Fibonacci | The mathematical part of a very special number Phi = 1.6 reveals a “divine proportion”, also called “golden number” for its presence in nature, in plants, animals and other forms of life, and also throughout the universe. Who did not notice and did not remain pleasantly surprised how much symmetry and order exist in nature?

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Probably many of us have already deduced that nature used in its “hazard” mathematical formulas that ultimately created everything that surrounds us. People are constantly trying to understand nature and its laws, to feel cosmic rhythms, to understand life more deeply, to achieve harmony with the environment.

## Fibonacci and the golden number

The applications of the golden number of the report as such are found in the proportion of works in architecture, painting, sculpture, aesthetics, and art in general, which confirms the long-standing interest in this number.

The divine proportion led to the construction of the Golden Rectangle, in which the ratio of the sides equals the number of gold.

This type of rectangle is considered to be particularly aesthetic and as a result has been and is heavily used in architecture and art.

For instance, it is considered that the face of Gioconda da Vinci falls into such a rectangle, and at least two such rectangles are found in the construction of the Parthenon of Athens.

There is the myth that Leonardo Da Vinci believed that GOLDEN PROPORTION was the proportion of the height and width of a “perfect” human face and that he had used the Golden Proportion in the realization of the Vitruvian man.

Although there is no evidence against this idea, there is no evidence in her favour, so the only reason to believe in this idea is faith itself.

The same is true of Botticelli’s famous painting “Birth of Venus” or in the case of Georges Seurat and his painting “The Parade of a Circus”.

There are also painters who intentionally used the Golden Proportion. Among them are Paul Serusier, Juan Gris, Giro Severini and Salvador Dali.

But they seem to have used P.A. only as an experimental technique, and not as an intrinsic aesthetic motif. The Cubists organized an exhibition called “Section d’Or” in Paris in 1912, but the name had no connection with the art exhibited.

There are also myths about Egyptian pyramids and graves built with Golden Proportion. Papyrus Ahmes of Egypt offers details of the construction of the Great Pyramid of Gizeh in 4700 BC with proportions according to a “sacred report”. The pyramid’s secret was written enormously, observing that the aisle of the aisle is centered on the polar star of that era with great precision: 4 minutes of the angle made relative to the “Alpha” star of the Dragon representing the north, and the four angles of the base is directed to the north, east, south and west with the same fairness.

The height of the pyramid multiplied by one billion is the distance between Earth and the Sun (150 million Km). The perimeter of the base divided by height gave “2 Pi”, double of 3.14, which could only be verified after 1670 Leibnitz.

But in this case, there is no evidence to support this claim. Just as there is no evidence to support the idea that some stone tablets indicate that the Babylonians knew the concept of P.A.

Once found this number, the story continues. The ancient Greeks apparently used the magic of numbers in architecture, a good example being the Pantheon in Athens.

Inspired by the Greeks, future generations of architects and designed buildings based on this wonderful proportion.

The painters did not ignore it either. It is said that Leonardo Da Vinci used the Golden Proportion to preserve the proportions of human figures in his paintings – so the proportion of gold reached the pages of Dan Brown’s short story.

Vitruvian man “The Man in Action” by Leonardo Da Vinci. We can draw many lines of rectangles in this figure. Then there are three distinct sets of Golden Rectangles: each for the head, body and leg area

The story is interesting, but … unfortunately, besides the fact that Euclid has solved the problem of dividing the line in his book “The Elements,” there is no other evidence to support the assertions about the Golden Proportion.

But there are good reasons to believe that all claims are false, as mathematician George Markowsky, of the University of Maine, pointed out in his article “Wrong notions about the proportion of gold” published in the College Mathematics Journal in January 1992.

But because the story, which unites pure mathematics with aesthetics, architecture, and painting, is much more interesting, the concrete arguments do not have much power over it.

Lately, an extension of the Golden Numbers series has been attempted in the space of three or more dimensions.

Thus, from a tridimensional point of view, one can speak of the Golden Volume, which defines a parallelepiped in which the ratio of length to height is equal to the ratio of height to width, this ratio, called the 3D Golden Number.

In fact, in this parallelepiped, harmony consists in the fact that the height is a geometric mean between length and width, which gives the structure a special unit.

The gold number is searched for in the most diverse and unexpected situations, for example, some are trying to find an explanation from this point of view even for the conversion factor of 1,609, very close to phi, which occurs in the transformation of miles in kilometres.

At the same time, Fibonacci numbers appear in many science issues, ranging from classical physics, chemistry, mathematics to the most modern fields of knowledge (synergy, fractal theory, chaos theory, neural computers and cellular automata).

Pseudo-random number generators, and various optimization methods and methods. They are found in the analysis of Euclid’s algorithm to determine the largest common divisor of two integers, to solve Hilbert’s problem in Zeckendorf’s theorem, and so on. In music, Fibonacci numbers are often used to make donations.

It is believed that Bèla Bártok’s String Instruments Music, String Instruments and Celtic Instrument was structured using the Fibonacci numbers.

The future and the need for people’s knowledge and understanding may give these unique numbers, new applications and interpretations, perhaps even on the uncertain ground of paranormal phenomena.

The Fibonacci string is a sequence of n

umbers in which each number is obtained from the sum of the previous two in the string.

Thus, the first ten numbers of the Fibonacci string are 1,1, 2, 3, 5, 8, 13, 21, 34, 55. The Fibonacci string in mathematics refers to the metaphysical explanations of the codes in our universe.

Fibonacci numbers are considered to be, in fact, the counting system of nature, a way of measuring the Divinity.

Fibonacci’s numbers appear all over nature, starting from the arrangement of the leaves, from the petals of a flower to the phalanx of the human hand, from birthday to the walls of the Pyramids.

It is said that there is a connection between the natural growth of plants and the Golden Number: the mysterious proportion of this number, represented either in Pythagoras’ golden triangle (isosceles), in the Golden Ellipse of the Hindu tradition or in the Golden Spiral which, through Fibonacci’s string, is shown to keep the ratio of 1,618.

We also find other things in the nature such as water spirals (spirals), spiral air movement, snail shell, arrangement of rose petals, or the leaves and seeds of the plant kingdom, which keep this perfect proportion showing that throughout the creation is preserved this proportion, perhaps the name of the “happiness formula” has also been drawn. This demonstrates the existence of a sphere of consciousness of harmony and beauty existing throughout the universe that guides him.

If we take a few squares equal to one of Fibonacci’s string numbers, and we stick these squares, then we draw lines like this each one comes out like the shape of a coil’s spiral.

Even the beauty of the human body is under the Fibonacci series. This string, revealed by Fibonacci in mathematics, refers to the metaphysical explanations of the codes in our universe.

Together, the ten digits gather together to form this message (say in esoteric circles): “In the twenty-first century, in these times of evolution, mankind will know Enlightenment”, so the Code states that in this age mankind will change its perception.

Everything that man has tried over the course of time will finally find a solution.

This solution would include all the principles of life, including how we relate to each other. It is said that these ten numbers, “disordered string, simple to absurd”, would be a numerical anagram.

Given the numerical significance of their numerical totals, in total ten numbers, it is revealed to us that this is significant in itself, the number 10 being an end in itself, is a return to the center, to the unity, to a new beginning and to the fulfillment of itself.

Ten represents a result, an achievement, this number encompasses and contains all the previous numbers, representing a cycle, forming, in turn, the beginning of a new cycle, being the great principle of all natural cycles, we can think of the ten fingers, the tree life and the source of youth.

In spirituality, being considered an endless cycle, it is also said that Fibonacci’s string turned out to be a key that would be likened to a five-petalled rose.

The five-petal rose pentagram is an extraordinary sacred symbol, this concept was initiated by putting together the five basic elements: EARTH, WATER, FIRE, AIR, and WATER EARTH. Figure five symbolizes the center, harmony, balance.

As far as the Golden Number, the divine section, another line that is also known as Phi, is a number very well known in the art, having its fundamental origins in nature, so that any element in nature is proportional to Phi.

If we replace the Phi letters with the corresponding numbers, we get 781, whose total sum is reduced to 7.

Adding the 1618 figures we see that it gives us 7, which is considered to be the most beautiful number in the universe, meaning the number of perfection, the number of God.

The ratio between the apotheke and the base of the triangles is 1.618, the Golden Number.

The number of gold is closely related to the Fibonacci string, where each term is the sum of the previous two (1, 1, 2, 3, 5, 8, 13, 21, 34, 55 …).

As we progress, the relationship between two successive terms of the Fibonacci string tends towards Phi.

The number of gold – the divine section, another line that is also known as Phi (1,618), is a very well-known number in the art with its fundamental origins in nature so that any element in nature is proportional to Phi.

Just as the Golden Section is found in the ensemble and beauty of nature, it can also be used to achieve beauty and balance in art.

The Golden Section has been extensively used by Leonardo da Vinci. Notice how all the key dimensions of the room and table in da Vinci’s painting, The Last Supper, were based on the Golden Section, which was known in the Renaissance period as the Divine Proportion.

Romanian scientist Henri Coanda has “hidden” the 1.61803 gold number in the Reaction Plane project.

Henri Coanda’s specialists, who had the task of taking pictures of the images of the first reaction plane photographed at the 1910 Paris Aeronautics Salon.

Noticed that the construction of the shape of the wing profile (cross-section) was used by Coanda in many elliptical shapes.

It was not surprising when they found that the ratio between the large radius and the small radius of the ellipse is even … The Golden Number.

## But who was actually Fibonacci?

Leonardo Pisano Fibonacci or Leonardo of Pisa (1170-1250), is considered one of the greatest European mathematicians of the Middle Ages.

He was born in Pisa, a famous Italian city for his inclined tower, which seems to fall.

His father, Guglielmo Bonacci, was a customs officer in the city of North Africa called Bougie (Bugia), so that Fibonacci grew up in the midst of North African civilization, receiving education specific to this area, but making many trips on the Mediterranean coast.

In his journeys he met many traders from whom he learned his arithmetical system, thus familiarizing himself with the counting system considered today by the Indo-Arab, but invented by the Vedic. Who else, if not the Ares of Ares (the Aryans)?

Fibonacci has finished his travels around 1200, after which he returned to Pisa, where he began writing a significant number of texts that played an important role in updating the mathematical knowledge of antiquity and added his own contributions.

In 1220 Fibonacci public “Practice geometry”, a collection of geometry and trigonometry, Fibonacci arrive at the solution of one of the equations mechanism at the time 10 x + 2 x 2 + x 3 = 20, the equation that Johannes of Palermo has been trying for some time to solve it.

## The Golden Proportion

Let’s make an insight into the history of numbers and proportions, in the art world and in nature, having as a common point the Golden Proportion. The common element that unites science, mathematics, art, nature, areas that apparently cannot be related is the “number/proportion of gold”.

Two quantities a and b are found in the golden proportion if a + b is equal to a / b. The numerical value of this ratio is (about, irrational number) 1,618 and was called the Golden Number.

Although this proportion has been known since antiquity, it was only in 1835 called “Golden Proportion” by Greek mathematician Martin Ohm (1792-1872), and from the beginning of the 20th century is symbolized by the Greek letter Phi as a tribute to the great the Greek sculptor Phidias, who used in his sculptures and in the construction of Parthenon dimensions in the Golden Proportion.

## Fibonacci numbers in nature

The Fibonacci sequence occurs in biological structures, such as the arrangement of tree branches, the laying of leaves around the plant stem, the shell spirals, the arrangement of a cone, the development of branches of a fern, the appearance of a pineapple, etc. It has been suggested that all of these can be partially understood as an expression of algebraic constraints specific to free systems.

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It is often said that floral arrangements similar to sunflowers have 55 spirals in the direction and 89 in the other (55 and 89 are adjacent numbers in the Fibonacci string), which is true for the inflorescences in the outer layer and which are most visible. Also, the number of petals of many flowers is part of the sequence.

## Fibonacci and human body

If we look at the hands of a man, we find other coincidences perhaps, what we remember the famous string. We have two hands, each with 5 fingers, and each with three phalanxes separated by two joints.

Coincidentally or not, the aspect is interesting, all the more so since measuring the length of the bones of the fingers, it seems that the ratio between the longest and the middle bone as well as the ratio between the middle bone and the shortest peak is the proportion of gold Phi.

On average, the phalanges are: 2 cm, 3 cm, 5 cm, and the palm bone is about 8 cm (2, 3, 5, 8 are numbers from the Fibonacci sequence). At the same time, the human face is aesthetically characterized by several main dimensions: the distance between the eyes, the distance between the mouth and the eye, the distance between the nose and the eye, the size of the mouth.

In aesthetics, it is appreciated that the face is all the more pleasing to the eye as these dimensions are better in keeping with Fibonacci’s sequence.

The proportion of gold is everywhere, but nowhere is it as impressive and as important as what we discover in the human body, more important than our DNA.

**For more insights watch the following video**:

**References:**

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