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
@yahlifenigstein5803 жыл бұрын
Awesome video👍I learned about this at school and I actually listened 😱
@yokokurama51743 жыл бұрын
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.
@nosuchthing83 жыл бұрын
Thank you for this ep
@michaelgrannen44173 жыл бұрын
at 8:34 3/1 = 1?
@spindoctor63853 жыл бұрын
Please pronounce the Ts in the word pattern, there are no Ds in it.
@pinmanko77983 жыл бұрын
How to make Fibonacci soup? You need : 1. Yesterdays soup 2. Day before yesterdays soup
@MariOmor13 жыл бұрын
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?
@malaquiasalfaro813 жыл бұрын
This is so funny why is no one liking this
@randomperson14183 жыл бұрын
@@MariOmor1true lol
@Win0909493 жыл бұрын
@@MariOmor1 make a new soup and mix it with that soup?
@tulip_hysteria3 жыл бұрын
@@MariOmor1 you dont wanna know
@Lifegotmid3 жыл бұрын
Funny Valentine has been real quiet since this has dropped
@Agilku1173 жыл бұрын
"I'll do anything for my country"
@ousamadearudesuwa3 жыл бұрын
@@Agilku117 "DIRTY DEEDS DONE DIRT CHEAP!"
@yunarukami143 жыл бұрын
@@ousamadearudesuwa Filthy Acts Done at An Unreasonable Price
@rubyred1863 жыл бұрын
@@yunarukami14 dimes for crimes.
@inr97513 жыл бұрын
@@Agilku117 My heart and actions are utterly unclouded! They are all those of "justice"!
@MedlifeCrisis3 жыл бұрын
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.
@shoaibakhtar43893 жыл бұрын
Hey doc please reply!
@serenevalor3 жыл бұрын
**chews carrot** 🥕 ehhh......what's up doc?
@apocalypse4873 жыл бұрын
The force uses the golden ratio.
@OtherTheDave3 жыл бұрын
Especially if it uses that intro 😂
@jaydeep-p3 жыл бұрын
You are like the elon musk of youtubers
@Hritthik_N_S Жыл бұрын
φ + didn't ask + golden ratio
@Z_kun114 ай бұрын
Ratio❌ Golden ratio✅
@RJ-hm9gi4 ай бұрын
2b + a 3b + 2a 5b + 3a 8b + 5a ...
@pħi3 ай бұрын
got roasted by myself 🔥🔥🔥
@azumio3 ай бұрын
I do love 1.618.
@soupstoreclothing2 ай бұрын
oh this is too clever
@dazc3 жыл бұрын
Gyro and Johnny taking notes, then airdropping em to Gappy as we speak
@johnnyjoestarsan22393 жыл бұрын
True
@CoulsonBarbell3 жыл бұрын
Do gappy get spin tho
@semag20903 жыл бұрын
@@CoulsonBarbell yes it turns out that snw bubbles are spinning
@christiankenney68903 жыл бұрын
@@semag2090 mp1pp0
@jd_elderberry3 жыл бұрын
Glad to know I wasn't the only one thinking about this
@bradensorensen96611 ай бұрын
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.
@sarynium9 ай бұрын
yes@TheUnitAce
@dr.michaelj.stefano81138 ай бұрын
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.
@Sue_Me_Too8 ай бұрын
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.
@RedLeg2178 ай бұрын
Mixing logic with relativism. Nice.
@thewizardofthecreek5 ай бұрын
@@dr.michaelj.stefano8113 Life finding order is fundamentally chaotic. All those pretty pictures of spirals in nature, nautilus shells, spiral galaxies, etc etc. Nobody ever checks them. People like pretty pictures. Usually the ratios aren't even *close* to the golden ratio. And certainly never exact matches as governed by some recurrence relation (the Fibonacci sequence). As fictional character Dr. Ian Malcolm wisely put in Jurassic Park: life finds a way
@shremp693 жыл бұрын
The fact that his name is Joe just makes this even more Canon to JJBA
@Amuneh3 жыл бұрын
I knew I'd find a jojo ref here
@creekline50093 жыл бұрын
So I wasn't the only one who started watching this for jjba
@johnnyjoestarsan22393 жыл бұрын
Joe joe bizarre adventure
@bjmoreno0433 жыл бұрын
@@Amuneh yes
@TheFool5533 жыл бұрын
it took me less than 2 seconds to find a jojo reference
@rezazazu11 ай бұрын
The paper leaf part was so amazing. Genuinely creative way of explaining science
@Iam_inevitabIe9 ай бұрын
never expected the video to take that turn
@thewizardofthecreek5 ай бұрын
Although this example of a paper leaf pattern using the phi ratio to be able to collect optimal sunlight might be a useful evolutionary for this plant, it is certainly not the golden ratio for all plants or life in general.
@matthiasfreaked3 жыл бұрын
What if you wanted to learn about the golden ratio, but then gyro said: _lesson 5_
@Handleisn_tAvailable3 жыл бұрын
Why did you have to remind me of lesson 5, I gonna cry
@lunagalaxybrain3513 жыл бұрын
Arigato Gyro
@thoticcusprime93093 жыл бұрын
@@Handleisn_tAvailable ?
@KoeSeer3 жыл бұрын
CHUMIMIIIIIN!
@joshuhigashikata92013 жыл бұрын
Tusk act 4!
@MrTv-sc5tm2 жыл бұрын
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
@arthurrafra95762 жыл бұрын
Don't worry, you would master it soon enough when you meet the president
@joeykitty86782 жыл бұрын
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 ! :)
@tammv23062 жыл бұрын
@@joeykitty8678 🤣🤣🤣
@37rainman2 жыл бұрын
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
@fazguy45472 жыл бұрын
For the unbased, jojo
@animationspace85503 жыл бұрын
Can we have more of Joe doing parodies of History Channel
@besmart3 жыл бұрын
Sure! Sometimes it just has to be done
@Jesse__H3 жыл бұрын
🖐️🤨🖐️ A L I E N S
@yokokurama51743 жыл бұрын
Finally a comment not made by a mainstream sheep.
@abelcheng20733 жыл бұрын
That would be awesome.
@TheAmethyz3 жыл бұрын
Basically thing that some ppl think proves god actually is yet another evidence for evolution. Time always wins.
@4chuyin6 ай бұрын
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 where people claim to see phi 10:02
@derfuchs32963 жыл бұрын
Him: Golden Ratio My brain: You mean Golden Spin?
@shoqiaimran86453 жыл бұрын
That's what it's all about
@shoqiaimran86453 жыл бұрын
That's what it's all about
@waffles97713 жыл бұрын
Johnny! This is how you spin spin okay?
@ph1l693 жыл бұрын
Ein deutscher jojo fan???
@huegosaki09daydreaming3 жыл бұрын
Jojo fans are now everywhere lmao
@luizguilhermedesouzahilara66273 жыл бұрын
Listen Joe, here goes our 5th and last lesson: The shortest route was a detour. It was the detour that was our shortest path!
@albumkosong3 жыл бұрын
Arigatou, Luiz
@hyperdemise97523 жыл бұрын
Chumimin!
@urangames4573 жыл бұрын
ORAORAORAORAORAORAORAORAORAORAORA
@SidewaysTrueno3 жыл бұрын
@@urangames457 okay this is getting cringe
@urangames4573 жыл бұрын
@@SidewaysTrueno tell that to Tusk whose line i quoted
@cliffmatthew82113 жыл бұрын
This is spinning my head because it's too bizzare
@CogHoarder3 жыл бұрын
I see what you did there
@wizzotizzo3 жыл бұрын
IS THAT A JOJO REFERENCE
@MariOmor13 жыл бұрын
Finally, a good f**ing comment
@WeirdTroll6663 жыл бұрын
lmao those references
@carpenterhillstudios832711 ай бұрын
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.
@maru93-c1x3 жыл бұрын
"Gyro, does this man know that technique?" "I don't know Johnny. I don't know."
@thepillarmen29603 жыл бұрын
There it is!
@MEMEGOOSE0253 жыл бұрын
I was hoping for a JoJo reference
@thepillarmen29603 жыл бұрын
@@MEMEGOOSE025 I refuse
@cithara89543 жыл бұрын
I saw the title of this video. Clicked on it just to find a Jojo comment. I'm not disappointed.
@crazyguyethan18483 жыл бұрын
* Infinitely rotates refresh button so you cant watch *
@gyrozeppeli003 жыл бұрын
When steel ball run finally got dropped, prepare yourselves to see golden ratio everywhere.
@D4_Four3 жыл бұрын
And yes that's gonna be a Ten years to wait for
@naipsiefilderussatser40673 жыл бұрын
Yea 8-10 years later
@joyconbulb37433 жыл бұрын
@@naipsiefilderussatser4067 nah Id say 5 years at most since stone ocean is gonna release soon
@funkydong53153 жыл бұрын
@@joyconbulb3743 I mean horses are a pain to animate
@joyconbulb37433 жыл бұрын
@@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.
@Gia1911Logous3 жыл бұрын
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.
@tridos25743 жыл бұрын
Arigato, History Egg.
@kratomleaf89373 жыл бұрын
How do i overcome addiction
@tridos25743 жыл бұрын
@@kratomleaf8937 self-control
@k4n4st43 жыл бұрын
@@kratomleaf8937 spin
@Bruhfried3 жыл бұрын
THANK YOU GYRO
@kspreetheunicorn6243 Жыл бұрын
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.
@yeetbigly58277 ай бұрын
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
@millie.3817 ай бұрын
@@yeetbigly5827 EVERYTHING happens in jojo
@tuskact49366 ай бұрын
''spinning balls(as well as nails) sounds wierd together don't u think( i read part 7 )
@dakotaforeman14 күн бұрын
@tuskact4936 you could say it's quite "Bizarre"
@ginlix88983 жыл бұрын
damn. jojo got so popular that humans made the golden ratio in real life
@Romeo-le2ez3 жыл бұрын
Luv u ani lr gito
@dariuscahyadi96073 жыл бұрын
As a human i can comfirm this
@Dexalium3 жыл бұрын
As a confirm i can human this
@pikachu-jf2oh3 жыл бұрын
a confirm as this can I human.
@rymaix3 жыл бұрын
as a jojo fan on part 7 i can confirm this
@yoyojackyo803 жыл бұрын
I can’t believe that opening sequence lasted 30 seconds haha. Joe is surprisingly funny
@bludfyre3 жыл бұрын
I found Uncle Carl to be funnier
@felicityggreene78313 жыл бұрын
Lol yeah, he had so much fun filming it, he had to show it again at the end! 😂
@kevinbuyks67883 жыл бұрын
It could have been an intro of History Channel's Ancient Aliens 🤣 Mystery, Conspiracy, lunacy 🤣
@marcvanleeuwen59863 жыл бұрын
Actually 32 seconds, which is almost 34. Aha! a Fibonacci number! Could that be coincidence??
@thewriteinpresident3 жыл бұрын
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!!!
@bucci63443 жыл бұрын
“This is the Golden Spiral” The comment section: *SPEEEEEEEN*
@emperorjacques72823 жыл бұрын
Nyo-ho!
@naipsiefilderussatser40673 жыл бұрын
CHUMIMINN!!!
@Playtiempo3 жыл бұрын
Lesson 5
@gaarakazekage16843 жыл бұрын
Doj~~~~~~~~yannnn
@jessegilman52513 жыл бұрын
ORA ORA!!!
@jdschneider58585 ай бұрын
Thank you! I'm an artist and have always heard and read about the Golden Rectangle. Artists and architects in the past were supposed to use it. I was skeptical! I've drawn out the golden rectangle and made a spiral, but it didn't really seem necessary for planning a painting. Nowadays, artists just say to divide the picture plane in thirds, both ways. And one's focal point should be at an intersection. But I don't know about that either! Thank you so much for a fascinating explanation of Phi, the math of it as well as the myth. My skepticism wasn't misplaced!
@philip851Ай бұрын
Myth?....
@weroleoify3 жыл бұрын
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".
@gyozakeynsianism3 жыл бұрын
Learning math takes hard work and patience. A bad teacher can make it harder, but nothing makes up for hard work and patience.
@legrandliseurtri74953 жыл бұрын
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.
@BygoneT3 жыл бұрын
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
@tylermcnally82323 жыл бұрын
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.
@DrWhom2 жыл бұрын
@@gyozakeynsianism and that is the truth
@botigamer90113 жыл бұрын
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
@gilgabro4203 жыл бұрын
What really bothered me is that he did not use averages.
@domhamai3 жыл бұрын
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.
@shoam21033 жыл бұрын
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.
@p.92273 жыл бұрын
@@domhamai But many other ratios can be intriguing and beautiful too, like pi. It all depends on your perspective.
@domhamai3 жыл бұрын
@@p.9227 absolutely!
@TheWanderstar3 жыл бұрын
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.
@@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.
@idlevillager37633 жыл бұрын
Math. Not even once.
@simonsenoner3541 Жыл бұрын
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!
@MasonGreenWeed3 жыл бұрын
Lesson 5 Johnny : the shortest route is the detour
@Gaia_Gaistar3 жыл бұрын
You're making my head spin.
@calus_bath_water3 жыл бұрын
Arigato gyro
@rikschaaf3 жыл бұрын
Shortest time-wise or distance-wise?
@devontekuykendall35653 жыл бұрын
Rest well Gyro
@MiniArts1593 жыл бұрын
Three after the pinned our breed is strong
@morizzd3 жыл бұрын
"The world is a messy place" - Looking around my home: wow, how did he know
@saiku90813 жыл бұрын
👁️👄👁️
@deheerschappij3 жыл бұрын
how did he know? Phi !!
@morizzd3 жыл бұрын
@@deheerschappij Oh no, I thought I had a chance to better myself. Damn universe
@RudolfJvVuuren3 жыл бұрын
Golden ratio baby!
@bestryfulhd21023 жыл бұрын
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.
@GroovingPict Жыл бұрын
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
@shonenchef72493 жыл бұрын
This video is gonna blow up after Jojo part 7 is animated
@roserose1093 жыл бұрын
facts. that's why I'm here loll
@lukedoglt3 жыл бұрын
Yep
@nothajzl3 жыл бұрын
Can you elaborate?
@hajar55953 жыл бұрын
lol
@logan56903 жыл бұрын
joj
@henrynewgate17753 жыл бұрын
Interesting how the only thing I knew about the golden rectangle before watching this video was Steel Ball Run's infinite spin
@Shawarma1013 жыл бұрын
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 :')
@saimongabamoguis45123 жыл бұрын
Same
@echmaster60292 жыл бұрын
Same
@Elijah_Yinkledoink3 жыл бұрын
The Fibonacci sequence and the golden ratio are a power couple.
@martinchristianaguilar51352 жыл бұрын
Like DIO & PUCCI
@rainbowlack2 жыл бұрын
love wins
@thesunnybeeLoL2 жыл бұрын
like obanai and mitsuri
@DiegoBasketPR2 жыл бұрын
They are the Clintons of math
@GeovanniCastro6662 жыл бұрын
They are the Truth of the universe
@holloworacle3140 Жыл бұрын
Will this teach me to shoot my fingernails
@RealSekiroGamerz6 ай бұрын
You need a stand to shoot but if you know these your shoot will be real accurate and powerful
@officialch.90514 ай бұрын
Don't shoot if you hesitate though
@killerbanana99473 ай бұрын
If you don't have a stand, this is still good to help you throw steel balls
@BadassBobY3 жыл бұрын
Him : Did you pick this one? Me : No I didn't- Him : *Because this is the most aestheticly pleasing rectangle* Me : oh ok sorry 👀
@bubblesa86533 жыл бұрын
i picked the one directly left to the phi one haha
@Officalvegeta7493 жыл бұрын
Correct
@wassuphoomanimyourlocalali37843 жыл бұрын
Same lol
@matthew_thefallen3 жыл бұрын
"Ape brain like pretty pattern" - Joe
@FairMiles3 жыл бұрын
And THAT's the true monkey puzzle!
@liamjedi53413 жыл бұрын
i broke the funny number likes
@ZentaBon3 жыл бұрын
@@liamjedi5341 no.
@hollanderson3 жыл бұрын
I lik preti pattn :3
@TheNasaDude3 жыл бұрын
Where banana ❌ Where pretty pattern ✅
@tommyvictorbuch69603 жыл бұрын
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.
@aur90353 жыл бұрын
How. How. how.
@theufakefe3 жыл бұрын
So awesome!
@Michael-dx8qz2 жыл бұрын
@@aur9035 change the rules of third to golden ratio
@shayanaman9952 жыл бұрын
mans mastered spin
@Tyrell_Corp20192 жыл бұрын
@@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 ✌️
@Oleg-mx8gr Жыл бұрын
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.
@jojom383 жыл бұрын
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
@xerotheprotogen42813 жыл бұрын
i see you are a man of culture
@xplitegaming82953 жыл бұрын
Read the maga
@Shawarma1013 жыл бұрын
not me who didn't know what a golden Ratio is until I read part 7 :')
@flamingaish2 жыл бұрын
wait why
@jojom382 жыл бұрын
@@flamingaish jojo reference
@akairyu12913 жыл бұрын
Gyro Zeppeli aproves this video
@tinhornname41173 жыл бұрын
Arigato, Gyro
@maru93-c1x3 жыл бұрын
@@tinhornname4117 He isn't gonna hear that. Oh wait, he can't.
@zen38813 жыл бұрын
lesson 5 😔✊
@funnyvalentine15923 жыл бұрын
I dont
@kocheng46033 жыл бұрын
@@funnyvalentine1592 ow
@Mars_Blends3 жыл бұрын
"Spin your nails in the golden ratio!... then you should have the ability to harness the power of infinity"
@valiroime3 жыл бұрын
_To infinity and beyond!_
@angychillface61463 жыл бұрын
Tusku acto 2
@funnyvalentine52052 жыл бұрын
D4c!!
@xs6819 Жыл бұрын
You mean the infinity stones?
@b1rd52 Жыл бұрын
nature is a JOJOOO REFERENCE
@artorias69693 күн бұрын
Instructions unclear i started spinning my fingernails and creating infinitely deep holes with a pink refrigerator to win a horse race
@som33463 жыл бұрын
Jojo fans already know this The golden spin
@KoeSeer3 жыл бұрын
I love how this video became jojo fanbase gathering spot.
@maraoi3 жыл бұрын
gyro is the only reason I clicked on the video
@officialgaming92033 жыл бұрын
@@loturzelrestaurant gaming
@loturzelrestaurant3 жыл бұрын
@@officialgaming9203 Yes? The user 'Gaming', will 'help'? Yes?
@loturzelrestaurant3 жыл бұрын
@@officialgaming9203 Gaming will kick some 'Karens', if he knows that term? Battle some Sexists and kick them off YT? Which would be quite cool?
@officialgaming92033 жыл бұрын
@@loturzelrestaurant gaming
@L4PLAC3_3 жыл бұрын
thirty-five minutes ago, this was posted already seven thousand views im so glad im not the only one learning for fun
@morgangreene19 Жыл бұрын
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.
@samyakbankar5022 Жыл бұрын
ADMIT IT ! ADMIT THAT STEEL BALL RUN IS YOUR FAV PART
@weebinit8011 Жыл бұрын
still havent read it, im gonna get the first 3 volumes in cristmas!!!
@lemonice Жыл бұрын
me when i falled off my horse because golden ratio is actually not everywhere in nature
@Remspamton Жыл бұрын
stone ocean is mine
@ronniescrazyadventures2478 Жыл бұрын
Yes
@brionesjohnmatthewc.2580 Жыл бұрын
Hell yeah
@cyanide69543 жыл бұрын
I love how the comment section just evolved into jojo. Everything is related to jojo nowadays
@jtg74963 жыл бұрын
everything is golden ratio everything is jojo reference golden ratio is jojo reference
@cyanide69543 жыл бұрын
@@jtg7496 yes
@Donneman3 жыл бұрын
everything is a jojo reference
@Stickman_Productions3 жыл бұрын
Everything is a jojo siwa reference because things exist in the show and things exist out of the show
@thisisrex16763 жыл бұрын
@@Stickman_Productions why does this make me physically recoil?
@jakobsonprofaned51683 жыл бұрын
"Our brain loves patterns, for example if we remember the position of a mouth, nose and eyes we later see faces everywhere" Amogus
@gifzwerk3 жыл бұрын
Get out of my head
@waspoppin47843 жыл бұрын
S I L E N C E
@jesseklaver89053 жыл бұрын
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)😎
@lebaeuhjunkyard47313 жыл бұрын
📮
@user-yp5ko8us9j3 жыл бұрын
Disgusting. Vile. Bring back tradition, reject modernity. Amogus shall fall, and Illuminati shall rise once more!
@rbkishere11 ай бұрын
when i finished jjba sbr i never thought that there is such a beautiful process behind golden ratio.
@lenn9393 жыл бұрын
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.”
@sarathchandran35033 жыл бұрын
kzbin.info/www/bejne/enrVp4BnnMihhrc Golden ratio More detailed explanation
@loturzelrestaurant3 жыл бұрын
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 KZbinrs) 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 KZbin and the Internet... cause it sure as fluff could need the help, tbh...
@loturzelrestaurant3 жыл бұрын
@@Ani-yt4nf ? What? ?
@exposingretards3 жыл бұрын
@@loturzelrestaurant "The Covid-Denier/Mask-Hater." You're a brain washed dunce 🙄
@loturzelrestaurant3 жыл бұрын
@@exposingretards 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...
@sibil-khan6213 жыл бұрын
Now i can spin my steel balls on my horse and use the infinity
@Rhakjellg3 жыл бұрын
can you elaborate?
@Shawarma1013 жыл бұрын
I did it! but now my friend with a ball made out of steel with a horse who makes really bad jokes died :(
@ChiknLorde3 жыл бұрын
@@Shawarma101 sayonara gyro
@angychillface61463 жыл бұрын
Same
@angychillface61463 жыл бұрын
Funni spin
@llgxz3 жыл бұрын
Literally anything: **exists** JoJo fans: "It's free real estate."
@Bleepbleepblorbus3 жыл бұрын
I think you fortnite because they steal *EVERYTHING*
@dragonic_ragecore3 жыл бұрын
I agree man, I'm tired of anime fans screaming in my ear.
@gusty71533 жыл бұрын
it's the golden anime
@angychillface61463 жыл бұрын
I mean this is true cuz this is free real estate
@Hrxxiti2 жыл бұрын
@@dragonic_ragecore lol, you'll never get rid of us
@nikolaysamusik314911 ай бұрын
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.
@StatedClearly3 жыл бұрын
Goldenly done!
@princetamrac11803 жыл бұрын
Coming from you, this is a real compliment. I agree, this was a fantastic video.
@flutterwind76863 жыл бұрын
Eyy my fav youtuber!
@eddraws97673 жыл бұрын
Golden comment
@PersonManManManMan3 жыл бұрын
Golden comment
@donandremikhaelibarra64213 жыл бұрын
Ok he went crazy after ONLY 1.618 SECONDS
@aarav_sharma3 жыл бұрын
Its official now "Jo"e has lost "it" And its "perfect" -Jo Mama
@glacierwolf21553 жыл бұрын
The golden ratio: _Exists._ The JoJo fanbase: "Hippity hoppity, this mathematical concept is our property!"
@giftedguitarist1613 жыл бұрын
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.
@taterds78583 жыл бұрын
@Captain Bruh hey man thats kinda rude
@Kongongongg3 жыл бұрын
@Captain Bruh no
@АннаКравцов-ш6р3 жыл бұрын
@Captain Bruh homestuck is 10x worse... believe me
@spindash643 жыл бұрын
@Captain Bruh If they’re capable of ruining the music for you, then did you really care about the music in the first place?
@cgthayer8 ай бұрын
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.
@shaggynoir3443 жыл бұрын
Finally I can spin a ball
@nreet3 жыл бұрын
JOJO
@nreet3 жыл бұрын
Part 7
@ultimor11833 жыл бұрын
Arigato, Gyro.
@sreejasrivaram82503 жыл бұрын
thank god.. I was looking for this!
@DIOsNotDead3 жыл бұрын
it has to be perfectly spherical tho for it to *speen* that way
@TheKopakah3 жыл бұрын
there must be a cool/perfect way to get the "golden angle" on paper besides eyeballing it with your protractor
@besmart3 жыл бұрын
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
@mehmeh38943 жыл бұрын
Step 1: Draw a pineapple
@pg91933 жыл бұрын
if you're using a protractor, then you're probably not eyeballing it, no?
@a2pabmb23 жыл бұрын
@@pg9193 You're eyeballing an irrational interval on an integer-denoted metric, so... yeah. You are.
@pg91933 жыл бұрын
@@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
@submarinemagnet79653 жыл бұрын
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
@inr97513 жыл бұрын
I had no single idea what to pick, lol.
@basti526310 ай бұрын
That intro hit me so hard, i was expecting the line: 'the golden ratio strikes back!'
@rocacoshi2 жыл бұрын
It’s so crazy, last time I did acid anywhere I looked I couldn’t stop noticing the golden spiral, it was amazing!
@craigford332 жыл бұрын
Saaaaame!
@cosmicraysshotsintothelight2 жыл бұрын
I was not on acid when I did this, but maybe got this good from doing it way back in the seventies... kzbin.info/www/bejne/maTQnKitpbtqn8U
@richardconner58802 жыл бұрын
You saw the torus🌀 in your crown chakra,you could have followed it into GOD. .Interestingly enough,in PMH Atwaters book about her NDE experience she saw 2 huge tornadoes 🌪one on top of the other in open space.A they spun,she saw them breathe in & out,than saw in the top tornadoe her future lives,in the bottom her past lives.In the middle where the spouts almost touched she saw brilliant flashes of light,That was GOD. That sounds like a matter-antimatter model for the universe,breathing out,expanding...than inhaling, contracting,Whose origins were created by GOD,AN IMPLOSION OF DARK MATTER,Using the sound-OM to start the process.
@Neptune_symbol02732 жыл бұрын
@@richardconner5880 you’re the type of person no one what’s to get high with.
@Neptune_symbol02732 жыл бұрын
The human embodiment of a bad trip
@why_though3 жыл бұрын
"I don't know who closely studies artichokes" At that exact moment something died inside every food scientist watching this video.
@aner_bda3 жыл бұрын
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.
@putraduha31763 жыл бұрын
Maybe its the human construct of number thats wrong
@marctreal3 жыл бұрын
There are loads of irrational numbers, that doesn't make phi that special.
@BernGoulart Жыл бұрын
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
@AverytheCubanAmerican3 жыл бұрын
You know what's also golden? This channel
@KaasIsLekker3 жыл бұрын
You're channel ;)
@cookiecrumbler23453 жыл бұрын
@@KaasIsLekker y o u a r e c h a n n e l
@FenrizNNN3 жыл бұрын
How can people still mess "you're" with "your"?
@KaasIsLekker3 жыл бұрын
@@FenrizNNN people can still mess with auto correct :) I will leave it like that but thanks for the tip :D
@FizzyToni3 жыл бұрын
Shower :)
@lyz74823 жыл бұрын
Me after finishing JoJo's part 7 yesterday: hmm interesting
@RealBelalMuhammed3 жыл бұрын
“Arigato Gyro”
@PlexorF13 жыл бұрын
😳
@cherrydragon31203 жыл бұрын
Whut¿
@rayz16853 жыл бұрын
You gonna start part 8?
@Gia1911Logous3 жыл бұрын
@@RealBelalMuhammed This truly... truly... was a long detour Thank you Gyro I don't know what else to say
@catalinasirbu33113 жыл бұрын
Cant believe that i watched a vid about math that (somehow) taught me more than school did.Also cool jojo reference.
@juanma8903 жыл бұрын
Is mista boy or girl, pleade answer my cuestion, i was living whit this so for several months, i cant sleep good because this interrogant, please help me
@smdll223 жыл бұрын
@@juanma890 male
@catalinasirbu33113 жыл бұрын
@@juanma890 hes a italian,good sir
@octazone25583 жыл бұрын
@@catalinasirbu3311 FEMALE
@spidyboi90973 жыл бұрын
PoV:știi română
@V8StealthBeetle11 ай бұрын
loved the content but enjoyed your delivery more... first time I've seen your channel... I'll be watching more
Wow this intro its really like those. 1:55 Golden Ratio number 2:10 - Pi é um numero Irracional pois ... 3:00 Euclidean pai da geometria 4:00 Golden triangle 5:00 Golden Spire 6:30 Fibonacci
@itzslopchaosz71083 жыл бұрын
Ó o Br kkkkkkkk
@CrashBandicootFan1003 жыл бұрын
Unironically stared at the golden rectangle first Also Jojo refference in spite of not reading Part 7 yet, will be waiting till SBR anime in my early 30's dear God.
@joshuhigashikata92013 жыл бұрын
Just start reading, it's worth it
@madhurgupta85273 жыл бұрын
You should read it so that you are not spooled about stuff in SBR
@solskissed3 жыл бұрын
theres a fandub look up sbr fandub they have all the chapters
@nika.5763 жыл бұрын
If theres any manga worth reading its SBR don’t wait
@Hrxxiti2 жыл бұрын
just watch it dude
@MrQuinnlord Жыл бұрын
This is the best PBS channel I feel confident in saying that after 2 videos
@mariozgjani63493 жыл бұрын
As a Greek person I feel a little bit happy about the fact he said "the Greeks AND the mathematicians" as if every Greek was just doin math as a hobby We da smart people
@putraduha31763 жыл бұрын
Your central bank clearly doesn't do it for the past decade
@emsa50343 жыл бұрын
@@putraduha3176 woah that took an abrupt turn
@papasscooperiaworker36493 жыл бұрын
@@putraduha3176 Elaborate.
@ni30703 жыл бұрын
Good for you that you made name, Indians barely get any credit
@RandomAmbles3 жыл бұрын
Eh, yall mostly just rediscovered Babylonian stuff. Seriously, name a Greek math development off the top of your head: Pythagorean theorem? -Nah. Euclidian stuff? -Nah. The Greeks did some amazing work, don't get me wrong, but they aren't the only smart people out there by a long shot.
@Artist_Keena Жыл бұрын
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!
@PinkishPlant Жыл бұрын
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
@samalass466 Жыл бұрын
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.
@gaerekxenos Жыл бұрын
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
@lucianocastillo69411 ай бұрын
@@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?
@ronniechilds200211 ай бұрын
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.
@mfaizsyahmi3 жыл бұрын
The post-credit be like: "They turned Dr Joe Hansen into a pineapple! Funniest *hit I've ever seen."
@TheNasaDude3 жыл бұрын
I have a Joe... I have pineapple... Hun! Joe pineapple!
@TheOnyomiMaster3 жыл бұрын
Yeah, but does he have sleeves?
@danknfrshtv Жыл бұрын
The "phi-ncone/phi-napple" gag earned a new sub 😂
@25jessieg3 жыл бұрын
23 minutes of Joe explaining something? What did we do to deserve such a treat!?
@stephenolan55393 жыл бұрын
Tom Scott just upped an interesting video about microwave ovens. Every bit as interesting as this video.
@satanofficial39023 жыл бұрын
"The numbering of numbers is numbered." ---Albert Einstein
@satanofficial39023 жыл бұрын
Fact checkers say..."Correct!"
@sarathchandran35033 жыл бұрын
kzbin.info/www/bejne/enrVp4BnnMihhrc
@badlydrawnturtle84843 жыл бұрын
"Which of these rectangles is the most balanced, the most beautiful?" Anybody who didn't pick the square is objectively wrong.
@pedroivog.s.68703 жыл бұрын
Makes sense
@neurofiedyamato87633 жыл бұрын
"most *balanced* " I mean... you aren't wrong. Square IS the most balanced... As all things should be.
@badlydrawnturtle84843 жыл бұрын
@@nadermunye4879 By standard definitions, yes it is.
@tripedal20633 жыл бұрын
@@nadermunye4879 It is, go to school
@a.lexandra033 жыл бұрын
@@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
@abiogreshajem-spj80353 жыл бұрын
We got the shape called the golden spiral. if that looks familiar it's probably because you've seen an image like THIS before. We, JJBA fans can always see them and we are close to making our fingernails spin.
@MysteryGeek20063 жыл бұрын
Yes yes yes. Y E S
@Chibi_Nagisa3 жыл бұрын
I want real life green steel ball
@ElleDiablo2 жыл бұрын
This has been something that bothered me as a kid learning about the ratio... it always seemed arbitrary. Like they'd use rectangles on a building but randomly placed. This and the "taste zones" always made me feel like maybe I'm doing something wrong?
@terryriley64102 жыл бұрын
You are most probably doing something wrong. Nobody's perfect.
@SquizzleGwen3 жыл бұрын
The leaf one is such a good activity to do with students
@LisaBeergutHolst3 жыл бұрын
School is prison lol
@MaxTax_3 жыл бұрын
a good prison or bad prison :)
@LisaBeergutHolst3 жыл бұрын
@@MaxTax_ What's a good prison?
@Rippone3 жыл бұрын
@@LisaBeergutHolst school
@LisaBeergutHolst3 жыл бұрын
@@Rippone Why lol
@tomadshead61334 ай бұрын
Amazing video! I did my further maths project on this, and I'm kinda glad I only saw this afterwards, theres no way I would've been able to compete!! Thanks again.
@remimarkable4834 Жыл бұрын
Little unknown fact: People who study fruit and other objects up closely are most commonly to referred to as stoners.
@littlefluffybushbaby7256 Жыл бұрын
You mean cherries, plumes, apricots etc. right? 🤭
@littlefluffybushbaby7256 Жыл бұрын
Doh! plums as well as plumes
@victorunger Жыл бұрын
Nah bruh I’m a stoner I ain’t fruity
@attien24 Жыл бұрын
Omg jojolion.
@ulalaFrugilega9 ай бұрын
Fineapple specialist here! We know what we are doing?
@YukiXK2 жыл бұрын
I remember watching ViHart's videos on the Fibonacci sequence in plants when I was little and it has always stuck with me to this day. She basically explains the same thing about the leaves and how efficiently they grow in nature to get the most sunlight.
@heehaaww Жыл бұрын
you unlocked a hidden memory in my brain i used to watch vihart all the time but i forgot about videos over time and now im back binging all of them.. i remember the spongebob pineapple example so clearly
@johndoh5182 Жыл бұрын
Yeah plants have had hundreds of millions of years to perfect their designs, or fade away. Considering how many have faded away it's pretty clear getting to more optimal patterns wasn't something most plants could do. Considering it's the flowering plants that dominate once a very successful pattern came about then it propagated and many variants came from it as pockets became isolated and they could develop into something slightly different. So, once a plant or animal develops a highly successful pattern that pattern is going to propagate. With humans now ending most biological diversity by spreading the plants/animals we want and spreading stuff around the world we've ended a lot of natural evolution.
@7Leo_7 Жыл бұрын
ic
@the_original_van_d3 жыл бұрын
On Bradley’s behalf, thank you for using that font when you said “sublime”.
@manog8713 Жыл бұрын
Fantastic, open mided and realistic account of the hype of Golden Ratio. Well done.
@jacobtaylor825011 ай бұрын
I wonder why gravity causes the spiral of galaxys to be the same as these plants
@tcl.223 жыл бұрын
ViHart's series on this subject from over 9 years ago is still one of my favorite works on yt
@HalfVastGamer3 жыл бұрын
When he got to the pinecones I searched the comments for a vihart shout out.
@ammieloris3 жыл бұрын
@@HalfVastGamer Me, too! I remember tracing spirals on pineapples and pinecones and gluing paper petals together using a folded paper "compass." Vihart's is a great video, and this one is fun, too.
@mostitoasty77653 жыл бұрын
jojo fans:u called? smart people: no im just looking at the golden rati- jojo fans:IS THAT THE GOLDEN SPIN
@B3RS3RK3RAH3 жыл бұрын
Math Jojo fans: YES IT IS!
@Liamjlm3 жыл бұрын
I went into this comment section hoping for a good discussion
@mostitoasty77653 жыл бұрын
@@Liamjlm welcome to jojo
@revanhaq2473 жыл бұрын
@@Liamjlm sorry mate
@Liamjlm3 жыл бұрын
@@revanhaq247 I forgive you
@davidparker2173 Жыл бұрын
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.
@gunslinger91719 ай бұрын
One number to rule them all!
@MedEighty Жыл бұрын
I watched this on a 16 by 10 screen and it was beautiful.
@joeschmo15043 жыл бұрын
he's basically saying the golden ratio is amogus of the old times
@user-mo4rf9cx7t3 жыл бұрын
I have end reading Jojo sbr like 4 minutes ago and I see this on my recommendations, amazing.
@blue-wl5xl3 жыл бұрын
Ikr
@usualunusualkid71493 жыл бұрын
what does sbr have to do with anything?
@dowowowowowow78783 жыл бұрын
@@usualunusualkid7149 read it
@dowowowowowow78783 жыл бұрын
@@usualunusualkid7149 the golden ratio
@usualunusualkid71493 жыл бұрын
@@dowowowowowow7878 What does the golden ratio and a chapter have to do with each other? I didn't even read the other parts
@mozvidz3 жыл бұрын
*If this were taught in class, I'd never pay attention, but I watched the whole video because it was told in a practical fun way. Teachers should be trained on this form of teaching!*
@bjh36123 жыл бұрын
yeah for ontroductions to.topics this format is.great, almost useless for mastery of a topic though. But a decent amount of this to break up the monotony of actually getting good at a subject is really needed in modern education.
@rociofp86303 жыл бұрын
The most of the times you hate/love a subject its because of the teachers.
@clarahajal98493 жыл бұрын
You're absolutely right
@Shuizid3 жыл бұрын
So I wrote a lengthy comment, but then decided to make it short: This is a 20min video, schooldays are about 6*45min = 270min lessons -> adding up to about 13 of such videos. So you can try and go ahead, watch 13 of these videos with standard school breaks inbetween and at the end write down what you learned and ask yourself, if this would add up to a good grade.
@charisma-hornum-fries3 жыл бұрын
He is really so good he should make KZbin videos. 🤪
@dichterwald91 Жыл бұрын
My friends argued with me when I tried say anything against this number. Thanks for criticism I was looking for!
@johnvananden35063 жыл бұрын
Enjoyed the video very much, and for one who can't "crunch the numbers", I've found the ratio quite useful in my design work. For me it's an easy way to divide and control proportion. So while I "understand" the mathematical constraints, the geometric (as applied to design) aspects are limitless. Thanks for posting this!