KZhead and the Internet... cause it sure as fluff could need the help, tbh...
@@Ani-yt4nf ? What? ?
@@loturzelrestaurant "The Covid-Denier/Mask-Hater." You're a brain washed dunce 🙄
@@exposinghypocrites4827 Your comment a week ago was pretty dumb. Not even sure how, but calling others brain washed is 'usually' dumb, so thats that. What was i brain-washed about, mate? Knowing that Vaccines are good and everyone should take them? Is that what i'm washed to believe? ...Oh buddy...
The golden ratio: _Exists._ The JoJo fanbase: "Hippity hoppity, this mathematical concept is our property!"
Thank you so much, Now I know why my JoJo viewing friend mentioned this concept and was adamant about talking about it. Seems like my hesitation and skepticism were somewhat warranted.
@Captain Bruh hey man thats kinda rude
@Captain Bruh no
@Captain Bruh homestuck is 10x worse... believe me
@Captain Bruh If they’re capable of ruining the music for you, then did you really care about the music in the first place?
The "phi-ncone/phi-napple" gag earned a new sub 😂
I remember as an engineering student before the magnificent invention of the Scientific Calculator by Hewlett Packard in the early 1970s doing math with a slide rule. Hard to believe the SR-71 was made before computers were as they are now, let alone calculators. Random processes do not pick the most efficient forms.
Gyro Zeppeli aproves this video
Arigato, Gyro
@@tinhornname4117 He isn't gonna hear that. Oh wait, he can't.
lesson 5 😔✊
I dont
@@funnyvalentine1592 ow
TL:DR You are increasingly likely to find a golden ratio in things, if you increase the number of things you measure, and you increase the allowable error bars. This is true for any ratio
What really bothered me is that he did not use averages.
The golden ratio is a 'beautiful' proportion though, and just because we find stretched representations does not take away from why it is so intriguing in the first place.
Good tldr! In some cases, yes. In other cases, it's the most appropriate ratio for the situation. Similar to how e is the most natural exponential.
@@domhamai But many other ratios can be intriguing and beautiful too, like pi. It all depends on your perspective.
@@p.9227 absolutely!
The DeLorean definitely belongs to somebody with safety on their mind. The third brake light was not required until 2 years after DeLorean cars went out of production. Having the high mount brake can only be a custom modification, and it's the sort of thing that improves safety and does not make the car look nicer (or make it look worse; it doesn't hurt, but it isn't a visual improvement to most people either).
You got a subscribe from me literally 15 seconds into your hilarious intro. Well done sir XD
Now i can spin my steel balls on my horse and use the infinity
can you elaborate?
I did it! but now my friend with a ball made out of steel with a horse who makes really bad jokes died :(
@@Shawarma101 sayonara gyro
Same
Funni spin
there must be a cool/perfect way to get the "golden angle" on paper besides eyeballing it with your protractor
There is! You can divide a line into the golden ratio segments with just a ruler and a compass: www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi2DGeomTrig.html
Step 1: Draw a pineapple
if you're using a protractor, then you're probably not eyeballing it, no?
@@pg9193 You're eyeballing an irrational interval on an integer-denoted metric, so... yeah. You are.
@@a2pabmb2 good point, I see what you mean and agree. I guess there's no way of not eyeballing it, unless you're using a machine/computer
This episode went by really fast. Very interesting stuff I didn't know, even if I have heard of it before.
I watched this on a 16 by 10 screen and it was beautiful.
"I don't know who closely studies artichokes" At that exact moment something died inside every food scientist watching this video.
Its official now "Jo"e has lost "it" And its "perfect" -Jo Mama
My love of cruciferous vegetables aside: The sequence of metallic ratios might themselves be observed in Fibonacci sequence. Where Phi, the Golden Ratio is n=1 and Phi = (1 + |√5|) / 2 Generally, the n-th metallic ratio = (n + |√(n² + 4)|) / 2 Continuing the Silver Ratio n=2 and the Bronze Ratio n=3 and so forth. (See also the Golden Circle and the Golden Ellipse (i.e., pi*phi).)
Very good video. Small correction, the golden angle is 360 * 1/(Phi)^2
It always tickles me that the golden ratio is actually in fact an irrational number. It's like we can never have things just perfectly.
Maybe its the human construct of number thats wrong
There are loads of irrational numbers, that doesn't make phi that special.
I find this extremely fascinating. As a photographer, I use the Golden Ratio all the time. It simply makes pictures better, no matter the genre.
How. How. how.
So awesome!
@@aur9035 change the rules of third to golden ratio
mans mastered spin
@@aur9035 In most photo editing programs you can place a grid over your photo as you are cropping it. Well, the grid that overlays can either be - boxes as thirds or - you have the option of overlaying a Golden Ratio Spiral. I use it myself to size things up. I assume that's what be spoken of here. Hope that helps ✌️
8:44 It would've been really spooky if Kepler had discovered it 10 years later than he did.
Opening with a History Channel roast was perfect lmao
That part where he made us choose a rectangle... I feel the pain of snapping those in place where it's perfectly aligned AND it felt like it was a magic trick that he knew what I picked
I had no single idea what to pick, lol.
The post-credit be like: "They turned Dr Joe Hansen into a pineapple! Funniest *hit I've ever seen."
I have a Joe... I have pineapple... Hun! Joe pineapple!
Yeah, but does he have sleeves?
why am i only finding you now - my life just made sense with this one video
That intro is something I didn't know I needed
You know what's also golden? This channel
You're channel ;)
@@KaasIsLekker y o u a r e c h a n n e l
How can people still mess "you're" with "your"?
@@FenrizNNN people can still mess with auto correct :) I will leave it like that but thanks for the tip :D
Shower :)
Finally I can spin a ball
JOJO
Part 7
Steel ball run
Arigato, Gyro.
thank god.. I was looking for this!
Historically τ and ρ were used to represent φ and 1/φ. I like that better because τ ρ = 1 and τ - ρ = 1, and all the identities are so much easier to derive.
Jojo fans already know this The golden spin
"Which of these rectangles is the most balanced, the most beautiful?" Anybody who didn't pick the square is objectively wrong.
Makes sense
"most *balanced* " I mean... you aren't wrong. Square IS the most balanced... As all things should be.
@@nadermunye4879 By standard definitions, yes it is.
@@nadermunye4879 It is, go to school
@@nadermunye4879 A rectangle is not a square, but a square is a rectangle. A rectangle needs four 90deg lines to close, while a square needs four equal 90 deg lines
As soon as you said a nautilus was a cut little shell floating around with a face full of spaghetti, I subscribed to your channel 😂
Your diagram 7:53 is wrong. The top arrow should start from month two. Pedantic but threw me for a second!! Great channel btw