Fibonacci sequence is a sequence of numbers where each number is obtained from the sum of the previous two series. Thus, the first 10 numbers of the Fibonacci sequence are:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
(first 2 numbers are predefined and the rest are obtained recursively from the sum of the previous two: 3 = 2 + 1 5 = 3 + 2, aso)
Fibonacci sequence has fascinated throughout history on many scientists, mathematicians, physicists, biologists, and continue to do so even today.
Fibonacci (1170 - 1240) is considered one of the greatest European mathematicians of the Middle Ages. He was born in Pisa, the Italian city famous for its leaning tower. His father was a customs officer in the city called Bougie in North Africa, so the Fibonacci increased among North African civilization, making, however, many trips around the Mediterranean coasts.
Fibonacci is known as one of the first who introduced arabic numerals to Europe, and numbers that we use today: 0, 1, 2, 3, .. 9.
Fibonacci and the nature
Plants have no way to know the Fibonacci numbers, but they develop in the most effective way. Thus, many plants have leaves arranged in a Fibonacci sequence layout around the stems. Some pine cones follow a layout on Fibonacci numbers, and also the sunflower.
Rings on the trunks of palm trees meet the Fibonacci numbers. The reason for this is to achieve an optimum, the maximum efficiency. Thus for example, following the Fibonacci sequence, the leaves of plants can be arranged so as to occupy a small space and obtain as much sun.
The idea in this leaves arrangement starts from the consideration of the golden angle of 222,5 degrees, divided by the entire 360 degrees will result in the number 0.61803398 ..., known as the Fibonacci sequence ratio.
Let me put it this way, the number of flower petals is often a Fibonacci sequence of numbers:
• iris, lily: 3 petals
• wild rose, violets, tulips, most flowers: 5 petals
• daisies can have 34 or 21 petals petals most common
and examples are endless.
It should be noted that the flowers with a number of petals which are not in the Fibonacci sequence, are rare and special: Euphorbia (2 petals).
Snail Shell
How many of you haven't studied a little the snail shell gone out "to walk" after a summer rain? . Its design follows a highly successful spiral, a spiral that we would find it rather hard to achieve by drawing it with pen. Being studied more thoroughly, it was concluded that this spiral follows the dimensions given by the Fibonacci sequence:
• the positive axis: 1, 2, 5, 13, and so on ...
• negative axis: 0, 1, 3, 8, aso. ..
The motivation for this arrangement is simple: this way the shell offers to snail the maximum security and space inside. It's still one of countless examples of the sequence in nature.
Human body
Fibonacci is known as one of the first who introduced arabic numerals to Europe, and numbers that we use today: 0, 1, 2, 3, .. 9.
Fibonacci and the nature
Rings on the trunks of palm trees meet the Fibonacci numbers. The reason for this is to achieve an optimum, the maximum efficiency. Thus for example, following the Fibonacci sequence, the leaves of plants can be arranged so as to occupy a small space and obtain as much sun.
The idea in this leaves arrangement starts from the consideration of the golden angle of 222,5 degrees, divided by the entire 360 degrees will result in the number 0.61803398 ..., known as the Fibonacci sequence ratio.
Let me put it this way, the number of flower petals is often a Fibonacci sequence of numbers:
• iris, lily: 3 petals• wild rose, violets, tulips, most flowers: 5 petals
• daisies can have 34 or 21 petals petals most common
and examples are endless.
It should be noted that the flowers with a number of petals which are not in the Fibonacci sequence, are rare and special: Euphorbia (2 petals).
Snail Shell
How many of you haven't studied a little the snail shell gone out "to walk" after a summer rain? . Its design follows a highly successful spiral, a spiral that we would find it rather hard to achieve by drawing it with pen. Being studied more thoroughly, it was concluded that this spiral follows the dimensions given by the Fibonacci sequence:
• the positive axis: 1, 2, 5, 13, and so on ...
• negative axis: 0, 1, 3, 8, aso. ..
The motivation for this arrangement is simple: this way the shell offers to snail the maximum security and space inside. It's still one of countless examples of the sequence in nature.
Human body
Human hand has five fingers, each finger with three phalanges, separated by two joints (numbers in sequence). The average size of phalanges are: 2cm, 3cm, 5cm. In continuation is a bone of the hand which is on average 8 cm.
Human face is characterized, in terms of aesthetic, through some several main dimensions: the main distance between the eyes, distance between mouth and eyes and the distance between the nose and eyes, and mouth size. The science of aesthetics is estimated to be even considered more pleasing to the eye as these dimensions better meet the Fibonacci sequence. 
Fibonacci numbers are considered to be actually the counting system of nature, a measure of Divinity. These numbers occur everywhere in nature, from the arrangement of leaves, up to the human hand, phalanges. If you divide 144 to 233 = 0.6180257, the result is close to "Theta"., Greek symbol for the golden number, golden spiral. (wherever there are spirals).
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