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Examples of Fibonacci Numbers in Nature

scienceray.com — This is a list of examples of Fibonacci Sequence in nature

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  • monicazir, on 05/17/2008, -1/+68So, WHY does nature find it efficient and useful to grow things this way? I know why a circle is a good form for bubbles( resulting in 3.14...pi), so there has to be a purpose for this calculation inherent in a physical process... I don't think it's any more magical than is the difficulty in conceptualizing the transcendental numbers or the trig functions that ultimately have to be calculated as limits but approximated in the practical every day measurements....
    • empiric, on 05/17/2008, -16/+0Okay, then, why?

      Weird how you ask a question like it's the answer.
      • jjb123, on 05/17/2008, -0/+7He didn't, he just stated he knows why circles are preferred but not Fibonacci numbers.
        • empiric, on 05/17/2008, -8/+0...while adding by implication the presumption it's simply "nature", as the sentence itself confesses he has no basis to think so.

          Also known as the logical fallacy of "begging the question". Seriously, the average Digger would agree 1=2 if that were a necessary premise of an atheistic argument.

    • endlessoul, on 05/17/2008, -8/+2I agree. However, the actual number of 1.618 seems off to me. It feels like our number system must be wrong in some way for this to happen.

      Regardless, all animal life on Earth is related in some way, so this correlates with the ratios of different species.
      • acetv, on 05/17/2008, -0/+14The existence of transcendental numbers implies that the number system is wrong? It doesn't make phi (for example) any less of a number. I'd be more concerned if we had a number system that represented how many apples you buy as a non-terminating decimal.
        • rrbest, on 05/18/2008, -2/+1But if that was our number system, you would be used to it and feel you understood it enough to not be concerned about it.
        • acetv, on 05/18/2008, -0/+1Well, yes, but it sure would be unwieldy, wouldn't it? The efficiency sacrificed to represent phi simply (for example, "10" in base-phi) for everyday use overshadows any possible gain -- if you can even think of one! That should give you some idea why our number system is as it is; it's simple and efficient for many tasks.
      • uhhNo, on 05/17/2008, -4/+2Step 1: x = 0.618
        Step 2: take x inverse
        Step 3: subtract 1
        Step 4: compare with the original number
        Step 5: note it's equality
        Step 6: ???
        Step 7: Profit!!!
    • hiPpymIck, on 05/17/2008, -1/+6its used in architecture
      because a room with those proportions looks/feels 'right'
      • matriculated, on 05/17/2008, -0/+3Not only architecture: most designs from paintings, graphic design, the rule of thirds used in photography, etc.
    • highlyhigh, on 05/17/2008, -9/+0why do you assume that the nature finds this process to be efficient and usueful? maybe it's got no choice but stuck in this logic due to physical laws. maybe it's ultimate goal is to eliminate uniformity and do away with this number- creating life as diverse as chaos itself. i'm just saying, don't assume why nature uses this ratio.
    • sega01, on 05/17/2008, -15/+5Perhaps it was designed? I think that most people (including Evolutionists) should admit that this in particular (at least at first glance) points more towards Creation (young or old earth) than Evolution by chance.
      • TokenBlack, on 05/18/2008, -1/+3I respect your decision that it might be the work of your God, but it's most likely not. How can something that is prevalent in nature automatically be accredited to something that we cannot prove?
    • MxM111, on 05/17/2008, -3/+11I always was puzzled with people making hoopla about this golden ratio. Even if some ratio is very roughly 1.6. like the ratio between the length and width of face, they say: Oh! Behold The Golden Ratio! How do they know that it was intended to be 1.618 and not pi/2?
      • MeHow, on 05/17/2008, -3/+12Because if you take the limit of that sequence it equals 1.618... not pi/2
        • MxM111, on 05/19/2008, -0/+1But how does it relate to face ratio?
      • lamiaconfitor, on 05/18/2008, -0/+6But if there is a pattern and i don't immediately see why, it HAS to be magic! why are you oppressing my belief structure?
    • moush, on 05/18/2008, -0/+3I guess evolution likes numbers too.
      • lamiaconfitor, on 05/18/2008, -1/+3or nature does. dont start treating "evolution" as if is "God" then you are totally missing the point. Evolution is not sentient, and math does not prove that sentient beings are governing the laws of physics.
    • denn2009, on 05/18/2008, -2/+2I've heard the Fibonacci Sequence allows for the most efficient collection of sunlight by the leaves of the trees. I don't know if that is true or not, but I said it was in a 10th grade math project presentation on phi, golden ratio, etc. It could explain why evolution has led to so many examples in nature.
    • rlbond86, on 05/18/2008, -0/+1Somehow, the way DNA works, it must be more efficient to follow an X[n]=X[n-1]+X[n-2] pattern than the pattern of doubling repeatedly in plant and animal growth. It's not a coincidence we see it as beauty; our DNA has the Fibonacci sequence built in.
  • Snokage, on 05/17/2008, -54/+12its unbelievable that everything is connected, and yet people wanna deny the possiblity of a creator? i don't understand, it can't be chance.
    • evilcaptain, on 05/17/2008, -4/+22why not?
      who created him?
      Isn't it better to say that we don't know yet, than to just say "god did it"
      Most of the "God did it" things through history, turned out to be "God isn't anywhere" :)
      • FutureSandwhich, on 05/17/2008, -4/+6Man is the creator of math.
        • consoneo, on 05/17/2008, -0/+8That may be true, but it is only a measurement term... that's just like saying "Man is the creator of time." Sure we are, but the delays that we measure with our "time" is still there whether or not we are able to measure it. Just like distances are still there whether or not we are able to measure them. Though, they may be viewable in many different ways, through different dimensions.

        • GawtMilk, on 05/18/2008, -2/+3@consoneo

          That's only partially correct. Years are not man-made, it's the time it takes the Earth to travel around the Sun.
        • evilcaptain, on 05/18/2008, -0/+1
          "Alan Watts - Time & The More It Changes "
          Alan describes the arbitrariness of the human made frames of reference.
          It's 51 minutes; if you search to 4m50s to get right to it.
          I Really think it's better from the beginning as it can be a really horizon broadening.
          http://video.google.com/videoplay?docid=1639135737 ...
      • Snokage, on 05/17/2008, -8/+4yes know one knows for sure. But one can have Faith, and theres nothing wrong with that. either way, I don't even wanna go down that path,.

        Man created Math? i dont enderstand where your going with that? so what? the numbers "created" only referance things not created by man...its like so we call large furry animals with four legs and a mouth a bear.
      • evilcaptain, on 05/17/2008, -0/+4I agree in part about the no one knows, but believing something without a reason sounds stupid to me.
        It also could stop any further study into the truth of something because you have a best guess that fits your present knowledge. That is also stupid.
        I've never had faith in anything, in my adult life, without a valid, logical reason for it. Could religion be a remnant of the faith we have in our parents to tell us the truth, when we were too young to formulate our own logical conclusions ?
      • Snokage, on 05/17/2008, -5/+1Saying you have never had faith, simply isn't true, even for silly things like having faith that your car will get you to work on time is an example of faith, but i understand what you trying to say, i just wanted to nit pick.
        and yeah, we'll find out whats true and what not when we die.
        i more or less found that arguements about faith go in huge circles, so i agree that our views on the things that surround us to be different. Can we get back to posting about how much we hate hillary : P
        • evilcaptain, on 05/17/2008, -0/+3I hope my car gets there on time. What leap of faith over which gap in the logic am I supposed to be making?
        • ClemsonPoker, on 05/18/2008, -0/+3That's not faith. That's a reasonable conclusion from the evidence that my car has gotten me to work on time 9 times out of 10 and the other 10% were my fault (left too late, forgot something, etc.).


      • Pritchard, on 05/18/2008, -0/+3I don't have faith that my car will get me to work on time. I base it on calculus. Yet again, ignorance turns you to faith. For those of you wondering about the calculus, consider the values we have to keep on hand:

        Distance from home to work
        Traffic Levels
        Probability of stopping for gas
        Road/Highway Transport
        Chances that the car is going to break down and/or I am going to get killed by a meteor.
      • Naryuu, on 05/18/2008, -2/+1since when do evolutionists still ask the "who created God?" question. he always existed. its that simple. he didnt create himself -- he was just always there.
    • Chunken, on 05/17/2008, -6/+7Everything is also connected in the theory of evolution.
    • consoneo, on 05/17/2008, -2/+4Also, I don't understand why it can't be chance. It could very easily not be chance without a creator. If everything started from that theorized primordial ooze, and one item of life started it all off... then it would make very much sense for that one item's relations to be in every other item that sprang from it.
      • empiric, on 05/17/2008, -3/+2Except starting with "primordial ooze" just redirects the probability question. The physical laws resulting in the "ooze" would have to be finely-tuned to result in that, at the point of the Big Bang.

        http://en.wikipedia.org/wiki/Fine-tuned_universe

        You can still fall back on the absurdity mentioned, the anthropic principle, which "explains" it by reversing causality and saying the cause is explained by the effect's perceiving it, though--since I expect that will be your predisposition.
        • Lewie, on 05/18/2008, -0/+2Why does it have to be fine tuned? The universe could have always been this way. If it weren't, we wouldn't be here, or existence might take a drastically different shape. Primordial ooze would mark the beginning of life on this planet, nothing else. To say that there had to be certain conditions for this to happen is true, but we can't conclude that we're special or there is an intelligent designer from that.

          I'm not sure where you're going with your Fine-Tuning argument, but even in your link there are many criticisms of it.
        • empiric, on 05/18/2008, -1/+0@Lewie:

          Could have been, but the probability of low-probability things happening by chance is... low.

          But on a more direct level, the sole source of the motivation of the original poster, and you, responding in the way you have is that you think it's of low probability while you claim it's not of low probability.

          By the way, nice avatar. I'm sure the similarity of ours was just random chance. ;)
        • Lewie, on 05/19/2008, -0/+1Low probability doesn't have to mean impossible. And, we don't really know how low it is. We find life in some of the most harsh environments on earth. We've only really been to the moon, with only small samples of what's on mars. Who knows how prevalent life is. I agree that the beginning of life has a low probability, but given billions of years and ever changing environments, I think it would be more surprising if it hadn't happened more than once. The chances of winning the lotto is quite small, but it still happens regularly.

          I actually think about this topic once in a while. After learning about this theory in my Philosophy of Science class, it remains one of two reasons I don't totally object to the possibility of there being a god (the other is human consciousness). But I still can't use them as reasons to believe because there are reasonable naturalistic arguments. The sciences aren't that old, so I'd be willing to wait a few lifetimes to see whether science can explain it or not.

          And, I did notice our similar avatars, and almost pointed it out. :)
    • julianrod, on 05/17/2008, -3/+4A person that understands how biologic forms of life grow and cells replicate understand why that ratio appears in nature. The illusion of design, people. It's called evolution. No designer needed.
    • Vincent21212, on 05/17/2008, -3/+5Give me a ***** break! FROM THE NAVEL TO THE KNEE? What kind of random ***** measurement is that??? And btw, 80% of those "facts" are ***** too. I mean who pulled those points of measurement out of their ass, that we should be so astounded about? Thats like me saying the distance from big toe to small toe and the distance from big toe to outer side of middle toe. No way! No ***** dice on the credibility. And when it comes to spirals, well, spirals are ***** spirals, big whoop! Gravity is a universal force that plays that deal.
      • talonstriker, on 05/18/2008, -0/+5I agree with your comments. Seems like these people just went around looking for random places were the golden ratio occurs without providing any justification how or why the golden ratio effects the distance between two body parts. I'm not calling BS on the occurance of golden ratio in nature--only the measurements in this article.
    • Naryuu, on 05/18/2008, -0/+4i agree with snokage, but everyone is entitled to their beliefs. so try to avoid getting fussy people.
  • monospaced, on 05/17/2008, -6/+11Great examples. Too bad it must be pointed out that these beautiful sequences account for a lot more than just shells, sunflower seed arrangements, and facial proportions; pretty much everything you see can be explained in a similar manner. Absolutely astounding.
  • HafizD, on 05/17/2008, -5/+29Another great example of how math can be COOL!
    • hmunkey, on 05/17/2008, -0/+5I think it's cool because behind every aspect of physical science, every object, everything, is math.
  • GhostWithToast, on 05/17/2008, -3/+12don't forget spiral galaxies.
  • possiblyneil, on 05/17/2008, -4/+137Has anyone heard the song Lateralus by Tool? All the lyrics are arranged in Fibonacci sequence.
    http://www.youtube.com/watch?v=wS7CZIJVxFY
    • bumblefoot, on 05/17/2008, -6/+16if you rearrange the songs in that album and play them in a fibonacci sequence type order they all flow into one another a lot better
      • i4mt3hwin, on 05/17/2008, -3/+15I like tool as much as the next guy, but this is retarded. 90% of the tracks have silence at the end and the ones that don't, don't fit at all.
      • allengeer, on 05/18/2008, -0/+3yea except you end up splitting parabol/parabola and that just doesnt make any ***** sense. Thats on the same lines as splitting up Wings for Marie and 10,000 days
        • bumblefoot, on 05/21/2008, -0/+1the 3 ways i've heard of it being rearranged are

          1,2,3,5,8,13,4,6,7,9,10,11,12 ("The Fibonacci Sequence"), 6,7,5,8,4,9,3,10,2,11,1,12,13 ("The Lateralus Prophecy"), or 6,7,5,8,4,9,13,1,12,2,11,3,10 ("The Holy Gift")

          i've only tried the middle one out and it sounded pretty good :)

          although quite how they worked out the orders out i dont know because none of them look like fibanacci sequences to me -_-
    • dylio, on 05/17/2008, -2/+21The drum beats in Lateralus are aligned with the fibbonaci sequence as well.
    • AndrewDB, on 05/17/2008, -2/+15That's absolutely crazy.

      Thank you for the wonderful link.
    • DigitAl56K, on 05/17/2008, -0/+5Also check out "1.618", a video by BT from his "This Binary Universe" DVD. All of the scenes are based around the golden ratio.
    • diggrnumber1, on 05/17/2008, -0/+4i've heard that song before, but i never know it was about math. it's really hard to understand the lyrics without the subtitles, but i probably still wouldn't have figured it out even if i had known the lyrics.
      • allengeer, on 05/18/2008, -0/+4its not about math. The "math" part is just used to illustrate on a different level the rules governing the natural world.
        its about understanding and appreciating the natural order of the world you exist in, accepting it and "flowing" with it. I think the meaning of the song is best summed up in this part:

        "over thinking, over analyzing separates the body from the mind.
        Withering my intuition leaving opportunities behind.
        Feed my will to feel this moment urging me to cross the line.
        Reaching out to embrace the random.
        Reaching out to embrace whatever may come."

    • danconia, on 05/17/2008, -0/+4If I remember right it's not perfectly aligned with the Fibonacci sequence. Just "loosely" aligned. Like it makes any difference to me though...
    • jaydoj, on 05/18/2008, -9/+2I am not familiar with this band you call 'Tool'. =]
    • happytedium, on 05/18/2008, -0/+4One of my favourite songs of all-time. :D
    • allengeer, on 05/18/2008, -0/+1black
    • Lateralis1, on 05/18/2008, -0/+1With my feet upon the ground I move myself between the sounds
      And open wide to suck it in, I feel it move across my skin
      I'm reachin' up and reachin' out, I'm reachin' for the random or
      Whatever will bewilder me, whatever will bewilder me
      And following our will and wind, we may just go where no one's been
      We'll ride the spiral to the end and may just go where no one's been

      Spiral out
      Keep going
  • greenblob, on 05/17/2008, -4/+21"There is no question that if the world had to be divided into the 'poetic dreamers' and 'rational thinkers' most people would place mathematicians in the latter category. Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics, and allows more freedom of expression than poetry, art, or music. Mathematics is the purest of the arts, as well as the most misunderstood."
    -Paul Lockhart
    • netant, on 05/18/2008, -3/+4As a corollary, I've always found the math geeks to be the most oddball to disturbed students on campus. Some people would think the theatre geeks are the most oddball, but I find them to be narcissistic posers suffering from identity problems. Stick them on a couch for a couple of years and pop them full of drugs, and they become quite manageable.

      Math geeks, on the other hand, have years of all that bottled up rage from the sex deprivation, relentless torture from jocks, the painful wedgies, and the isolation lockers.

      The movie Pi showed the evils of trying to understand math. In the movie, Falling Down, the guy off his nut was an engineer, i.e. math geek. Al Nobel, the inventor of dynamite, was so guilt ridden by his creation, he gave all the money he made on weapons of death to intellectual pursuits, in the hope of making a better world. But even he knew better than give his money to a mathematician. And finally remember, Theodore Kaczynski, the unibomber, was a math professor, before math drove him mad.
  • GOVStooge, on 05/17/2008, -1/+3For a good read on Fibonacci try this, it's one of my favorite books.

    http://www.amazon.com/Golden-Ratio-Worlds-Astonish ...
  • buffyangel108, on 05/17/2008, -13/+8Wow. It's like the Da Vinci Code. But for clever people.
    • MusicalFeedback, on 05/17/2008, -0/+1I was thinking that too. Every example in that article was mentioned in The Da Vinci Code. Except Dan Brown has better grammar.
    • AndrewDB, on 05/17/2008, -1/+6Except for the Da Vinci Code is fake and the Fibonacci spiral is real.
      • netant, on 05/18/2008, -0/+1The Da Vinci Code is fake, but secret societies for hundreds of years ran around, thinking they were preserving the bloodline of Jesus and Mary. The Holy Roman Empire, and royalty throughout Europe, indulged in the myth they came from the bloodline of God.
  • pigducksheep, on 05/17/2008, -2/+21Michael Scofield knows all about Fibonacci.
  • Hefelumpman, on 05/17/2008, -10/+72http://en.wikipedia.org/wiki/Golden_ratio#Disputed ...

    Buried for inaccuracy and pseudo-scientific mumbo-jumbo.
  • PPCG4, on 05/17/2008, -7/+2The new comment system rocks.
  • bluelightnin90, on 05/17/2008, -1/+20Pics or it didn't happen.

    Seriously, how are you going to have an article on examples of Fibonacci sequences in nature without pics. I believe the article, but it was boring without pics.
  • LukeBeaumont, on 05/17/2008, -1/+4We did this stuff in Biology this week very briefly, it really is amazing how most of nature conforms to the sequence. There a lot more examples than what the article said, especially with the logarithmic spiral.
    There is also some stuff like this with the Lucas Numbers.
    • Yeknom, on 05/18/2008, -2/+2With things like the Fibonacci sequence, I find it impossible for someone to deny any kind of design behind the universe
    • djk21108, on 05/18/2008, -0/+1Design by natural evolution of the most efficient pattern?

      Seems more logical then God deciding on an arbitrary ratio and giving it to all living creatures for no reason.
      • Gamer2k4, on 05/19/2008, -0/+1But you JUST said it was the most efficient pattern. If that's the case, than God choosing it wouldn't be arbitrary at all.
  • Piontek, on 05/17/2008, -28/+4so what, all asians arent made by god because their faces have ***** up proportions :P
    • JulyZerg, on 05/18/2008, -1/+8No one was made by "god". Just like no one was made by allah.
  • koft, on 05/17/2008, -2/+16I have some stock prediction software to sell.
    • missingdigits, on 05/17/2008, -2/+1LOl... I have read a couple of books on Fibonacci numbers and stock prices and have studied some charting using them. It's just another way that traders try to predict a stocks movement given no other parameters other than psychological reasons (similiar to moon phases and stock prices). It's interesting, but like all other "tools' such as this one can find many examples that fit it perfectly and a million more where it does not.


    • diggrnumber1, on 05/17/2008, -1/+2the only way to do well in the stock market is through experience. ask warren buffett, carl icahn, george soros, kirk kerkorian, john paulson, ron perelman, li ka-shing, prince alwaleed, carlos slim, bernard arnault, etc. learn from them - don't learn from the fibonacci sequence.
    • octoberism, on 05/18/2008, -0/+3Was I right to think of the movie 'Pi'?

      Plus, buried for inaccuracy and general poor quality. (The link, not the comment.)
  • Robcataus, on 05/17/2008, -8/+1yawn
  • JustinDM, on 05/17/2008, -11/+22Pretty interesting. However I was turned off after the writer said God was trying to tell us something. More like there is something efficient about 1.618.
  • seabass341, on 05/17/2008, -1/+10Just in case anyone wanted to know, the golden ration is the number that satisfies the equation: x^2-x=1. It presents itself often in nature because it is considered efficient and aesthetically pleasing. It is also important to realize that a lot of claimed "examples of the golden ratio" are the product of people looking for it wherever they can find it. If you look hard enough for something in nature, you'll find it.
    • NathanielJ, on 05/17/2008, -0/+5Just as a bit of a nitpick... the golden ratio is ONE of the numbers satisfying that equation; the other number is the golden ratio - 1.

      I completely agree though with the last part of your comment. All the stuff in the article about the golden ratio being the ratio of your forearm length to your hand length is complete BS. People will say that it's the golden ratio if it's anywhere between 1.5 and 1.75 because they assume it must be if it's not a nice fraction.
    • mclewell, on 05/17/2008, -0/+1The correct measurement of the Golden Ratio is:
      (a+b)/a = (a/b) = phi

      Solving this equation will give one quadric solution:

      [1 + sqrt(5)] / 2 = 1.618.....

      Wikipedia has a good explanation of this: http://en.wikipedia.org/wiki/Golden_ratio
      • seabass341, on 05/24/2008, -0/+1you are right but if u had read to the end of the wikipedia page you would see that the equation you have given eventually is reduced to the one I have given and then solved.
    • Dystisis, on 05/17/2008, -0/+0Aesthetically pleasing... why do you think that is?

      Obviously nature follows the laws of mathematics (and numbers) because everything is numbers/organization. Want proof? Look at how atoms are organized into molecules. We can only use mathematics (and geometry) as a tool that lets us see, in our own applied methods, the way nature is built.
      www.hyperflight.com
  • Pinkertinkle, on 05/17/2008, -6/+10Most logarithmic spirals actually aren't golden ratio spirals, just plain ol' logarithmic spirals. But don't tell this guy, his head might explode if God wasn't always on point.
  • julianp, on 05/17/2008, -3/+369:22, Personal note: When I was a little kid my mother told me not to stare into the sun, so once when I was six, I did. At first the brightness was overwhelming, but I had seen that before. I kept looking, forcing myself not to blink, and then the brightness began to dissolve. My pupils shrunk to pinholes and everything came into focus and for a moment I understood.
    • Acglaphotis, on 05/17/2008, -8/+2You understood the consequences of looking directly on to the sun?
      • Acglaphotis, on 05/17/2008, -1/+1Oh, sorry about that, he was quoting the 1998 movie Pi, how didn't i notice?
    • tommah, on 05/17/2008, -0/+26My hypothesis: within the stock market there is a pattern as well. Right in front of me. Hiding behind the numbers.

      12:50, Press return.
    • Clouse, on 05/17/2008, -6/+0*applause*
    • ultraJesus, on 05/17/2008, -6/+2I heard thats bad for your eyes man.
    • PocketWatch, on 05/17/2008, -0/+1411:15, restate my assumptions: 1. Mathematics is the language of nature. 2. Everything around us can be represented and understood through numbers. 3. If you graph these numbers, patterns emerge. Therefore: There are patterns everywhere in nature.
    • thebrokenlight, on 05/17/2008, -0/+6You guys are really good at quoting movies.
    • Ecuno, on 05/18/2008, -1/+1That is the movie Pi. Although IIRC he does mention Fib sequence a few times.
    • greenblob, on 05/18/2008, -4/+1Mistakes in Pi:
      They use theta instead of phi
      He divides two large Fibonacci numbers and says that it approaches "theta" (phi). You don't get a limit when you divide two numbers.
    • netant, on 05/18/2008, -0/+1The truth will make you blind?
    • jjremy, on 05/18/2008, -0/+1*goes to look for his Pi dvd*
  • 0260, on 05/17/2008, -6/+7Apparently "god did it" is better than a damn citation. buried
  • rguinn, on 05/17/2008, -0/+12This article should definitely come with visual examples. Buried out of principle...
  • Zecchetti, on 05/17/2008, -10/+5Proof of the Creator. Come on, don't be stubborn. It is a manifest sign!
    • Chunken, on 05/17/2008, -5/+4Or it's just a pattern that exists in nature like many other patterns.
      I won't believe "god did it" until someone tells me how god came to be. And so far nobody has even come up with a theory other than evolution. But religious folk sure don't like the idea of god being created by evolution lol.
      • Gamer2k4, on 05/18/2008, -0/+2Apparently someone doesn't understand that supernatural beings are not bound by natural laws...

        Incidentally, you believe that the Big Bang happened without knowing how all the particles, energy, laws, and physical constants came to be, don't you? Why is that any more plausible than God?
        • Zecchetti, on 05/18/2008, -0/+1some people are deaf, dumb, and blind, despite having the senses
      • Zecchetti, on 05/18/2008, -0/+1How God came to be? He always is, always was, and always will be. Difficult to comprehend?
    • talonstriker, on 05/18/2008, -1/+1/s?
      I'm sorry I have my sarcasm detector turned off..
  • slahser, on 05/17/2008, -13/+9"I felt that God wanted to tell us something". Stopped reading there; Religious fanatics opinion about a fantasy being created in their minds does not interest me. Go ahead and bury me Christians.
    • Cyrus042, on 05/17/2008, -3/+5Not a Christian, but still burying you. Read the article for what it is instead of being bullheaded.
    • Dystisis, on 05/17/2008, -3/+1Christians want nothing to do with mathematics or sacred geometry. They call it occultism.

      Stop being an idiot and looks at the writing on the wall. Or better yet, look at the wall itself and realize it is made up of bricks.
  • hiPpymIck, on 05/17/2008, -0/+3i once saw a documentary about a mathematical garden - literally a garden designed around mathematics

    it was a guided tour by this math professor
    it was pretty big garden there were lots of different things
    illustrating loads of high level mathematical concepts - including Fibonacci sequences
    unfortunately i cant remember the exact details (its harder with stuff youre only half-familiar with)

    i assume its pretty famous - ive tried googling for it but i cant find anything
    if anyone knows the place i mean..
  • applemachome, on 05/17/2008, -10/+1Wow were nerds. I keep realizing how much of a nerd I am every time I read one of these articles and know what its talking about, then try to explain it to someone because no one else has any idea.
    • Memnochxx, on 05/17/2008, -1/+2Being educated doesn't make you a nerd.
    • mbraynard, on 05/17/2008, -1/+3Apparently, being a nerd doesn't mean you understand basic grammar.
      • applemachome, on 05/18/2008, -0/+1I wasn't meaning to make it sound like a bad thing. Grammar apparently doesn't matter on this website, or I would be more inclined to check for it. Lazy one line responses, who cares about grammar. I've seen worse in article titles that got hundreds of diggs.
  • Terasiel, on 05/17/2008, -1/+21I call ***** on some of these. Distances on one's body can be dramatically different from person to person. For a 1.618 ratio to always exist, people with wider shoulders would always have shorter necks, people with small mouths would always have small noses, people with tall heads would always have thin faces. This is another example of scientists giving each other a pat on the back without proving themselves beyond doubt.
    • awwe, on 05/17/2008, -1/+3Only beautiful people meet the ratios exactly. I measured all of my ex-girlfriends. None of them met the ratios. :(
    • parkamark, on 05/17/2008, -0/+1It's a difficult thing to prove, but I suggest you take a look at:

      http://goldennumber.net/beauty.htm

      something called, the Beauty Mask. The more closely a face fits this mask, the more attractive it is (the mask is based on the golden ratio of 1:1.618). If you don't believe me, grab a template image of the mask (google) and overlay it onto a forward facing picture of a hot celebrity. It will fit pretty much exactly. And the closer the fit (down at eye contour level), the more "hot" they will be.

      Of course, not everyone fits this mask. As you say, some people will have smaller noses or, to give a concrete example, wider eyes than what the mask dictates (Kate Moss is a classic example of this) but that is actually what makes her and individual people unique and beautiful in their own right.
    • Dystisis, on 05/18/2008, -0/+0It's not really about beauty, because beauty lies in the eye of the beholder.

      However, it is about generalization. You should know by now that the way nature works is not that it follows organization in the strictest sense (on a macroscopic level, anyway), but rather that it generalizes towards a pattern. An example of this is how not every leaf on a tree looks exactly the same, but still: They all are green in the summer and heart-shaped. Why is it so? The conditions of its surroundings, and... further, the state of the entire universe, made it so. I believe everything is connected.
  • teambosun, on 05/17/2008, -9/+4The universe is such a big, complex, unimaginable thing, and yet it's governed by such a simple rule such as this.

    Amazing.
    • PhantomPhoenix, on 05/17/2008, -0/+3The entire universe isn't governed by just this. This is just a small part of how the universe orders itself.
      • Dystisis, on 05/18/2008, -1/+0The one rule of the universe is organization.
  • eminiguy, on 05/17/2008, -8/+4Nothing beats 666.66, the original price of Apple I in US dollars. Or was it Apple II?

    And I am even not an Apple fanboy, so no flames, although I do admit that I am a fan of Woz.
  • johnnyashcan, on 05/17/2008, -0/+6Wow. One page of broken English and no pictures. There must be countless visual examples that he could have provided and there are none. Why is this on the front page of Digg?
  • andrew606, on 05/17/2008, -5/+11did someone bring up tool yet?
    if not,
    tool.
  • hthaya2, on 05/17/2008, -6/+2The ratio is 1.618 and this ratio represents universal proportionality. Read The Da Vinci Code!
  • Hoprot, on 05/17/2008, -0/+6Logarithmic spirals - called 'the marvellous spiral' by Jakob Bernoulli - are actually the usual type of spiral shape found in nature. The golden spiral can be approximated by a logarithmic spiral, but many types of logarithmic spiral are more common in nature than the golden spiral. No one spiral defines all those found in nature. Logarithmic spirals describe things in nature either because of the geometrically increasing rotation and attraction towards the centre of a spiral galaxy or cyclone, or because when shells such as the nautilus grow they expand in an irregular extension with a common ratio of growth.

    This article is inaccurate; the golden ratio is interesting, but it is not proof of God. Fibonacci discovered it when describing the growth of population of rabbits, using difference equations, the discrete analogue of differential equations.
  • iMoth, on 05/17/2008, -7/+1milhouse is a meme
  • jeexbit, on 05/17/2008, -6/+1Nature is number.

    The Absolute (0) manifests itself (1) through duality (2) in three dimensions (3).
    • Hoprot, on 05/17/2008, -0/+3Don't you mean at least 4? A 3 dimensional slice of 4D space-time is arbitrary, exemplified in the relativity of simultaneity - certainly not nature in its fullest.
  • thespi007, on 05/17/2008, -4/+1whole thing copied from da vinci code
  • alarmist, on 05/17/2008, -2/+8god is a mathematician
    • greenblob, on 05/18/2008, -1/+7Biologists say that they're organic chemists. Organic chemists say that they're chemists. Chemists say that they're chemical physicists. Chemical physicists say that they're physicists. Physicists say that they're God. As for God, he claims to be a mathematician.
  • Godmil, on 05/17/2008, -1/+5Another astounding example of a golden ratio is the number of socks I own compared to the number of books on the second top bookshelf above me... isn't nature amazing!
  • plopper, on 05/17/2008, -1/+5Respect the numbers or else Joey Fibonacci will make you an offer you can't refuse.
  • PhantomPhoenix, on 05/17/2008, -1/+5I love the Fibonacci Numbers!
    1-1-2-3-5-8-13-21-34-55-89-144-...

    I also like multiples of five...especially 25.
  • Dystisis, on 05/17/2008, -0/+2Alot more interesting info on this (and other refreshing views on science) can be found for example here: www.hyperflight.com

    It should be noted that the usage of the term "Fibonacci Numbers" is wrong in this context though. The Fibonacci numbers are the following: 1, 1, 2, 3, 5, 8, 13, etc. The two last numbers add up to make a new number in the sequence. The ratio you eventually get closer and closer to between the last number and the one before it is the Golden Ratio/Golden Mean, whatever you wish to call it. Test it for yourself.

    Geometrically, additive (or multiplicative) number sequences such as the Fibonacci sequence is taking the form of spirals. The numbers in a sequence dictating the progression of any spiral.
  • FuckXboxx, on 05/18/2008, -0/+2Ever since I saw "Donald in Mathmagical Land" I've been trying to "spiral out"....as Lateralus has taught me is the term for my growth.
  • dsa202, on 05/18/2008, -5/+0How is this even remotely cool?
  • diggFM, on 05/18/2008, -2/+154 8 15 16 23 42
  • slothlovechunk, on 05/18/2008, -0/+4I don't buy all of these human body measurement ratios. It's like their just picking random ***** and then saying, ok, which of these measurements is close to 1.6 or so. Of course you can find that ratio if you are looking.

    Not only that, but people are different. I really doubt the precision of this ratio to be even to 2 significant digits. A lot of people are probably 1.5 or 1.7 for these same measurements, maybe more. I mean, I measured the ratio of my ***** length to my arm length and it was 1:1, and I hear most people are more like 1:5

    Count the sunflowers, measure the shell, but quit measuring my belly button and my knee or whatever other retarded ratios you pull out of your ass to make your life more interesting.
    • HalKessler, on 05/18/2008, -0/+2It must be hard to go through life with such short arms.
      • Gamer2k4, on 05/18/2008, -0/+0ZING!

        Or, as we on the internet say, "I see what you did there."
    • Gamer2k4, on 05/18/2008, -0/+0I'm pretty sure the ratio is in reference to some ideal, not to what people actually are.

      Incidentally, having a two foot penis is just as freakish and undesirable as having a two inch penis, and you're an idiot if you think otherwise.
  • Mjhavok, on 05/18/2008, -1/+2Fib00naCCi for the win.
  • IceOfDiamonds, on 05/18/2008, -0/+1dont forget cereal boxes
  • Birdman3, on 05/18/2008, -0/+1Why is this article on the front page of Digg? The topic is interesting, but the article is terribly written and cites no sources. And, as Dystisis pointed out, the use of the term "Fibonacci numbers" is not quite right in this context. Look at this: "In mathematics, the limit of Fibonacci series is called as Golden Ratio. This ratio is approximately equal to 1.618." What was that? There is a relationship between the Fibonacci sequence and the Golden Ratio, but this article does not explain it.

    And it's a shame the author has to bring religion into this: "When I first read about Fibonacci numbers and examples of Fibonacci numbers in nature, I felt that God wanted to tell us something."

    I feel so mean now. But really, why does this have 700 diggs? There are far better sources on Fibonacci numbers and the Golden Ratio in nature, like http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibon ...

    • netant, on 05/18/2008, -0/+1Its geek humor. Either you find it amusing or fascinating, you just don't get it.

      And after the barrage of Obama/Clinton/McCain, how Bush has f-ed over the country, and stupid trivial distractions, this is merely a change of pace (but a stupid, trivial distraction).
      • Birdman3, on 05/18/2008, -0/+0Nope, this article isn't intended to be humorous, and if you look at the comments you'll see that nobody interpreted it that way. The topic is interesting, but it's a bad article.
  • Junkyboy55, on 05/18/2008, -0/+0Actually most of the examples in this article are relating to Phi. Phi is the Greek letter to which denotes the mathematical constant for the golden ratio.
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