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The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. If the Fibonacci sequence is denoted F ( n ), where n is the first term in the sequence, the following equation obtains for n = 0, where the first two terms are defined as 0 and 1 by convention:
F (0) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
In some texts, it is customary to use n = 1. In that case the first two terms are defined as 1 and 1 by default, and therefore:
F (1) = 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci (named after, he did not discover). Fibonacci's sequence was first introduced to the western world in 1202 by Fibonacci, the sequence had been noted by Indian mathematicians as early as the sixth century.
Fibonacci used the arithmetic series to illustrate a problem based on a pair of breeding rabbits:
"How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?" The result can be expressed numerically as: 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
Fibonacci numbers are of interest to biologists and physicists because they are frequently observed in various natural objects and phenomena. The branching patterns in trees and leaves, for example, and the distribution of seeds in a raspberry are based on Fibonacci numbers.
A Sanskrit grammarian, Pingala, is credited with the first mention of the sequence of numbers, sometime between the fifth century B.C. and the second or third century A.D. Since Fibonacci introduced the series to Western civilization, it has had a high profile from time to time. Recently, in The Da Vinci Code , for example, the Fibonacci sequence is part of an important clue.
Another application, the Fibonacci poem , is a verse in which the progression of syllable numbers per line follows Fibonacci's pattern.
What
is
a Fib?
A poem
mathematical
Syllables are arranged in lines
according to Fibonacci's sequence of numbers:
One, one, two, three, five, eight, thirteen, twenty-one, thirty-four, fifty-five and so on.
Thus 1+1=2, 1+2=3, 2+3=5 and so on.
This simple, seemingly unremarkable recursive sequence has fascinated mathematicians for centuries. Its properties illuminate an array of surprising topics, from the aesthetic doctrines of the ancient Greeks to the growth patterns of plants (not to mention populations of rabbits).
[video=youtube_share;SjSHVDfXHQ4]http://youtu.be/SjSHVDfXHQ4[/video]
Ok, now we're done with the boring explanatory part, let's move on to the fascinating part of the thread;
The Fibonacci Sequence in Nature
The fibonacci also defines how the density of branches increases up a tree trunk, the arrangement of leaves on a stem, and how a pine cone's scales are arranged. Yet you will not see the fibonacci everywhere, as nature has many different methods and shades of survival. Here are some examples of it in nature.
The fibonacci spiral appears not only in the perfect nautilus shell,
But also in events and objects viewed from a far. An energy system in the shape of a fibonacci moves with limited losses. Hurricane Irene.
The fibonacci as some of the largest structures in the universe. Spiral galaxies are the most common galaxy shape. Galaxies group together in superclusters and superclusters group together in walls. Currently the largest known structures are these walls or filaments of numerous superclusters that are gravitationally bound and separated by large areas of void. The Milky Way's dust obstructs us from seeing the depth of these filaments or sheets, so we do not yet know the exact shape of these walls.
The fibonacci appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner. Here, a microscopic view of the ovary of an Anglerfish.
Fibonacci as a starting point of life.
Romanesque brocolli is a striking example of the fibonacci.
As is the sunflower.
All pinecones have it.
Pangolin's armor
Snails and human fingerprints
Waves
Water falls into the shapes of a fibonacci during numerous events.
From the shape of DNA, to the shape of seashells, trees, fingerprints, waves and even entire Galaxies the enigmatic Fibonacci Sequence is underlying almost every aspect of the physical structure of our reality.
Scientists dont know what holds the Universe together, the answer is sound and unseen forces. Matter is governed by sound frequencies. There is much more to life than we can perceive with our 5 senses. The question then becomes "who or what governs unseen forces?" What is behind the symmetry throughout nature? (Golden Ratio, Phi, Fibonacci Sequence etc.). Could it all be a crazy coincidence? What do you think?
F (0) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
In some texts, it is customary to use n = 1. In that case the first two terms are defined as 1 and 1 by default, and therefore:
F (1) = 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci (named after, he did not discover). Fibonacci's sequence was first introduced to the western world in 1202 by Fibonacci, the sequence had been noted by Indian mathematicians as early as the sixth century.
Fibonacci used the arithmetic series to illustrate a problem based on a pair of breeding rabbits:
"How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?" The result can be expressed numerically as: 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
Fibonacci numbers are of interest to biologists and physicists because they are frequently observed in various natural objects and phenomena. The branching patterns in trees and leaves, for example, and the distribution of seeds in a raspberry are based on Fibonacci numbers.
A Sanskrit grammarian, Pingala, is credited with the first mention of the sequence of numbers, sometime between the fifth century B.C. and the second or third century A.D. Since Fibonacci introduced the series to Western civilization, it has had a high profile from time to time. Recently, in The Da Vinci Code , for example, the Fibonacci sequence is part of an important clue.
Another application, the Fibonacci poem , is a verse in which the progression of syllable numbers per line follows Fibonacci's pattern.
What
is
a Fib?
A poem
mathematical
Syllables are arranged in lines
according to Fibonacci's sequence of numbers:
One, one, two, three, five, eight, thirteen, twenty-one, thirty-four, fifty-five and so on.
Thus 1+1=2, 1+2=3, 2+3=5 and so on.
This simple, seemingly unremarkable recursive sequence has fascinated mathematicians for centuries. Its properties illuminate an array of surprising topics, from the aesthetic doctrines of the ancient Greeks to the growth patterns of plants (not to mention populations of rabbits).
You must be registered for see images
[video=youtube_share;SjSHVDfXHQ4]http://youtu.be/SjSHVDfXHQ4[/video]
Ok, now we're done with the boring explanatory part, let's move on to the fascinating part of the thread;
The Fibonacci Sequence in Nature
The fibonacci also defines how the density of branches increases up a tree trunk, the arrangement of leaves on a stem, and how a pine cone's scales are arranged. Yet you will not see the fibonacci everywhere, as nature has many different methods and shades of survival. Here are some examples of it in nature.
The fibonacci spiral appears not only in the perfect nautilus shell,
You must be registered for see images
But also in events and objects viewed from a far. An energy system in the shape of a fibonacci moves with limited losses. Hurricane Irene.
You must be registered for see images
The fibonacci as some of the largest structures in the universe. Spiral galaxies are the most common galaxy shape. Galaxies group together in superclusters and superclusters group together in walls. Currently the largest known structures are these walls or filaments of numerous superclusters that are gravitationally bound and separated by large areas of void. The Milky Way's dust obstructs us from seeing the depth of these filaments or sheets, so we do not yet know the exact shape of these walls.
You must be registered for see images
The fibonacci appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner. Here, a microscopic view of the ovary of an Anglerfish.
You must be registered for see images
Fibonacci as a starting point of life.
You must be registered for see images
Romanesque brocolli is a striking example of the fibonacci.
You must be registered for see images
As is the sunflower.
You must be registered for see images
All pinecones have it.
You must be registered for see images
Pangolin's armor
You must be registered for see images
Snails and human fingerprints
You must be registered for see images
Waves
You must be registered for see images
Water falls into the shapes of a fibonacci during numerous events.
You must be registered for see images
From the shape of DNA, to the shape of seashells, trees, fingerprints, waves and even entire Galaxies the enigmatic Fibonacci Sequence is underlying almost every aspect of the physical structure of our reality.
Scientists dont know what holds the Universe together, the answer is sound and unseen forces. Matter is governed by sound frequencies. There is much more to life than we can perceive with our 5 senses. The question then becomes "who or what governs unseen forces?" What is behind the symmetry throughout nature? (Golden Ratio, Phi, Fibonacci Sequence etc.). Could it all be a crazy coincidence? What do you think?
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