The Fibonacci Sequence in Nature

by Rodallega, May 17, 2008

In mathematics, the limit of Fibonacci series is called as Golden Ratio. This ratio is approximately equal to 1,618. In nature, one can come across this ratio in many areas of art and science.

I kept on researching over it on the net and wanted to see them by naked eyes. Everything I read was completely true and the realm was really amazing. This is a list of Fibonacci numbers in nature. I believe that some of the facts will astonish you.

The distribution of seeds in sunflower is spiral. The seeds of the sunflower spiral outwards in both clockwise and counterclockwise directions from the center of the flower. The number of clockwise and counterclockwise spirals are two consecutive numbers in the Fibonacci sequence.

The shells of the snails follow the Fibonacci sequence. In the same way, the shells of the nautilus follow the same rule. The only difference between these two is that nautilus' shells grow in a three-dimensional spiral, whereas snails' shells grow in a two-dimensional spiral.

Pine cones are one of the well-known examples of Fibonacci sequence. All cones grow in spirals, starting from the base where the stalk was, and going round and round the sides until they reach the top.

Another notable example is human body.In human body, the ratio of the length of forearm to the length of the hand is equal to 1.618, that is, Golden Ratio. Another well-known examples on human body are:

The ratio between the length and width of face
Ratio of the distance between the lips and where the eyebrows meet to the length of nose
Ratio of the length of mouth to the width of nose
Ratio of the distance between the shoulder line and the top of the head to the head length
Ratio of the distance between the navel and knee to the distance between the knee and the end of the foot
Ratio of the distance between the finger tip and the elbow to the distance between the wrist and the elbow

The same sequence exists on the leaves of poplar, cherry, apple, plum, oak and linden trees.

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#1 by tracy sardelli, May 17, 2008

very interesting article, thank you for sharing.

#2 by salvatore, May 17, 2008

great article, thank you for sharing.

#3 by citations, May 17, 2008

Please cite your sources for these facts, thanks!

#4 by antemon, May 17, 2008

interesting...
but why is it important that it merits a dig?

#5 by Zescape, May 17, 2008

Ummmm... Sources? How about any Biology textbook anywhere?

#6 by Wiki, May 17, 2008

Sources would be good. So would images.
I expected more from the front page of Digg.

Also, the ratios of human features obviously vary from person to person--this only represents an "ideal" here.

#7 by Pet Mule, May 17, 2008

Fibonacci numbers in nature? It is quite the opposite, how do think Leonardo Pisano came up with the concept - your claim is nothing short of childish

#8 by Ryan Gaphie, May 17, 2008

lrn2math and quit spreading fake science or at least differentiate between a logarithmic spiral and a golden spiral

#9 by Nova, May 17, 2008

"In mathematics, the limit of Fibonacci series is called as Golden Ratio. This ratio is approximately equal to 1,618." The Fibonacci series does not have a limit. It has a closed form solution which involves the golden ratio, but is not it...

In fact, except for the sunflower seed example, every time you mention the Fibonacci sequence, you should be using the Golden Ratio.

#10 by anonymous, May 17, 2008

sage

#11 by citations, May 17, 2008

...would render the article false. That's why they are not needed.

#12 by annoyed, May 17, 2008

rubbish. bad pop-sci strikes again

#13 by Josh, May 17, 2008

The "ratios" you use seem quite arbitrary. You can pick any length between two points on the body, and then just be careful to find another set of points that makes the ratio close to 1.618.

What the hell does the length of the mouth have to do with the width of the nose? Well, I guess EVERYTHING if you want it to fit with some "magical" number.

#14 by Whatever, May 17, 2008

In fact, you said God is trying to tell us something?
no, more like God is trying to tell you to grow up and take a good look at the real word.

try and measure the deaths relating to religious intolerance, try and measure the abuse of corporations, the greed of western idiocracy, the blind militant crusade that will end up devastating our world both thru science and religion.

follow that sequence and you will find the cause of natures most viral outgrowth ( mankind )

#15 by RJB, May 17, 2008

Thought the article was interesting? Get a tape measure and measure some of those items yourself. Several are simply not true.

Heck, you don't even need to do that. Just think critically. Does everyone have the same proportions? Ever meet someone with a really long or wide face?

#16 by Person, May 17, 2008

I agree in the seemingly arbitrary points of measurement. And yes, you DO need sources. We\'re not lazy if we don\'t bother to do our own research on an article. That\'s what articles are for. They bring information to us. I could have gotten more useful information if I was bored and decided \"Hm. I\'ve done math problems on Fibonacci numbers before. I wonder where they are used?\" and simply read the first few pages. Instead this \"writer\" is supposed to have done that for me and compile all the information into a neat little article where I can read it. However, I can not assume any of this to be true because of the outrageous claims, therefore I will have to research this subject on my own making any work this person claims to have done completely useless.

#17 by smift, May 17, 2008

I got as far as "I felt that God wanted to tell us something\"..

#18 by Unofre Pili, May 17, 2008

Nice article. Albert Einstein for one in his boyhood discovered Fibonacci series in arrangement of leaves. Leaving him this lasting empression of nature's mathematical predictabilty, he pursued Physics.Thus, the Special and General Theory of Relativity.

#19 by hi, May 17, 2008

You are confusing the golden ratio, which happens in nature, to the Fibonacci Sequence which is similar, but not quite the same thing.

#20 by Euler, May 17, 2008

Most of the examples are false. The golden ratio appears in shells and sunflowers but that's about it. Saying that these appearances are hidden messages from a god is bizarre to say the least. These appearances have scientific explanations that have nothing to do with superstition. Pi appears in the human eye because it's round. Is this also a hidden message? Of course not.

#21 by Jon, May 17, 2008

http://en.wikipedia.org/wiki/Golden_ratio#Disputed_sightings_of_the_golden_ratio

#22 by a Reader, May 17, 2008

If I were an omnipotent deity that wanted to provide evidence of my existence I think I could come up with something better than a few numerical coincidences considered significant only if all the non-occurrences are ignored.

#23 by Kosova, May 17, 2008

well the only part about this article were comments
i guess maybe the witter just had a bad day or choose a wrong topic to prove gods existence.

#24 by Kosova, May 17, 2008

The golden section is a line segment sectioned into two according to the golden ratio. The total length a+b is to the longer segment a as a is to the shorter segment b
http://en.wikipedia.org/wiki/Golden_ratio#Disputed_sightings_of_the_golden_ratio
hmm for a sec i thought that god exists and left us few hidden messages

#25 by steve, May 17, 2008

See the movie pi. This kind of stuff will drive a person mad.

#26 by Obviously, May 17, 2008

There is no God. Seriously. Wake up.

#27 by Greg, May 17, 2008

No, it just means that where the Golden Ratio doesn't exist, god hates it, therefore it should be destroyed.

#28 by DwayneCarterJr., May 17, 2008

Honestly, who doesn't already know most of that?

#29 by rprebel, May 17, 2008

Oh, how I love reading about what people 'know'. I wonder what we'll know tomorrow.

#30 by Yecats, May 17, 2008

business cards and standard paper are also Golden Ratio.

#31 by Anonymous, May 17, 2008

"business cards and standard paper are also Golden Ratio."

Standard paper is 8.5"x11". That is a ratio of 1.294, not the golden ratio.

Here is a list of standard business card sizes:
http://en.wikipedia.org/wiki/Business_card

Not one of them is the golden ratio. The closest is:
Australia/New Zealand (most common) 90 × 55 3.54 × 2.165

Which is a ratio of 1.63636364 : 1.

Nice try.

#32 by Peter Thomas, May 18, 2008

Simulation of sunflower spirals in Java:

http://ptrthomas.wordpress.com/2007/09/30/fibonacci-spiral-fun-with-java3d/

#33 by NickC, May 18, 2008

One question, don't shoot me if its been asked before cuz im posting at 1 am, WTF is the Fibonacci Numbers anyway?

#34 by Jim, May 18, 2008

Where do you find 2 dimensional snails?

#35 by Ibelieveyou, May 18, 2008

Let\'s see, what does God want to tell us ...

The ratio of 1,618 occurs widely in nature, and provides humanity the clue that God is there, as long as we ignore the rest of the cases when that ratio doesn\'t apply ...

And God spelled backwards is Dog ...
Words spelled backwards occurs widely in English, and provides people the clue of what that word really means, as long as we ignore the rest of the cases when that rule produces incoherent words ...

I BELIEVE NOW! Thank you God (er, Dog!), how could I have ever doubted your existence! Must find a nearest fundamentalist church/new age retreat ASAP!

#36 by fatdadfatdadfatdad, May 18, 2008

some piece of time ago,critical thinking was to look at the ground foraging for our daily sustenance.If every person throughout our on this spinning orb stayed solely within the confines of critical thought,imagine if you would,or could, just how much fun you would have deciding how critical,or not, it was whether you were having T-rex crap or some eggs for dinner.Seemingly ridiculous tangents/theories/religious fantasies/foolhardiness proper.Who is the mental giant deciding how true, how much truth,nonexistence of truth exists in any thing,idea,fact?Progress definetly comes to bear through independent,truly private mental excursions.Because I do not see it does not make it nonexistent,because I can see it does not mean that it is there.Who believed the fool who said\"here is a computer, look what it can do\"Critical thought keep it.

i

if every person throughout time

#37 by Taantrik.org, May 18, 2008

As far as i know the ratio 1.63636364 : 1 is the ratio which our eyes like the most. Only the most beautiful faces have this ratio with respect to other organs and looks. Not only face, this ratio also satisfy our appetite of good looking figure of a human body. Good painters always this this in his heart (may be he is totally unaware of the fact)
________________________________________________
If in more than millions of creature we get a few of them having a special sequence (If it is, without proof no theory is actually a theory) like square or cube of something than what?

#38 by lizardboi, May 18, 2008

I really like this thing as a visual person. It's like how certain leaves are growing on a treebranch representing the double helix of the human DNA (just google it).
BUT we can also say: if you are looking for a pattern really hard, you will find it everywhere.

#39 by Ronald Marbles, May 18, 2008

Lonely, this was one hell of a good article. You have improved a lot and I am glad you did. I really enjoyed reading this one as it was written well and was very informative.

For those who don't know, the simple meaning of a Fibonacci sequence is 1,1,2,3,5,8,13,21,34 etc etc. If you want a better explanation either Google it or read The Da Vinci Code.

#40 by Ahmad, May 18, 2008

Are you guys still not believing in oneness of God. Every thing is conincidence? there is yut more to discover.

#41 by xiel, May 18, 2008

this reminded me of someone special to me.

#42 by MindIT, May 19, 2008

Very interesting information!

#43 by Anon, May 19, 2008

Thomas you just showed us how big your IQ is. And please mind the sarcasm.

#44 by Viola King, May 19, 2008

I think this is a really fascinating article, and I believe every word of it. Everyone trying to say this article is stupid has no concept of the world around them. Great job on this!

#45 by Ted, May 19, 2008

Fibonacci grids used for numerical weather prediction:

http://www3.interscience.wiley.com/journal/114123276/abstract?CRETRY=1&SRETRY=0

One problem with standard grid generators is that the numerical cells vary too much in size. A grid based on fibonacci spirals is extremely well balanced except for very small regions at the poles. This slight deficiency is acceptable for weather models, because not much happens there.

#46 by PAR, May 19, 2008

Fibonacci sequence is quite interesting as many people reacted on this phenomenon if we may call it. When existence and non-existence is discussed, that means it's a reality. What people think, believe, see, and feel takes shape and become a part of one's life.

#47 by dayes, May 19, 2008

i remember them saying this when i was learning the Fibonacci sequence in school. gawd... i feel so geeky. =P

#48 by nobert bermosa, May 20, 2008

very interesting,
thanks lonely and congrats!

#49 by iwrite, May 20, 2008

The information this article contains (whether factual or not) are not new to me. I've read some, if not most, of it in Dan Brown's The Da Vinci Code. It's worth noting that The Da Vinci Code is fiction.

#50 by Glynis, May 21, 2008

Right or wrong I would have liked an introduction to what the Fibbonaci and all it's ratios are as I am not well read in this area, I think articles like this can be valuable...in the art of debate having read the responses to it!

#51 by pilarsophia, May 21, 2008

Interesting concept, i can't stand math either! Good work

#52 by Plastic, May 23, 2008

You can\'t live until you die....

#53 by Heart Stone, May 23, 2008

Hey,

So clever of you. Good thing to know this. I didn't know this until now.

Shine on.

#54 by Kai, Jun 1, 2008

THIS ARTICLE IS WRONG. The limit of the Fibonnaci sequence is not the Golden Ratio!

#55 by Miller, Jun 1, 2008

Explain this one:

Q: What is the shortest chapter in the Bible?
A: Psalms 117

Q: What is the longest chapter in the Bible?
A: Psalms 119

Q: Which chapter is in the center of the Bible?
A: Psalms 118

Fact: There are 594 chapters before Psalms 118 
Fact: There are 594 chapters after Psalms 118 
Add these numbers up and you get 1188.

Q: What is the center verse in the Bible? 
A: Psalms 118:8

Does this verse say something significant
about God's perfect will for our lives? 

Psalms 118:8 (NKJV)
 "It is better to trust in the LORD than to put confidence in man."

Now doesn't that just frost your arss.

#56 by bob, Jun 1, 2008

has anyone said 'Fractals' yet?

#57 by Sophilius, Jun 1, 2008

Before one can connect the Golden Ratio and nature, let alone, a god, one must clearly and accurately explain the Golden Ratio and the Fibonacci Sequence. The Fibonacci sequence has an infinite number of numbers in its sequence beginning with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... a given number of this sequence is obtained by adding the previous two numbers (examples: 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, etc.). There is an equation to produce any number in the Fibonacci Sequence and I provide it at the end of my comments for those interested. If you take a relatively large number from the Fibonacci Sequence and divide it by the number that comes before it, the result is close to the Golden Ratio. The larger the number (and the previous number) selected from the Fibonacci Sequence, the closer it approaches the Golden Ratio. The Golden Ratio equals (1+square root of 5)/2. Now that the foundation has been established, we can move forward.
Equation to produce \"F\" which is the \"x\"th number in the Fibonacci Sequence (Note: \"sq5\" means the square root of 5; \"^\" is the symbol for exponent or power, \"*\" is multiplication, and \"/\" is division): F = (1/sq5) * ({[(1+sq5)/2]^x}-{[(1-sq5)/2]^x})
For example: If x=5, then F=5; If x=6, then F=8.
Thank you

#58 by Sean, Jun 1, 2008

@Kai While the "well-known examples" of the appearance of the Golden Ratio in nature largely bogus, it certainly is the case that the ratio of successive numbers in the Fibonacci Sequence converges to the Golden Ratio, and it's easy to prove.

#59 by Sharjeel, Jun 2, 2008

I guess you have been reading the "DA Vinci Code"..

#60 by Ernie Wong, Alta Dena Ca, Jun 16, 2008

I believe in the the golden ratio... Michelangelo used it quite frequently in his paintings and I believe it does raise an eyebrow when that number is magically struck in nature. I don't know that there is any one governing rule in nature that overrides the diversity and place of all the others found all around us - meaning: the universe is diverse and constantly breaking the boundaries of our minds and challenging what we think we know and believe. The universe has devised a plan to consume our lives, baffled by it's intricacies, in vain trying to decipher what we feel and think, in an effort to make a mark. An effort to be remembered. I want to believe in the golden rule because it is easy to live in a universe where I know where to place things. 1.6 is an easy number to go to when I'm having a creative block. So in that way it becomes a sort of equilibrium I use when I lose my way. A "golden rule" in more ways then one.

#61 by your mom, Jul 1, 2008

it crap

#62 by your mom, Jul 1, 2008

soz *its crap

#63 by KaTEnerd, Jul 4, 2008

thanks for helping me with my maths. this is very interesting!! :)

#64 by lili, Aug 25, 2008

nice , nice ,very //////////////////

#65 by lili hotie, Aug 25, 2008

whatever loser/// GREG

#66 by lil Jade, Sep 8, 2008

It should be broke down so it is more clear to read!!!

#67 by bradley , Sep 17, 2008

this is awesome

#68 by tim, Sep 24, 2008

so interesting...can you give another application about fibonacci in nature- more interesting than human body?

#69 by Jess, Oct 1, 2008

Youre fake!!!!
I found this exact article somewhere else.
Stop Copying!

#70 by diziet, Oct 21, 2008

There is no doubt about it, a lot of the people here are very up tight and very, very odd.

#71 by Hattie , Nov 2, 2008

thank you that was all my maths holiday work right there ..

and you will find a pattern in anything if you look hard enough it is rubbish.

#72 by aaaaaaaabbbbbbbbcccccccc, Nov 17, 2008

the fibonacci sequence is very confusing but very magnificant because God created it!!!!

#73 by hey hey hey, Nov 21, 2008

smoke weed every day!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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The Fibonacci Sequence in Nature

In mathematics, the limit of Fibonacci series is called as Golden Ratio. This ratio is approximately equal to 1,618. In nature, one can come across this ratio in many areas of art and science.

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