This was one of the best Numberphile videos ever.

@math.mouraa

6 жыл бұрын

Ersen Couldn't agree more

@MrPacoHamers

6 жыл бұрын

I never liked the golden ratio because the way I learned it was: 1. greek dude came up with a series 2. divide 2 following numbers in it 3. WOW! flowers grow this way 4. the end This was a very unsatisfying explanation, because the whole 'WHY?!?' was missing. Thanks for giving me some love for the golden ratio.

@limbridk

6 жыл бұрын

I agree. This one is up there as a top candidate for the best one ever. (And I have of course seen every single one, as we all have. Surely.)

@ultimateman1234

6 жыл бұрын

I was going to post the same thing. But I knew someone else already must have. So I found your comment, liked it, and...

@wierdalien1

5 жыл бұрын

asd i mean he looks like a judge who dropped his wig in the mud

π = 3 + a bit. Going to use this in all of my code from now on.

@acorn1014

6 жыл бұрын

π = 3; π += a bit;

@DarkwingD

6 жыл бұрын

private double aBit = Math.random(); private double giveOrTake = Math.random(); if (giveOrTake > aBit) { aBit += giveOrTake; } if (giveOrTake private final static double PI = 3 + aBit;

@anselmschueler

6 жыл бұрын

pi = pi + bit

@PhilerinoBTW

6 жыл бұрын

> 'in my code' > has MissingNo as a profile pic I love you :^)

@KauanRMKlein

6 жыл бұрын

so π will be either 6 or 7 depending on the value of that bit :P

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

@USER-G291

4 жыл бұрын

Mark O did you go to school marko

@TempestGotThatTrash

4 жыл бұрын

Imchattingabsolutefuckingshit username checks out

@ahobimo732

4 жыл бұрын

@pyropulse You seem upset. You wanna talk about that?

@gretsyuk1387

4 жыл бұрын

pyropulse pretty rude for no reason

@kakonya2994

4 жыл бұрын

pyropulse I mean I found it interesting that this could be a way to visualize how closely can an irrational number be approximated by smaller numbers, and I think using the language he used to explain - “more or less irrational” is an easy way to express my thoughts in this context

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

@ethann6573

3 жыл бұрын

For me it was the sound dinosaurs that did it.

@RaineriHakkarainen

2 жыл бұрын

The golden ratio is 1,618

@p0tatobiden250

Жыл бұрын

Establishment is training Al to learn from revised/censored reality of mediiaa and internet (mostly peaceful 👍), manufactured by NewNormal agenda. Starting the systemic use of Al with special interest focus is pure corruption at the root,. thanks Sillyc0nVally

@justArandomfellar

10 ай бұрын

Nature is so precise. And yet many people still call themselves "atheists".

@PC_Simo

10 ай бұрын

@@RaineriHakkarainenApproximately. It’s really 1,618…. Since it’s irrational (as indicated by its infinite continued fraction and its precise formula: (1 + sqrt(5))/2 (which is just sqrt(5) with some rational tweaks); as 5 is not a square number, its square root has to be irrational), and a bunch of other things, I’m sure), it has an infinite, non-periodic decimal expansion. 1,618 is a rational number that can be expressed as a precise fraction: 809/500.

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

@niamhoconnor8986

4 жыл бұрын

Nice

@zoklev

3 жыл бұрын

no, the rhs is equivalent to "I'll be there in a a bit"

@XnoobSpeakable

3 жыл бұрын

400th like

@deletingthis00

3 жыл бұрын

You made me smile and giggle just alittle bit lol. :)

@mariafe7050

3 жыл бұрын

So you'll be there in a 1/(pi-3)-7?

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

@SCWood

5 жыл бұрын

It uses the least irrational number: 1

@worldisfilledb

5 жыл бұрын

S.C. Wood why isn’t 0 the least irrational number?

@Good_Hot_Chocolate

5 жыл бұрын

@@worldisfilledb how is nothing less irrational than something?

@rohancrawley4131

4 жыл бұрын

@@Good_Hot_Chocolate Why should there be something

@dahlkzer

4 жыл бұрын

@Dirty Sack it does noth exist

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

"Flowers can cancel fractions" - Ben Sparks, 2018

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.

@numberphile

6 жыл бұрын

Great. Glad you (sort of) liked it.

@abdiazizissa5706

6 жыл бұрын

.

@PhilBoswell

6 жыл бұрын

Is the code for the animation, or anything like it, available anywhere…maybe on GitHub?

@a_diamond

5 жыл бұрын

AGREED! (and yes, that required caps.. lol)

@codemiesterbeats

5 жыл бұрын

yea but to me math is like super complicated but at the end of the day it seems to me its just like a never ending mandelbrot set. it seems we have came up with infinite amounts of knowledge to describe something we should have already known all along lol idk man im having one of those "bruh i just figured out how the universe works" moments.

Believe in the rotation, Johnny.

@Skullman367

5 жыл бұрын

The Masked Man The spin is the power of infinity!!

@sarabeatriz5569

5 жыл бұрын

GYROOOOOOO

@calamari2875

5 жыл бұрын

arigato, gyro

@franciscopetrucci

4 жыл бұрын

Is... Is this?! Could it be? Is this a Jojo's reference?!

@superiorf

4 жыл бұрын

I opened this video only to see if there was a JoJo reference in it, thank you

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

@progect3548

3 жыл бұрын

@Arbnora Vezaj Elsi

@ekananda9591

3 жыл бұрын

Lol

@ryanolsen294

2 жыл бұрын

CS major? Counter strike major?

@Padeir0

2 жыл бұрын

@@ryanolsen294 Obviosly not. It's Coconut Science major.

@shmillsyshmillsy6624

2 жыл бұрын

@@Padeir0 at my school it's called ECS (Engineering in Coconut Science of course)

Everyone: I finally understand the golden ratio Me: SPINN

@skyebluee

3 жыл бұрын

SPEEEENNN

@matteussilvestre8583

3 жыл бұрын

Nyo-ho!

@j.hawkins8779

3 жыл бұрын

@@skyebluee S P E E E E E E E E E E E E N

@alexandrufedericis9578

3 жыл бұрын

SPaIN

@EclipseSystem

3 жыл бұрын

SPEEEEEEEEEN

Instructions Unclear. Accidentally produced an infinite spin.

@shrikaradeshpande7280

5 жыл бұрын

Lesson 5 Johnny

@meowmeowmeowmeow1

4 жыл бұрын

eventually, he stopped thinking

@vaspelifilms1608

4 жыл бұрын

@@meowmeowmeowmeow1 Magenta Magenta

@pereraddison932

3 жыл бұрын

@@meowmeowmeowmeow1 ... the yen to ken zen means, nothing's gonna change your world ...

@timsonins

3 жыл бұрын

How. It's impossible

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

@alpo789

6 жыл бұрын

Spectrally Mathologer did a video on this once. I think it was even titled "the most irrational number"

@E1craZ4life

6 жыл бұрын

An unpublished interview with Steve Mould had him mentioning the Golden Ratio as the most irrational number.

@vitakyo982

6 жыл бұрын

It doesn't make lot of sense , if (1+sqr(5))/2 is the most irrational number , multiplying this number by 2 & substracting 1 shouldn't drasticly change it's properties , does it mean sqr(5) is extremely irrational ?

@alexpotts6520

6 жыл бұрын

Sqrt(5) has the continued fraction 2+1/(4+1/(4+1/(4+1/(4+... It's a similar beast in that it has a continuing fraction that repeats the same number over and over again. You can prove it in a similar way to the way he proved the all-1's continued fraction equals phi.

@grex2595

6 жыл бұрын

sqrt(5) = 2+1/(4+1/(4+1/(4+...), so according to this video, it would be more rational than sqrt(2) and sqrt(7). It has to do with proximity to a perfect square. sqrt(2) = 1+1/(2..., and sqrt(5) = 2+1/(4..., and sqrt(10) = 3+1/(6... If you look at the numbers, you get sqrt(1+x^2) = 1+1/(2x..., which means that when you take the square root of a number, the closer that number is to a perfect square, the more rational it will be (according to this video).

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.

@fibonaccisequins4637

2 жыл бұрын

What a wholesome comment. I’m going back to school soon and I’m going to remember this to motivate myself.

*IF YOUR HEART WAVERS, DO NOT SHOOT*

@sinbad4696

3 жыл бұрын

Is that a JoJo's reference

@iforgottbh4488

3 жыл бұрын

Zero Two it’s making me head spin

@kevinsaidhi875

2 жыл бұрын

@@iforgottbh4488 it’s making my nails spin

@uocgimaythgconguoiyeuchethet

2 жыл бұрын

Then a new gate will open to you

@frfr843

2 жыл бұрын

The corpse was "JEs0s" for some reason

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

@prathameshdusane2619

5 жыл бұрын

Nailed it Bro!

@prathameshdusane2619

5 жыл бұрын

Flee for your lives!

@Timbot2002

5 жыл бұрын

And killing it at maths

@MrSam1804

5 жыл бұрын

That's exactly what i thought when i saw the thumbnail. lol

@Lyle-xc9pg

5 жыл бұрын

I said that too!

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.

@simonshugar1651

6 жыл бұрын

r/iamverysmart

@iMutt-yy6vf

5 жыл бұрын

I'd never actually seen the derivation of (1 +- sqrt5 ) / 2 before. This was very helpful!

@gguioa

5 жыл бұрын

Well he didn't said he understood everything @@simonshugar1651

@SSM24_

5 жыл бұрын

Same. I knew about most of the properties of the golden ratio that were shown here, but I was never quite able to put together _why_ it was the case. When he went from the continued fraction representation straight to "x = 1 + 1/x" it just blew my mind.

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!

"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*

We need an hour long animation of the flower at the end.

@bgoggin88

6 жыл бұрын

Libor Kundrát yes.

@celinak5062

6 жыл бұрын

Libor Kundrát same

@benjabean1

6 жыл бұрын

slower, or looping?

@liborkundrat185

6 жыл бұрын

MamboBean Slower. Imagine it spinning slowly with a hypnotyzing music as it crosses the milestones. (the larger fractions, the golden ratio, etc.) Looping wouldn't really have much meaning.

@retepaskab

6 жыл бұрын

Make it 10 hours.

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!

@TimpBizkit

8 ай бұрын

It's a different metric but I thought of transcendental numbers as the most irrational but things like "e" and pi are close to 3 so will make curly spokes if you try to use 1/e or 1/pi to space seeds.

Johnny you've gotta watch this Numberphile video to learn the power of the spin, Trust me Johnny

@kakyoindonut3213

3 жыл бұрын

"johnny johnny" "yes gyro"

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!

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

@Radianx001

6 жыл бұрын

Let epsilon < 0

@fovlsbane

6 жыл бұрын

Turn the sign around.

@Radianx001

6 жыл бұрын

Fovlsbane no

@ice_wall_offcom1175

6 жыл бұрын

TURN IT!

@fukpoeslaw3613

6 жыл бұрын

RainbowMash Noooo! Don't turn it!

Johnny, you must spin your nail based in the shape of the golden rectangle！

@worldisdoomed9994

4 жыл бұрын

I can't do it Gyro!

@felixargyle1285

4 жыл бұрын

@@worldisdoomed9994 Say that 3 more times then I'll give it to you

@sinbad4696

3 жыл бұрын

Pizza mozzarella

@alejandrite9

3 жыл бұрын

cant ruin 314 likes :/

@lifeisagameofknowingyourro6327

3 жыл бұрын

No

I have no idea how I came across this video nor have I the slightest clue of anything that was just explained, but, I watched all 15:12 in complete wonderment.

@marshallpartington

Жыл бұрын

Wonderment lies in the question more than the answer, doesn’t it?

Nature: *Exists* Mathematicians: _That's Irrational_

@jhomastefferson3693

2 жыл бұрын

Irrational in math means something else compared to irrational in reality. Rational typically means "in accordance with logic." In that sense it's latin root. Irrational in that sense means not according to logic. However, that is not the etymological root of mathematical rational and irrational. The english started using ratio, which has the same root at rational, to refer to a relationship(by division) between two numbers. Rational in that sense means able to be described in a ratio and irrational simply means unable to be described in a ratio, not that the number is illogical - since numbers kind of can't be illogical because of how they're defined.

@DouglasButner

2 жыл бұрын

@@jhomastefferson3693 thanks for explaining

@DouglasButner

2 жыл бұрын

@@jhomastefferson3693 but you forgot to sat ratios of integers or other rational numbers. All are a ratio

Best Numberphile video yet!

@cuter.

5 жыл бұрын

What would You think are the other best videos on this channel? Or better, what are, in your opinion, the best videos from Numberphile, Computerphile and other science-related channels? I would even go as far as asking what are the best videos You've ever seen on KZread?

Best Numberphile video in a while

@thesmallestatom

6 жыл бұрын

Easily.

@ultimateman1234

6 жыл бұрын

Absolutely brilliant.

@DBFIU

6 жыл бұрын

Agreed

@TheBelrick

5 жыл бұрын

Denethor is that you?

@cuter.

5 жыл бұрын

What would You think are the other best videos on this channel? Or better, what are, in your opinion, the best videos from Numberphile, Computerphile and other science-related channels? I would even go as far as asking what are the best videos You've ever seen on KZread?

Arigato, Gyro.

I love how he just mentioned "you can count the spokes and if you do you get fibonacci numbers"

That flower animation at the end really creeped me out for some reason.

@anybodynoname8767

6 жыл бұрын

Mister Apple You have floweranimationmathsthingphobia?

@ctrlaltshift

6 жыл бұрын

I want it as my screensaver.

@EchoHeo

6 жыл бұрын

Mister Apple the way it changes the circles' size is really disturbing

@teckyify

6 жыл бұрын

Sentinels from matrix

@jwrm22

6 жыл бұрын

It's more likely the music.

PI=3+a bit I knew it, PI is something between 3 and 4.

@alant84

6 жыл бұрын

Nobel prize incoming...

@fennlyxerxich7091

6 жыл бұрын

*Fields Medal

@HappyBeezerStudios

6 жыл бұрын

Between 3 and 4 Between 3 and 3 2/5 (or 12/5) Between 3 and 3 1/7 (or 22/7) and so on

@gyaneshwarigunaseelan2575

6 жыл бұрын

Isnt pi = 3.2? Yeah..

@felipesteinck6984

6 жыл бұрын

embrace yourself and pi=22/7 is coming!

I love how when at 10:48 he mentions Matt Parker, there is a tiny flash of Parker Square in the bottom right corner :-)

This was so interesting and I really couldn't understand exactly why the golden ratio was so important and this really blew my mind, thank you!

Brilliant video! Captivating from start to finite end. We are off to go measure flowers now.

@oscarpritzker6278

3 жыл бұрын

If there's an end, 100% of the times it will be finite. There is no such thing as "infinite" with an end. I'm still confused about your thought process.

@dr.killakill960

3 жыл бұрын

@@oscarpritzker6278 did you have high expectations for a kids channel?

@doublecircus

3 жыл бұрын

@@oscarpritzker6278 i mean... you can technically “complete” an infinite series

@oscarpritzker6278

3 жыл бұрын

@@doublecircus No we can't. There's a reason why it's called infinite, but I agree that there's always an end, we just can't calculate it, so it's correct to say that infinite just means immeasurable and not endless.

@doublecircus

3 жыл бұрын

@@oscarpritzker6278 I was referring to something like Zeno’s paradox, and probably could find a few other examples

This guy is a fantastic teacher. He clearly understands what he's talking about. For me, the subject is quite interesting in the first place, but even still he's so clear and concise in his explanations. Great video!

@numberphile

6 жыл бұрын

Thanks and glad you enjoyed it.

Flowers canceling fractions is the coolest sentence I've heard today.

This guy is by far the best explainer you have on numberphile

@sinbad4696

3 жыл бұрын

Nah gyro Zeppeli is better

@AdelaeR

2 жыл бұрын

That is your opinion and you should state it as such. Other people may have other opinions because liking someone is not easily quantifiable.

Some hard thinking has gone into this, I would never have thought of this!

@ShoM1nam1moto

6 жыл бұрын

They actually taught us exactly this in uni at a number theory course

@Luftbubblan

6 жыл бұрын

Quite different to be taught something compared to be the one that figured it out. Uff, one part of me wants to study again since i never got much education. Now at older age knowledge interest me more :D

@andrewkelley7062

6 жыл бұрын

Mine was actually pretty easy it was simply a matter of all actions being compressed into a series of yes no and i do not know from there you simply compress the possible repetitive calculations down to a reasonable form like holographic in a particular way then no matter what question you have as long as the answer is yes or no you have a direct path from question and answer in the fractal patterns of that holographic that eventually themselves repeat and the world becomes yours. Took me less than a day to figure out and usually just takes a few seconds on paper.

@galesx95

6 жыл бұрын

Andrew Kelley what exactly have you find out? and how again the world becomes yours?

@andrewkelley7062

6 жыл бұрын

just do the equation I have in my post

This is, by far, the best explanation about how math helps to explain natural occurences. I am a high school geometry teacher with a degree in secondary mathematics education. I always feel that when I start to talk about Fibonacci numbers, the Golden Ratio, etc, I tend to lose people. Most high schools students, and students beyond high school, really sort of start to glaze over when talking about sequences. I absolutely love this explanation and animation. I feel like anyone could understand it because it's so beautifully done. Also, to be honest, I never thought about the fact that some irrational numbers are more irrational than others. This video was so cool! Thank you!

@jorisbeijers7539

Жыл бұрын

5d75dv6e

You guys rock! My favorite numberphile video yet. Ben you’re awesome, I found you through the Mandelbrot set video which I loved!

Compelled to come here because of Steve Mould’s 1 million subscriber video. Great content.

All the videos with Ben Sparks have been fantastic on numberphile, looking forward to more!!

@numberphile

6 жыл бұрын

Here’s his playlist: bit.ly/Sparks_Playlist

The true power of lesson 5...

@alanlowen2766

3 жыл бұрын

which lesson?

@r35ct12

3 жыл бұрын

@@alanlowen2766 you probably wont get it

@emptyvending8964

3 жыл бұрын

@@alanlowen2766 Lesson 5 Johnny, it was the most roundabout path

@rhodesmusicofficial

2 жыл бұрын

GAH NOOO NO JOJOS IN MY MATH AAAAAAAAA

"The words a bit are not mathematically recognized terminology" Computer scientists: :/

The most clearly explained video on Numberphile. Was following along quite nicely all the way through!

The best Acid trip I ever had on youtube.

@momo-dm3rw

5 жыл бұрын

I believe you.

@AbhinavTallapally

5 жыл бұрын

did anyone ever make a video of the animation with that music yet?

@PanduPoluan

4 жыл бұрын

Mandelbrot Deep Zoom would like to have a word with you...

@Kakerate2

4 жыл бұрын

i watched this tripping and it was entertaining af

@simohayha6031

4 жыл бұрын

Do mandelbrot zoom in

Lol the Parker square.

@MichaelLikvidator

6 жыл бұрын

Love such easter egg.

@wynarator

6 жыл бұрын

Parker square will never die, love you guys :D

@Bellonging

6 жыл бұрын

It'll never be let goooo.

@TKNinja37

6 жыл бұрын

Parker Square flash for a frame or two, then suggesting the video for it immediately afterward. You cheeky sorts. 😂

@arturzathas499

6 жыл бұрын

it has become like one of those small fish that lives on the surface of a much bigger fish. chances are the small fish will show it self whilst you are admiring the big fish

_Lesson 4: Pay your respects_

Considering that flowers have had about 250 million years of evolutionary trial and error to progressively find more and more efficient seed packing methods, is it any surprise that eventually they would get to the most perfect method mathematically possible?

@General12th

5 жыл бұрын

Not even then, since flowers don't have any sort of "choice" about where they grow seeds anyway. That's all determined by the behavior of the proteins down at the molecular level.

@oggyreidmore

5 жыл бұрын

Exactly. When I said flowers "found" the best solution, I didn't mean consciously. I meant in the sense that a repeating computer algorithm might "find" the best solution to something if it cycles through the problem enough times.

@SuperQuwertz

5 жыл бұрын

Then every plant should have this structure. But they dont.

@brokenwave6125

5 жыл бұрын

@@SuperQuwertz not every plant has the same goal... Other plants with different goals find other uncannily mathematical sequences. Like how leaves grow on a tree for example.

@SuperQuwertz

5 жыл бұрын

@@brokenwave6125 the goal should be to survive. therefore after millions of years everything should be more or less equal. there is no need to be "beautiful". bees dont care about the perfect geometry of a flower. Or do you think the lotus is repelling dirt and is using perfect geometry in order to survive better?

So flowers are smarter than me, thanks.

@IETCHX69

5 жыл бұрын

..."me (period )Thanks capital " T " .

@johnnyknight6447

4 жыл бұрын

your "stupidity" is a learned behavior. GL

@Kyle-li8wi

4 жыл бұрын

Selective processes are the way to go!

@alveolate

4 жыл бұрын

flowers had 250 million years of trial and error to get phi. you basically understood 250 million years of work in about 15mins.

@toatahu2003

4 жыл бұрын

No, flowers are just like that after billions of years of Evolutionary trial and error. The real question is why is the universe so specifically, logically ordered such that this is the universal best ration of flower petals, among other things...

This is the most *brilliant* and *fascinating* video on Phi that I’ve ever seen in my life!! Well done!!

Watched all this and really enjoyed it...now I'm going to watch again and code my own version. I love when mathematical concepts show some element of symmetry or beauty when you never expect it.

"I'm not saying flowers are thinking about this", ibelieve you

Next time I get in a fight with a romantic partner, I’m going to shout “(1+/- sqrt(5))/2 “ to let them know JUST HOW IRRATIONAL they’re being.

@jewelsbarbie

4 жыл бұрын

*Bahaha* 👏🏼😂 me too!

@CosmicEpiphany

4 жыл бұрын

Might want to save that for a time when they are being the most irrational.

@sahelipaul8436

4 жыл бұрын

Please don't spoil the comment section by making such bad jokes

@General12th

4 жыл бұрын

But what if you never have another romantic partner ever again?

@DanielDF11

4 жыл бұрын

I was wondering if anyone in the comments was going to connect this to people and how they act in relationships. Do I really need to elaborate?

what a time to be alive!! thank you for this video, it actually helps my eyes understand what I been seeing... I've been seeing the spirals but my eyes used to readjust focus (which hurts), but this model lets me know my eyes weren't broken

I've had a backstage obsession with the golden ratios (and other numbers/mathematical anomalies), and this blew my mind. Thank you sir

I had already heard that the golden ratio was found everywhere in nature, but I never could understand why. This video made me see why! I think that the explanation is thorough, understandable and very well presented. Great video!

Ben (or "Mr Sparks" as he was to me) was my teacher for the first year of A Level maths. Sadly he wasn't there for my second year. Needless to say I did a lot better the first year than the second. He was one of the best teachers I ever had, and that's a pretty high bar!

@SparksMaths

Жыл бұрын

Hi James!

Oh boy! I'm ready to watch a nice video and learn about the golden ratio! I sure do hope there aren't any references to this Japanese cartoon in the comment section!

@sinbad4696

3 жыл бұрын

😂😂😂😂😂😂😂😂

@victorthevictor1976

3 жыл бұрын

Username checks out

@diavoloisamasochist4986

3 жыл бұрын

@@sinbad4696 omg chica I am a huge fan

@sinbad4696

3 жыл бұрын

@@diavoloisamasochist4986 aren't you miyuki's dad omg i'm a huge fan

@diavoloisamasochist4986

3 жыл бұрын

@@sinbad4696 YES! I AM!

THANK YOU for that snap frame, it made it a lot easier to stop on the frame to study it a bit

"Hey are you the gold ratio, because you're behaving extremely irrational right now"

@involute2831

6 жыл бұрын

Probably not your go-to pickup line, not gonna lie

@UnderScorePT

6 жыл бұрын

Daamn

@Sonny_McMacsson

6 жыл бұрын

Message from the Save the Adverb Foundation: *irrationally

@CraftQueenJr

6 жыл бұрын

embustero71 where can I join the Save the Adverb Foundation. I am from the Adjective Protection Agency.

@SRPhantoms

6 жыл бұрын

hey are you a fire alarm, because you are loud and annoying

Continued fractions are always fun. They make me wonder if a musical interval of 1/phi should be the harshest possible ratio, not the tritone (which is 1/sqrt(2)). But if you try to make 1/phi, what you hear is a sharp minor sixth, closely approximated by 8 semitones and 33 cents. The next question is on the 36 tone scale, where would this golden interval resolve?

This is amazing!! I always wanted to know a bit about the sunflower patterns. Can you post the GeoGebra file of the simulation... It would be great. Thank you.

Excellent video!! What makes this video so great is the way quadratic equation is solved, so slick. This is why I watch this channel!

So this was the point of lesson 5... Arigato, Gyro...

@hollandgraves1912

5 жыл бұрын

Darkness! Get back to Kazuma!

@mickginny6075

5 жыл бұрын

It took 6 comments to get to a JoJo reference. It’s a new record

@abbacchio2502

5 жыл бұрын

"Arigatou, Gyro..." "I think that's all I can say" ~Johnny Joestar

@memelordmarcus

4 жыл бұрын

unexpected jojo

flower seem to be better at math than me.

@thumper8684

6 жыл бұрын

They use an evolutionary algorithm. They do not know that they are solving a maths problem, but nature put in the constraints and they just blasted out that optimum. Maybe there were Root Two seeder sunflowers kicking around for a while before their Golden Ratio cousins took over.

@idlingdove5217

6 жыл бұрын

+Thumper Maybe you're right. But if it's the Root Two seeders followed by the Golden Ratios, who's next? Maybe the Eulers? (Check out the evolution at 1/e, or around 0.36788, where the seeding looks maybe even more random than at 0.618...)

@IgnusNilsen

6 жыл бұрын

Its biology whose smarter then u

@brcoutme

6 жыл бұрын

idling dove nice thinking on evolution, poor thinking mathematically. Did you even watch the video the Golden ratio was the ultimate randomness factor because it is the 1/(1+1/(1+...)))... so 1/e would be less 'irrational'. On the other hand their could have been 1/e sunflowers already that also got beaten out by the Golden Ratio ones. Also maybe some sunflowers are closer to the golden ratio than others and they are still evolving towards that perfect design (only to go extinct due to completely unrelated climate or ecological changes).

@geoff7936

6 жыл бұрын

I believe there are still some plants that use a slightly less irrational number in the angular spacing of their branches. Maybe evolution is satisfied or is still busy optimising

13:39 right around there you can see it unwrapping as it becomes 1/2.

I have a pic of a sunflower that demonstrates the golden ratio extraordinarily well... Just looks really amazing. Started noticing the other flowers in that batch had some of that also.

That is one simple, clear and truly amazing video you put together here Brady !

0:23 that joke, though

Ty for zooming through all the possible curves at the end, very illustrative

Ben is my favourite contributor to this channel. All his videos are fantastic

I've studied about the golden ratio many times and nothing in this video is new to me, but this is an amazing summary and really blew my mind. I love it!

@numberphile

6 жыл бұрын

Cheers

@hariman7727

5 жыл бұрын

Now if only I could actually figure out the arcane nightmare that is Quadratic Equations as explained by a rather garbage textbook, I could at least say I had that much in math.

@dickrichads1979

5 жыл бұрын

@@hariman7727 its easy, watch a video about it

This exchange was absolutely captivating; consequently, I was completely entranced by the lecturer's presentation of the subject matter. I could listen to this man speak about mathematics all day. These statements are coming from someone who has historically always had a feeling of dread when approaching math. This man's enthusiasm overrode the dread and made me want to learn and participate.

One of the coolest videos on Phi I have seen. Hats off!

The Golden ratio is our lesson for this semester. Thanks for the clear explanation ☺️

My most excellent digital guitar effects pedal has a setting on it called the "Golden Ratio" (related to the number and style of delayed repeats to an input tone) and I always wondered why it sounded so musical and pleasing no matter what I played into it. I got a lot out of this video and even broke out my trusty hp 12c calculator to follow along. Thanks. Am a new subscriber.

Great video. I really dislike the rectangle explanation of the golden ratio, it makes it seem so arbitrarily. Saying "it's the least rational number" is a much better way of highlighting its importance.

@rosiefay7283

6 жыл бұрын

I think that must be a legacy from the Ancient Greek mathematicians. For them, numbers were for quantifying lengths (and areas and volumes), so the shape or aspect ratio of a rectangle comes out naturally.

This is a wonderful explanation of irrational numbers, and it gives me an entirely different perspective on "the golden ratio". Thank you!

just WHOW. best video ive seen today. wont be able to get it out from mind and keep thinking about how gorgeously this man explains.

completing the square - man, that's throwing back the years to my school life

the pattern of the last flower animation was 1, 5, 4, 3, 5, 2, 2, 5, 3, 4, 5, 1 amount of spokes

I first came across this property of phi in golden angle-based MRI approaches as part of my doctoral studies. The basic idea is that when you're scanning, the thing you're scanning is evolving with time, but you can only scan one point in k-space at a time. (k-space is a spatial frequency space, but you could think of it as real/image space without losing the take-home here.) If you want to get the "most uncorrelated" data and therefore use your scan time most wisely, or if you want to be able to bin your scans and create a timeseries that "shares" data in a window as it evolves, you should scan in golden angle spirals.

I can't explain what I've felt watching this video... simply amazing, thanks a lot

The bumps on my popcorn ceiling were moving similarly to 3:30 when I was on shrooms 🤔

You built the image on a counter clock wise build . The golden ratio presents a build that is identical in a clockwise progression as well. (+/- √5) ( I feel kinda number numb)

Thank you, finally this is explained easily! They always mention this in math classes and nature shows, and I've always seen this explanation of cutting golden rectangles into pieces forming a spiral that looks nothing like a flower, and then some sort of a half-assed explanation of, "see, you can form a spiral with the golden rectangle, so spirals in nature contain golden ratios and fibonacci sequences," always leaving me thinking the golden spiral looks nothing like the spirals in sunflowers, and that any rectangle can be cut into a spiral, thus a totally useless explantion. Thank you for fixing this. Finally!

I need to learn more math. This actually is super interesting!. I've been lacking omitvation to learn triangles in highschool but these videos really motivate me to get to know the intrications of our numeric system

I want an app that will let me do that spirally thing.

@mgregory22

5 жыл бұрын

I think they probably used Processing (processing.org)

@stanleydodds9

4 жыл бұрын

The app is called... just about any programming language. As an added bonus, they also lets you do every else that is computable.

@ponsi83

4 жыл бұрын

I‘m pretty sure you‘ll find something like that on Wolfram Demonstrations...

@JosueMartinez-ww1vj

4 жыл бұрын

I wonder why the hippies didn't use this video to represent hippiness?

@SexySnorlax

4 жыл бұрын

let an indian do it for 15$

I don't understand half of it but it sounds and looks cool! Nice video

Very well explained. It seems the seeds are most densely packed when they go around with this ratio. Nature knows how to maximise its efficiency! I forgot it was symbolized with a phi (capital or lower case?) and what its value was, but then it's not a number I have used for anything else other than as a curiosity to occasionally look up.

Excellent and very clear explanation of the particular irrationality of Phi, very illuminating!

I watched this high and I was changed forever

Thanks! I known this. And yet... Now I have the feeling I deeply understand it, which is quite different. This is the power of the Numberphile videos. So, thanks again

Thanks much prof Ben . I loved this video and i cant stop seeing it again n again

Authority is not given to you to deny the return of the King, Steward.

this is incredibly interesting, and explained very well.