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

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  • Опубликовано: 22 дек 2024

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  • @soranuareane
    @soranuareane 6 лет назад +4055

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

    • @acorn1014
      @acorn1014 6 лет назад +278

      π = 3;
      π += a bit;

    • @DarkwingD
      @DarkwingD 6 лет назад +145

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

    • @anselmschueler
      @anselmschueler 6 лет назад +64

      pi = pi + bit

    • @PhilerinoBTW
      @PhilerinoBTW 6 лет назад +58

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

    • @KauanRMKlein
      @KauanRMKlein 6 лет назад +13

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

  • @DhulstDirk
    @DhulstDirk 5 лет назад +1241

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

    • @ethann6573
      @ethann6573 4 года назад +10

      For me it was the sound dinosaurs that did it.

    • @RaineriHakkarainen
      @RaineriHakkarainen 3 года назад +4

      The golden ratio is 1,618

    • @p0tatobiden250
      @p0tatobiden250 Год назад

      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
      @justArandomfellar Год назад

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

    • @PC_Simo
      @PC_Simo Год назад +3

      @@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.

  • @ahobimo732
    @ahobimo732 5 лет назад +4240

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

    • @GH29111
      @GH29111 4 года назад +31

      Mark O did you go to school marko

    • @TempestGotThatTrash
      @TempestGotThatTrash 4 года назад +79

      Imchattingabsolutefuckingshit username checks out

    • @ahobimo732
      @ahobimo732 4 года назад +185

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

    • @gretsyuk1387
      @gretsyuk1387 4 года назад +89

      pyropulse pretty rude for no reason

    • @kakonya2994
      @kakonya2994 4 года назад +64

      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

  • @LMacNeill
    @LMacNeill 6 лет назад +808

    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
      @numberphile  6 лет назад +80

      Great. Glad you (sort of) liked it.

    • @abdiazizissa5706
      @abdiazizissa5706 6 лет назад +2

      .

    • @PhilBoswell
      @PhilBoswell 6 лет назад +9

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

    • @a_diamond
      @a_diamond 6 лет назад +2

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

    • @codemiesterbeats
      @codemiesterbeats 6 лет назад +3

      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.

  • @yeet3673
    @yeet3673 2 года назад +188

    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

    • @eugene7518
      @eugene7518 6 месяцев назад

      Why do they call it the golden ratio?

  • @allison5169
    @allison5169 5 лет назад +909

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

    • @niamhoconnor8986
      @niamhoconnor8986 4 года назад +3

      Nice

    • @zoklev
      @zoklev 4 года назад +3

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

    • @Xnoob545
      @Xnoob545 4 года назад

      400th like

    • @deletingthis00
      @deletingthis00 3 года назад +1

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

    • @mariafe7050
      @mariafe7050 3 года назад

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

  • @blacxthornE
    @blacxthornE 6 лет назад +4664

    This was one of the best Numberphile videos ever.

    • @math.mouraa
      @math.mouraa 6 лет назад +31

      Ersen Couldn't agree more

    • @MrPacoHamers
      @MrPacoHamers 6 лет назад +152

      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
      @limbridk 6 лет назад +32

      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
      @ultimateman1234 6 лет назад +11

      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
      @wierdalien1 6 лет назад +6

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

  • @huruey
    @huruey 5 лет назад +1997

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

    • @SCWood
      @SCWood 5 лет назад +110

      It uses the least irrational number: 1

    • @worldisfilledb
      @worldisfilledb 5 лет назад +11

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

    • @Good_Hot_Chocolate
      @Good_Hot_Chocolate 5 лет назад +78

      @@worldisfilledb how is nothing less irrational than something?

    • @rohancrawley4131
      @rohancrawley4131 5 лет назад +23

      @@Good_Hot_Chocolate Why should there be something

    • @nomadical95
      @nomadical95 5 лет назад +10

      @Dirty Sack it does noth exist

  • @steve1978ger
    @steve1978ger 4 года назад +1780

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

    • @progect3548
      @progect3548 3 года назад +2

      @Arbnora Vezaj Elsi

    • @ekananda9591
      @ekananda9591 3 года назад +5

      Lol

    • @ryanolsen294
      @ryanolsen294 3 года назад +44

      CS major?
      Counter strike major?

    • @Padeir0
      @Padeir0 3 года назад +78

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

    • @shmillsyshmillsy6624
      @shmillsyshmillsy6624 3 года назад +33

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

  • @yamomwasthebomb7159
    @yamomwasthebomb7159 6 лет назад +147

    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
      @simonshugar1651 6 лет назад +3

      r/iamverysmart

    • @iMutt-yy6vf
      @iMutt-yy6vf 6 лет назад +1

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

    • @gguioa
      @gguioa 6 лет назад +2

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

    • @SSM24_
      @SSM24_ 6 лет назад +1

      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.

  • @hliask903
    @hliask903 6 лет назад +584

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

    • @Timbot2002
      @Timbot2002 6 лет назад +11

      And killing it at maths

    • @MrSam1804
      @MrSam1804 5 лет назад +10

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

    • @Lyle-xc9pg
      @Lyle-xc9pg 5 лет назад +2

      I said that too!

    • @sirbillius
      @sirbillius 5 лет назад +5

      Hlias K
      Gosh damn it. I knew he looked like someone.

    • @marloucabalquinto7514
      @marloucabalquinto7514 5 лет назад +3

      *Gandalf joined the chat

  • @staculette1919
    @staculette1919 4 года назад +52

    "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*

  • @dalitas
    @dalitas 6 лет назад +589

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

  • @Joel-co3xl
    @Joel-co3xl 6 лет назад +649

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

    • @alpo789
      @alpo789 6 лет назад +31

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

    • @E1craZ4life
      @E1craZ4life 6 лет назад +8

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

    • @vitakyo982
      @vitakyo982 6 лет назад +12

      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
      @alexpotts6520 6 лет назад +27

      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
      @grex2595 6 лет назад +11

      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).

  • @gosugosu1280
    @gosugosu1280 4 года назад +65

    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!

  • @fraiseld2183
    @fraiseld2183 6 лет назад +909

    Instructions Unclear. Accidentally produced an infinite spin.

  • @GuerreroMisterioso95
    @GuerreroMisterioso95 6 лет назад +1793

    Believe in the rotation, Johnny.

    • @Mushin367
      @Mushin367 5 лет назад +123

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

    • @sarabeatriz5569
      @sarabeatriz5569 5 лет назад +82

      GYROOOOOOO

    • @calamari2875
      @calamari2875 5 лет назад +89

      arigato, gyro

    • @franciscopetrucci
      @franciscopetrucci 5 лет назад +61

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

    • @superiorf
      @superiorf 5 лет назад +53

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

  • @aysoodaagh3167
    @aysoodaagh3167 3 года назад +95

    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
      @fibonaccisequins4637 2 года назад +4

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

    • @eugene7518
      @eugene7518 4 месяца назад

      Who named it the golden ratio?

  • @meghanstrudwick4100
    @meghanstrudwick4100 5 лет назад +348

    "Flowers can cancel fractions"
    - Ben Sparks, 2018

  • @KimAlexisG
    @KimAlexisG 5 лет назад +191

    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
      @TimpBizkit Год назад +2

      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.

  • @hollyhensler5589
    @hollyhensler5589 4 года назад +44

    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!

  • @liborkundrat185
    @liborkundrat185 6 лет назад +803

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

    • @bgoggin88
      @bgoggin88 6 лет назад +6

      Libor Kundrát yes.

    • @celinak5062
      @celinak5062 6 лет назад

      Libor Kundrát same

    • @MamboBean343
      @MamboBean343 6 лет назад +11

      slower, or looping?

    • @liborkundrat185
      @liborkundrat185 6 лет назад +22

      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
      @retepaskab 6 лет назад +9

      Make it 10 hours.

  • @lindsayhout673
    @lindsayhout673 5 лет назад +49

    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!

  • @roskoced6598
    @roskoced6598 4 месяца назад +2

    I don't know how many times I watched this episode by now but it's probably my all time favourite because of the beautiful flower seeds animation and the mindblowing awesomeness of thinking about irrational numbers in terms of how irrational they are.

  • @conordoran8273
    @conordoran8273 6 лет назад +32

    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
      @numberphile  6 лет назад +6

      Thanks and glad you enjoyed it.

  • @IvanIvan1974
    @IvanIvan1974 6 лет назад +255

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

  • @contessawillis
    @contessawillis 2 года назад +18

    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
      @marshallpartington Год назад +1

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

  • @jakeroosenbloom
    @jakeroosenbloom 6 лет назад +962

    Best Numberphile video in a while

    • @thesmallestatom
      @thesmallestatom 6 лет назад +3

      Easily.

    • @ultimateman1234
      @ultimateman1234 6 лет назад +6

      Absolutely brilliant.

    • @DBFIU
      @DBFIU 6 лет назад +5

      Agreed

    • @TheBelrick
      @TheBelrick 6 лет назад +2

      Denethor is that you?

    • @cuter.
      @cuter. 6 лет назад

      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 RUclips?

  • @GetMeThere1
    @GetMeThere1 6 лет назад +155

    Best Numberphile video yet!

    • @cuter.
      @cuter. 6 лет назад +1

      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 RUclips?

    • @eugene7518
      @eugene7518 6 месяцев назад

      Why do they call it the golden ratio

  • @micaelaroyo4837
    @micaelaroyo4837 4 года назад +20

    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!

  • @flyingchineseman6901
    @flyingchineseman6901 6 лет назад +458

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

  • @Hierophant750K
    @Hierophant750K 6 лет назад +102

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

    • @numberphile
      @numberphile  6 лет назад +5

      Here’s his playlist: bit.ly/Sparks_Playlist

    • @eugene7518
      @eugene7518 4 месяца назад

      Who named it the golden ratio?

  • @quakeroats2007
    @quakeroats2007 3 года назад +68

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

  • @KidToyTesters
    @KidToyTesters 6 лет назад +603

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

    • @oscarpritzker6278
      @oscarpritzker6278 4 года назад +9

      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
      @dr.killakill960 4 года назад +6

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

    • @doublecircus
      @doublecircus 3 года назад +1

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

    • @oscarpritzker6278
      @oscarpritzker6278 3 года назад +1

      @@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
      @doublecircus 3 года назад

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

  • @MisterAppleEsq
    @MisterAppleEsq 6 лет назад +1578

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

    • @anybodynoname8767
      @anybodynoname8767 6 лет назад +108

      Mister Apple You have floweranimationmathsthingphobia?

    • @ctrlaltshift
      @ctrlaltshift 6 лет назад +44

      I want it as my screensaver.

    • @EchoHeo
      @EchoHeo 6 лет назад +53

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

    • @teckyify
      @teckyify 6 лет назад +19

      Sentinels from matrix

    • @jwrm22
      @jwrm22 6 лет назад +128

      It's more likely the music.

  • @ultragamer4465
    @ultragamer4465 5 лет назад +377

    *IF YOUR HEART WAVERS, DO NOT SHOOT*

  • @davidsweeney111
    @davidsweeney111 6 лет назад +1206

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

    • @ShoM1nam1moto
      @ShoM1nam1moto 6 лет назад +12

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

    • @Luftbubblan
      @Luftbubblan 6 лет назад +11

      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
      @andrewkelley7062 6 лет назад +1

      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
      @galesx95 6 лет назад +2

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

    • @andrewkelley7062
      @andrewkelley7062 6 лет назад

      just do the equation I have in my post

  • @user-wg4hz3bk4f
    @user-wg4hz3bk4f 6 лет назад +393

    So flowers are smarter than me, thanks.

    • @IETCHX69
      @IETCHX69 5 лет назад +7

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

    • @johnnyknight6447
      @johnnyknight6447 5 лет назад +4

      your "stupidity" is a learned behavior. GL

    • @Kyle-li8wi
      @Kyle-li8wi 5 лет назад +1

      Selective processes are the way to go!

    • @alveolate
      @alveolate 5 лет назад +20

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

    • @toatahu2003
      @toatahu2003 5 лет назад +7

      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...

  • @Fun_maths
    @Fun_maths 4 года назад +27

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

  • @oggyreidmore
    @oggyreidmore 6 лет назад +1009

    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
      @General12th 6 лет назад +76

      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
      @oggyreidmore 6 лет назад +226

      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
      @SuperQuwertz 6 лет назад +23

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

    • @brokenwave6125
      @brokenwave6125 5 лет назад +139

      @@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
      @SuperQuwertz 5 лет назад +20

      @@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?

  • @gregs_on_tracks
    @gregs_on_tracks 5 лет назад +503

    The best Acid trip I ever had on youtube.

    • @momo-dm3rw
      @momo-dm3rw 5 лет назад +3

      I believe you.

    • @AbhinavTallapally
      @AbhinavTallapally 5 лет назад +4

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

    • @PanduPoluan
      @PanduPoluan 5 лет назад +9

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

    • @Kakerate2
      @Kakerate2 5 лет назад +6

      i watched this tripping and it was entertaining af

    • @simohayha6031
      @simohayha6031 5 лет назад

      Do mandelbrot zoom in

  • @DouglasButner
    @DouglasButner 4 года назад +96

    Nature: *Exists*
    Mathematicians: _That's Irrational_

    • @jhomastefferson3693
      @jhomastefferson3693 3 года назад +11

      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
      @DouglasButner 3 года назад +1

      @@jhomastefferson3693 thanks for explaining

    • @DouglasButner
      @DouglasButner 3 года назад +1

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

    • @eugene7518
      @eugene7518 4 месяца назад

      Who named it the golden ratio?

  • @matteogauthier7750
    @matteogauthier7750 6 лет назад +9

    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!

  • @sciencecompliance235
    @sciencecompliance235 6 лет назад +260

    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
      @jewelsbarbie 5 лет назад

      *Bahaha* 👏🏼😂 me too!

    • @CosmicEpiphany
      @CosmicEpiphany 5 лет назад +17

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

    • @sahelipaul8436
      @sahelipaul8436 4 года назад +4

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

    • @General12th
      @General12th 4 года назад +2

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

    • @DanielDF11
      @DanielDF11 4 года назад

      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?

  • @TheTimelyTurtle
    @TheTimelyTurtle 4 года назад +39

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

  • @jamesboultbee1353
    @jamesboultbee1353 5 лет назад +13

    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!

  • @BulletTheEnforcer
    @BulletTheEnforcer 5 лет назад +25

    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.

  • @jordandocherty5132
    @jordandocherty5132 5 лет назад +43

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

    • @sinbad4696
      @sinbad4696 4 года назад +4

      Nah gyro Zeppeli is better

    • @EaglePicking
      @EaglePicking 3 года назад

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

  • @NeoBoneGirl
    @NeoBoneGirl 6 лет назад +197

    The true power of lesson 5...

    • @alanlowen2766
      @alanlowen2766 3 года назад +3

      which lesson?

    • @r35ct12
      @r35ct12 3 года назад +8

      @@alanlowen2766 you probably wont get it

    • @emptyvending8964
      @emptyvending8964 3 года назад +16

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

    • @rhodesmusicofficial
      @rhodesmusicofficial 3 года назад

      GAH NOOO NO JOJOS IN MY MATH AAAAAAAAA

  • @abramthiessen8749
    @abramthiessen8749 6 лет назад +32

    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?

  • @HunnitAcreWoods
    @HunnitAcreWoods 5 лет назад +3

    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

  • @WannesMalfait
    @WannesMalfait 6 лет назад +344

    Lol the Parker square.

    • @MichaelLikvidator
      @MichaelLikvidator 6 лет назад +9

      Love such easter egg.

    • @wynarator
      @wynarator 6 лет назад +26

      Parker square will never die, love you guys :D

    • @Bellonging
      @Bellonging 6 лет назад +1

      It'll never be let goooo.

    • @TKNinja37
      @TKNinja37 6 лет назад +4

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

    • @arturzathas499
      @arturzathas499 6 лет назад +1

      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

  • @z-beeblebrox
    @z-beeblebrox 6 лет назад +268

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

    • @involute2831
      @involute2831 6 лет назад +28

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

    • @UnderScorePT
      @UnderScorePT 6 лет назад +2

      Daamn

    • @Sonny_McMacsson
      @Sonny_McMacsson 6 лет назад +8

      Message from the Save the Adverb Foundation:
      *irrationally

    • @CraftQueenJr
      @CraftQueenJr 6 лет назад +7

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

    • @SRPhantoms
      @SRPhantoms 6 лет назад +6

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

  • @christophercaron3042
    @christophercaron3042 4 года назад +21

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

  • @ayo2036
    @ayo2036 6 лет назад +16

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

  • @OlbaidFractalium
    @OlbaidFractalium 6 лет назад +887

    flower seem to be better at math than me.

    • @thumper8684
      @thumper8684 6 лет назад +51

      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
      @idlingdove5217 6 лет назад +7

      +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
      @IgnusNilsen 6 лет назад

      Its biology whose smarter then u

    • @brcoutme
      @brcoutme 6 лет назад +5

      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
      @geoff7936 6 лет назад +4

      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

  • @coloradolove7957
    @coloradolove7957 2 года назад +5

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

  • @Denpasuzy
    @Denpasuzy 6 лет назад +241

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

    • @hollandgraves1912
      @hollandgraves1912 5 лет назад +3

      Darkness! Get back to Kazuma!

    • @mickginny6075
      @mickginny6075 5 лет назад +17

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

    • @abbacchio2502
      @abbacchio2502 5 лет назад +2

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

    • @memelordmarcus
      @memelordmarcus 5 лет назад

      unexpected jojo

  • @AmateurSuperFan
    @AmateurSuperFan 6 лет назад +23

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

  • @telejeff
    @telejeff 2 года назад +3

    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!

  • @madichelp0
    @madichelp0 6 лет назад +22

    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
      @rosiefay7283 6 лет назад +4

      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.

  • @HansLemurson
    @HansLemurson 6 лет назад +216

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

    • @mgregory22
      @mgregory22 5 лет назад +3

      I think they probably used Processing (processing.org)

    • @stanleydodds9
      @stanleydodds9 5 лет назад +23

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

    • @ponsi83
      @ponsi83 5 лет назад +1

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

    • @JosueMartinez-ww1vj
      @JosueMartinez-ww1vj 5 лет назад +1

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

    • @SexySnorlax
      @SexySnorlax 5 лет назад +1

      let an indian do it for 15$

  • @joshsvoss
    @joshsvoss 5 лет назад +6

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

  • @MasterChakra7
    @MasterChakra7 6 лет назад +6

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

  • @blabby102
    @blabby102 6 лет назад +7

    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
      @numberphile  6 лет назад +1

      Cheers

    • @hariman7727
      @hariman7727 6 лет назад

      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
      @dickrichads1979 6 лет назад

      @@hariman7727 its easy, watch a video about it

    • @eugene7518
      @eugene7518 4 месяца назад

      Who named it the golden ratio?

    • @eugene7518
      @eugene7518 4 месяца назад

      ​@numberphile who named it the golden ratio?

  • @questionable-cf1tt
    @questionable-cf1tt 5 лет назад +2

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

  • @hj8607
    @hj8607 5 лет назад +9

    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)

  • @ryanrichardson1169
    @ryanrichardson1169 3 года назад +6

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

    • @eugene7518
      @eugene7518 4 месяца назад

      Who named it the golden ratio

  • @Twisted_Code
    @Twisted_Code Год назад +1

    I notice I'm not the only one to have replayed around 10:47 to catch the Parker Square that was flashed on the screen momentarily
    While it's not the most replayed segment of the video, it is one of the hills on the graph that shows above the seek bar.

  • @dusty6299
    @dusty6299 5 лет назад +82

    So basically a flower is better in math then me. Nice to know.

    • @Kathayne636
      @Kathayne636 4 года назад

      *than I.

    • @johantheking7874
      @johantheking7874 4 года назад +5

      D. It’s funny because that’s actually wrong

    • @chappie3642
      @chappie3642 4 года назад

      Take the L

    • @jonasa.3040
      @jonasa.3040 4 года назад +1

      Your whole body is based off of 1.618

    • @kkounal974
      @kkounal974 3 года назад +2

      I mean evolution did the job but ok.

  • @tex73smith
    @tex73smith 3 года назад +3

    I was horrible at math in schools but as I grew older I started to understand it better because I had to use it daily. I’m still no mathematician but I am fascinated by ratios and their capabilities.

  • @VivekYadav-ds8oz
    @VivekYadav-ds8oz 3 года назад +4

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

    • @eugene7518
      @eugene7518 4 месяца назад

      Who named it the golden ratio?

  • @diavoloisamasochist4986
    @diavoloisamasochist4986 4 года назад +180

    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!

  • @pondrthis1
    @pondrthis1 3 года назад +3

    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.

  • @AlonsoRules
    @AlonsoRules 6 лет назад +19

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

  • @justcarcrazy
    @justcarcrazy 6 лет назад +52

    All I could think of was "On the Run" by Pink Floyd. How irrational is that?

    • @johnpossum556
      @johnpossum556 6 лет назад +15

      There was some great math in that album. The bossa nova beat (7/8) was used. The heartbeat also continues the entire album. It was all done manually before they had computers to sync it all up. You want to meet a genius behind that google Alan Parsons.

    • @jadegecko
      @jadegecko 6 лет назад +3

      Same here. Did you ever see the old Arthur C Clarke documentary "Fractals: The Colors of Infinity?" He actually used some Pink Floyd / David Gilmour music in that.

    • @Oleander410
      @Oleander410 6 лет назад

      that's me, HaHaHaaaaaa!

  • @user-rd7jv4du1w
    @user-rd7jv4du1w 5 лет назад +246

    The fact that there's JoJo comments on a math video

    • @flux202
      @flux202 4 года назад +7

      JoJo?

    • @screamsinrussian5773
      @screamsinrussian5773 4 года назад +17

      is disgusting
      Always have to plug in your shitty Annie Mays into something that is not even related to your damn Taiwanese cartoon, don't you

    • @georgeruiz9211
      @georgeruiz9211 4 года назад +49

      @@screamsinrussian5773 Its Anime, Its a Japanese art style, most importantly, ITS A JOKE

    • @felixargyle1285
      @felixargyle1285 4 года назад +26

      @@screamsinrussian5773 I can your parents were comedians because you sir, are a joke

    • @moonrock07
      @moonrock07 4 года назад +13

      @[screams in Russian] Anime is Japanese not Taiwanese you racist bonehead

  • @tristramgordon8252
    @tristramgordon8252 5 лет назад +28

    I'm curious, do these numbers apply to music, or sound waves, as in perfect fifths, thirds, 7ths, etc?

    • @PanduPoluan
      @PanduPoluan 5 лет назад +20

      Serious answer: Not really. Music is related to harmonics. which are themselves truly rational.

    • @rhumgyhnofficial477
      @rhumgyhnofficial477 5 лет назад

      ... Sounds and the alphabet apply to Numbers....

    • @charlotteskiftun753
      @charlotteskiftun753 4 года назад +2

      Absolutely.....play the TORAH... each Hebrew letter is a musical note

    • @kakonya2994
      @kakonya2994 4 года назад

      Have you watched the video about the length of sound waves and harmonies?

    • @sanderwals3689
      @sanderwals3689 4 года назад +3

      If the golden ratio is the most irrational number, it would be the less harmonious, most out of tune interval, that can possibly exist.

  • @nazrael8826
    @nazrael8826 4 года назад +19

    _Lesson 4: Pay your respects_

  • @fifthwallrenaissance3433
    @fifthwallrenaissance3433 5 лет назад +3

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

  • @f1at111
    @f1at111 5 лет назад +5

    So, in case you missed it, the perfect design is actually a toroid or torus. Look up magnetic vortices also. It is life itself and can be seen un one cones, flowers, trees (hyperbaloids), DNA, and many other things in nature. Including all forms of energy. And we have one as well as all atoms.

  • @ken-je9oi
    @ken-je9oi 3 года назад +4

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

  • @taatyavinchoo
    @taatyavinchoo Год назад +1

    Andy serkis talking about golden ratio is my favorite thing about this channel

  • @TheDaedalus07o
    @TheDaedalus07o 6 лет назад +16

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

  • @progect3548
    @progect3548 3 года назад +3

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

    • @eugene7518
      @eugene7518 4 месяца назад

      Who named it the golden ratio

  • @jaimecassar8427
    @jaimecassar8427 5 лет назад +1

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

  • @ykeim
    @ykeim 6 лет назад +10

    Want to try myself ! Any tips for using GeoGebra?

  • @rickseiden1
    @rickseiden1 6 лет назад +56

    "Stop trying to make Parker Square a thing!"

  • @NueUzrnem
    @NueUzrnem 3 года назад +1

    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.

  • @jojobod
    @jojobod 5 лет назад +49

    YOU HAVE TO SAY “THERE’S NO WAY I CAN DO THIS!” 4 TIMES!

  • @tanujgangrade
    @tanujgangrade 5 лет назад +4

    Any way the flower seeds design emulator can be used publicly? Like through an app or downloaded or coded? I loved the way it represents any turn!

  • @jamesparkersculpture
    @jamesparkersculpture Год назад +1

    I've just finished a sculpture design which relies on spirals consisting of sequential fibonacci numbers. It was a massive challenge because of the fact that the seed positions are so irrational. I got a bit of a shock when I figured out the lowest common denominator of 8,13 and 21! The completed sculpture will be worth the effort.

  • @VondaInWonderland
    @VondaInWonderland 5 лет назад +58

    Now I feel like I need to plant my garden in a Fibonacci spiral ♥

    • @BuhBaBiBeBo
      @BuhBaBiBeBo 3 года назад +1

      The golden rectangle as well :D

    • @VondaInWonderland
      @VondaInWonderland 3 года назад

      @@BuhBaBiBeBo Indeed!!! That's what I wound up doing ♥

  • @WillyKillya
    @WillyKillya 5 лет назад +3

    It was so cool to see a computer generation really explaining how numbers relate to Nature, it just feels so right

  • @jewelsbarbie
    @jewelsbarbie 5 лет назад +1

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

  • @blafoon93
    @blafoon93 4 года назад +3

    The mathematical explanation was great! Better than anything else I have been told about the golden ratio yet. It leaves just a small question in regards to seed packing. Phi is no doubt the most efficient number to pack seeds in a 2 dimensional plane but plants do have 3 dimensions and a sphere would certainly be even more efficient and provide a higher density of seeds. There are loads of spherical flowers and seed containers but on average they seem to be in the minority. I wonder what other things plants have to 'keep in mind' that spherical seed packing is less distributed than using the golden ratio.

    • @stevenmiller7731
      @stevenmiller7731 Год назад +1

      Pollinators i.e. insects etc. would not be able to reach the interior blossoms of the sphere. So, many less pollinated/fertilized seeds would be produced, and that would be a waste of the plant's energy. Very inefficient for survival and evolutionary success.

    • @PC_Simo
      @PC_Simo Год назад

      @@stevenmiller7731 That’s very true 👍🏻.

  • @tristanridley1601
    @tristanridley1601 5 лет назад +3

    I have never found the golden ratio interesting before (hence not watching this video for over a year).
    This status as the number that's worst approximated by any fraction, IE the most irrational number suddenly makes me care. Very cool.
    I also absolutely love the relationship with root 2.

  • @breakthrough3091
    @breakthrough3091 5 лет назад +2

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

  • @benjaminbustamante7924
    @benjaminbustamante7924 4 года назад +6

    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

  • @vincent-ls9lz
    @vincent-ls9lz 5 лет назад +8

    this is incredibly interesting, and explained very well.