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.
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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95 Responses to “The Fibonacci Sequence in Nature”
On May 17, 2008 at 9:32 am
very interesting article, thank you for sharing.
On May 17, 2008 at 9:32 am
great article, thank you for sharing.
On May 17, 2008 at 4:44 pm
Please cite your sources for these facts, thanks!
On May 17, 2008 at 4:51 pm
interesting…
but why is it important that it merits a dig?
On May 17, 2008 at 4:52 pm
Ummmm… Sources? How about any Biology textbook anywhere?
On May 17, 2008 at 4:55 pm
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.
On May 17, 2008 at 4:59 pm
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
On May 17, 2008 at 5:03 pm
lrn2math and quit spreading fake science or at least differentiate between a logarithmic spiral and a golden spiral
On May 17, 2008 at 5:07 pm
“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.
On May 17, 2008 at 5:07 pm
sage
On May 17, 2008 at 5:22 pm
…would render the article false. That’s why they are not needed.
On May 17, 2008 at 5:30 pm
rubbish. bad pop-sci strikes again
On May 17, 2008 at 5:42 pm
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.
On May 17, 2008 at 5:45 pm
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 )
On May 17, 2008 at 6:25 pm
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?
On May 17, 2008 at 6:27 pm
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.
On May 17, 2008 at 6:32 pm
I got as far as “I felt that God wanted to tell us something”..
On May 17, 2008 at 6:34 pm
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.
On May 17, 2008 at 6:43 pm
You are confusing the golden ratio, which happens in nature, to the Fibonacci Sequence which is similar, but not quite the same thing.
On May 17, 2008 at 6:46 pm
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.
On May 17, 2008 at 6:52 pm
http://en.wikipedia.org/wiki/Golden_ratio#Disputed_sightings_of_the_golden_ratio
On May 17, 2008 at 7:20 pm
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.
On May 17, 2008 at 7:49 pm
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.
On May 17, 2008 at 7:52 pm
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
On May 17, 2008 at 8:18 pm
See the movie pi. This kind of stuff will drive a person mad.
On May 17, 2008 at 8:38 pm
There is no God. Seriously. Wake up.
On May 17, 2008 at 8:43 pm
No, it just means that where the Golden Ratio doesn’t exist, god hates it, therefore it should be destroyed.
On May 17, 2008 at 8:54 pm
Honestly, who doesn’t already know most of that?
On May 17, 2008 at 9:36 pm
Oh, how I love reading about what people ‘know’. I wonder what we’ll know tomorrow.
On May 17, 2008 at 9:45 pm
business cards and standard paper are also Golden Ratio.
On May 17, 2008 at 10:26 pm
“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.
On May 18, 2008 at 1:23 am
Simulation of sunflower spirals in Java:
http://ptrthomas.wordpress.com/2007/09/30/fibonacci-spiral-fun-with-java3d/
On May 18, 2008 at 1:56 am
One question, don’t shoot me if its been asked before cuz im posting at 1 am, WTF is the Fibonacci Numbers anyway?
On May 18, 2008 at 2:00 am
Where do you find 2 dimensional snails?
On May 18, 2008 at 3:01 am
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!
On May 18, 2008 at 3:01 am
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
On May 18, 2008 at 3:20 am
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?
On May 18, 2008 at 4:10 am
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.
On May 18, 2008 at 7:01 am
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.
On May 18, 2008 at 3:29 pm
Are you guys still not believing in oneness of God. Every thing is conincidence? there is yut more to discover.
On May 18, 2008 at 9:42 pm
this reminded me of someone special to me.
On May 19, 2008 at 4:11 am
Very interesting information!
On May 19, 2008 at 5:41 am
Thomas you just showed us how big your IQ is. And please mind the sarcasm.
On May 19, 2008 at 8:34 am
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!
On May 19, 2008 at 11:34 am
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.
On May 19, 2008 at 5:11 pm
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.
On May 19, 2008 at 7:13 pm
i remember them saying this when i was learning the Fibonacci sequence in school. gawd… i feel so geeky. =P
On May 20, 2008 at 2:04 am
very interesting,
thanks lonely and congrats!
On May 20, 2008 at 10:47 pm
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.
On May 21, 2008 at 1:55 am
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!
On May 21, 2008 at 9:01 pm
Interesting concept, i can’t stand math either! Good work
On May 23, 2008 at 10:13 am
You can’t live until you die….
On May 23, 2008 at 11:14 am
Hey,
So clever of you. Good thing to know this. I didn’t know this until now.
Shine on.
On June 1, 2008 at 4:17 pm
THIS ARTICLE IS WRONG. The limit of the Fibonnaci sequence is not the Golden Ratio!
On June 1, 2008 at 6:23 pm
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.
On June 1, 2008 at 6:58 pm
has anyone said ‘Fractals’ yet?
On June 1, 2008 at 7:21 pm
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
On June 1, 2008 at 7:31 pm
@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.
On June 2, 2008 at 12:19 am
I guess you have been reading the “DA Vinci Code”..
On June 16, 2008 at 3:11 am
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.
On July 1, 2008 at 8:22 am
it crap
On July 1, 2008 at 8:22 am
soz *its crap
On July 4, 2008 at 3:22 am
thanks for helping me with my maths. this is very interesting!!
On August 25, 2008 at 9:39 pm
nice , nice ,very //////////////////
On August 25, 2008 at 9:42 pm
whatever loser/// GREG
On September 8, 2008 at 12:52 pm
It should be broke down so it is more clear to read!!!
On September 17, 2008 at 1:57 pm
this is awesome
On September 24, 2008 at 10:27 pm
so interesting…can you give another application about fibonacci in nature- more interesting than human body?
On October 1, 2008 at 1:32 pm
Youre fake!!!!
I found this exact article somewhere else.
Stop Copying!
On October 21, 2008 at 8:22 am
There is no doubt about it, a lot of the people here are very up tight and very, very odd.
On November 2, 2008 at 3:36 pm
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.
On November 17, 2008 at 9:02 pm
the fibonacci sequence is very confusing but very magnificant because God created it!!!!
On November 21, 2008 at 5:37 pm
smoke weed every day!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
On December 5, 2008 at 10:44 am
You should watch the movie titled Pi.
http://www.imdb.com/title/tt0138704/
“A paranoid mathematician searches for a key number that will unlock the universal patterns found in nature.”
He specifically discusses the fibonacci sequence and spiral shells.
On January 5, 2009 at 7:49 am
ummmmmmm, dunno wot to say lol except from it is very confusing!!very
On January 16, 2009 at 2:40 pm
God does exist, even if a “pattern” doesn’t. For all of you who deny the existence of God just because you don’t believe that the Fibonacci sequence exists, let me say something very simple: God is not the Fibonacci sequence. Chew on that for awhile if you have brains enough to comprehend it.
On January 17, 2009 at 3:19 pm
suckish.
On January 19, 2009 at 2:16 pm
yeah right >=(
On February 8, 2009 at 9:42 am
i think the fabinacci sequence is totally boring!!!
On March 26, 2009 at 11:41 am
very bad article
nothing was informative
On March 30, 2009 at 8:37 pm
it was crap
On April 12, 2009 at 1:25 am
the info above r tru
On April 19, 2009 at 1:50 pm
Well done, you each get a cookie. Sadly none of you have been extended an invitation to have tea and crumpets with the ‘Almighty’, because he’s a little annoyed that you have wasted so much of your precious lives researching, debating and commenting on largely irrelevant subjects. If you’re all so infinitely intelligent or at least supremely confident enough to be so opinionated then would you please do something more useful with your time.
On April 20, 2009 at 1:35 pm
wot the hell ??
I don’t even know what the hell your on about!
who believes in God? (dog) woof
On May 27, 2009 at 5:20 am
I dunno what to believe with this. this particular artical isnt very imformative though
On May 27, 2009 at 5:21 am
Jesus was ‘ere 123 BC
On May 27, 2009 at 11:14 am
thanks for the info
On May 28, 2009 at 5:13 am
All right, I must have read a different article than exist above.
I read and re-read and still was unable to find the religious reference in article. Surely I must have overlooked it.
everything is relevant, but it appears that more info is seemingly demanded. here is a link that will pretty much address any question left unaddressed and many of them that were.
If one can read and process the depth of the information and relevance of the material contained, then possible, you won’t be too harsh on the author. As depicted in the article below, there is a significance to the sequence as well as a benefit to those that work in the field. Not to mention it is interesting, but isn’t all of math interesting….???
here is the link that has MUCH more info.
http://en.wikipedia.org/wiki/Fibonacci_number
I can’t vouch for the validity of every aspect of this particular article, but from what I did read, I have read other presentations of same and I felt it to be informative.
Guess comment sections are here to keep us amused as well…
Seems like so many people need to relax and take it all in…
Life IS good…
On May 31, 2009 at 1:36 pm
nice job. its amazing how entertaining it is to read how you guys have been fighting. thanks for all the laughs!!!!!
On June 4, 2009 at 2:16 pm
what is this
On June 10, 2009 at 8:57 pm
I think you should all just chillax. It sounds so annoying!All of you who had this super long entry was faking it. I bet ya that they just copied and pasted it from some website. Chill and go play or read or somethin’.
Peace!!=)
On July 26, 2009 at 4:14 am
thanks that wasn’t that good
On August 29, 2009 at 7:52 am
fibonacci is all over my body !! get rid of him !!
LOL it’s well-known that fibonacci appears in sunflower and nautilus shell.
nice article.
On November 5, 2009 at 3:18 pm
need sources definitly
On November 15, 2009 at 6:25 am
Great article, really helped with my homework, thanks a lot for sharing!!!
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