He will talk about the concept of the Fibonacci series and how it is related to the theory of waves, and will also refute the applicability of the series to natural processes.
, which the master developed in the 30s of the last century, is one of the most exciting sections. In itself, it was separated into a new chapter of science, which studies graphs. It is based on the developments of other experts in the field of theory (I advise you to read the book by author).
So, for example, the great Italian mathematician Leonardo Fibonacci is considered one of the scientists (about whom I have already spoken in the articles -), who created the basis for Eliot’s theory.
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Digital series of Fibonacci numbers – golden ratio and coefficients or correction levels + video. Fibonacci numbers in nature.The specialist lived back in the 13th century. The scientist published a work called “The Book of Calculations.” This book introduced Europe to an important and not only discovery for those times - the decimal number system. This system introduced the familiar numbers from zero to nine into circulation.
The emergence of this system was the first important achievement of Europe since the fall of Rome. Fibonacci preserved the science of numbers for the Middle Ages. He also laid the deep foundations for the development of other sciences, such as higher mathematics, physics, astronomy, and mechanical engineering.
Watch the video
How numbers and their derivatives appeared
While solving an applied problem, Leonardo came across a curious series of Fibonacci numbers, at the beginning of which there are two units.
Each subsequent term is the sum of the previous two. The most interesting thing is that the Fibonacci number series is a remarkable sequence in that if any term is divided by the previous one, the result is a number that is close to 0.618. This number was given the name " Golden ratio».
It turned out that this number has been known to mankind for a very long time. For example, in ancient Egypt they built pyramids using it, and the ancient Greeks built their temples on it. Leonardo da Vinci showed how the structure of the human body obeys this number.
Nature uses Fibonacci numbers in its most intimate and advanced areas. From atomic structures and other small forms like DNA molecules and microcapillaries of the brain to huge ones like planetary orbits and galactic structures. The number of examples is so large that it must be argued that there is indeed some basic law of proportions in nature.
Therefore, it is not surprising that the Fibonacci series and the golden ratio have made their way onto stock charts. And not just the number 0.618, but also its derivatives.
If you raise the golden ratio number to the first, second, third and fourth powers and subtract the result from unity, you get a new series called “ Fibonacci retracement ratios" All that remains is to add the mark of five tenths - this is fifty percent.
However, this is not all that can be done with the golden ratio. If we divide one by 0.618, we get 1.618; if we square it, we get 2.618; if we cube it, we get 4.236. These are the Fibonacci expansion ratios. The only missing number here is 3,236, which was proposed by John Murphy.
What do experts think about consistency?
Some might say that these numbers are already familiar because they are used in technical analysis programs to determine the magnitude of corrections and extensions. In addition, these same rows play important role in Eliot's wave theory. They are its numerical basis.
Our expert Nikolay is a proven portfolio manager at the Vostok investment company.
- – Nikolay, do you think that the appearance of Fibonacci numbers and its derivatives on the charts of various instruments is accidental? And is it possible to say: “Fibonacci series practical application” takes place?
- – I have a bad attitude towards mysticism. And even more so on stock exchange charts. Everything has its reasons. in the book “Fibonacci Levels” he beautifully described where the golden ratio appears, that he was not surprised that it appeared on stock exchange quote charts. But in vain! In many of the examples he gave, the number Pi appears frequently. But for some reason it is not included in the price ratios.
- – So you don’t believe in the validity of Eliot’s wave principle?
- - No, that’s not the point. The wave principle is one thing. The numerical ratio is different. And the reasons for their appearance on price charts are the third
- – What, in your opinion, are the reasons for the appearance of the golden ratio on stock charts?
- – The correct answer to this question may be able to earn Nobel Prize in economics. For now we can guess about the true reasons. They are clearly not in harmony with nature. There are many models of exchange pricing. They do not explain the designated phenomenon. But not understanding the nature of a phenomenon should not deny the phenomenon as such.
- – And if this law is ever opened, will it be able to destroy the exchange process?
- – As the same wave theory shows, the law of changes in stock prices is pure psychology. It seems to me that knowledge of this law will not change anything and will not be able to destroy the stock exchange.
Material provided by webmaster Maxim's blog.
The coincidence of the fundamental principles of mathematics in a variety of theories seems incredible. Maybe it's fantasy or customized for the final result. Wait and see. Much of what was previously considered unusual or was not possible: space exploration, for example, has become commonplace and does not surprise anyone. Also, the wave theory, which may be incomprehensible, will become more accessible and understandable over time. What was previously unnecessary will, in the hands of an experienced analyst, become a powerful tool for predicting future behavior.
Fibonacci numbers in nature.
Look
Now, let's talk about how you can refute the fact that the Fibonacci digital series is involved in any patterns in nature.
Let's take any other two numbers and build a sequence with the same logic as the Fibonacci numbers. That is, the next member of the sequence equal to the sum the previous two. For example, let's take two numbers: 6 and 51. Now we will build a sequence that we will complete with two numbers 1860 and 3009. Note that when dividing these numbers, we get a number close to the golden ratio.
At the same time, the numbers that were obtained when dividing other pairs decreased from the first to the last, which allows us to say that if this series continues indefinitely, then we will get a number equal to the golden ratio.
Thus, Fibonacci numbers do not stand out in any way. There are other sequences of numbers, of which there are an infinite number, that as a result of the same operations give the golden number phi.
Fibonacci was not an esotericist. He didn't want to put any mysticism into the numbers, he was simply solving an ordinary problem about rabbits. And he wrote a sequence of numbers that followed from his problem, in the first, second and other months, how many rabbits there would be after breeding. Within a year, he received that same sequence. And I didn't do a relationship. There was no talk of any golden proportion or divine relation. All this was invented after him during the Renaissance.
Compared to mathematics, the advantages of Fibonacci are enormous. He adopted the number system from the Arabs and proved its validity. It was a hard and long struggle. From the Roman number system: heavy and inconvenient for counting. She disappeared after french revolution. Fibonacci has nothing to do with the golden ratio.
There are an infinite number of spirals, the most popular: spiral natural logarithm, Archimedes spiral, hyperbolic spiral.
Kanalieva Dana
In this work, we studied and analyzed the manifestation of the Fibonacci sequence numbers in the reality around us. We discovered an amazing mathematical relationship between the number of spirals in plants, the number of branches in any horizontal plane, and the Fibonacci sequence numbers. We also saw strict mathematics in the human structure. The human DNA molecule, in which the entire development program of a human being is encrypted, the respiratory system, the structure of the ear - everything obeys certain numerical relationships.
We are convinced that Nature has its own laws, expressed using mathematics.
And mathematics is very important tool of cognition secrets of Nature.
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MBOU "Pervomaiskaya Secondary School"
Orenburg district, Orenburg region
RESEARCH
"The Mystery of Numbers"
Fibonacci"
Completed by: Kanalieva Dana
6th grade student
Scientific adviser:
Gazizova Valeria Valerievna
Mathematics teacher of the highest category
n. Experimental
2012
Explanatory note………………………………………………………………………………........ 3.
Introduction. History of Fibonacci numbers.……………………………………………………...... 4.
Chapter 1. Fibonacci numbers in living nature.........……. …………………………………... 5.
Chapter 2. Fibonacci Spiral.................................................... ..........……………..... 9.
Chapter 3. Fibonacci numbers in human inventions.........…………………………….. 13
Chapter 4. Our research……………………………………………………………....... 16.
Chapter 5. Conclusion, conclusions………………………………………………………………………………...... 19.
List of used literature and Internet sites…………………………………........21.
Object of study:
Man, mathematical abstractions created by man, human inventions, the surrounding flora and fauna.
Subject of study:
form and structure of the objects and phenomena being studied.
Purpose of the study:
study the manifestation of Fibonacci numbers and the associated law of the golden ratio in the structure of living and non-living objects,
find examples of using Fibonacci numbers.
Job objectives:
Describe a method for constructing the Fibonacci series and Fibonacci spiral.
See mathematical patterns in the human structure, flora And inanimate nature from the point of view of the Golden Ratio phenomenon.
Novelty of the research:
Discovery of Fibonacci numbers in the reality around us.
Practical significance:
Using acquired knowledge and skills research work when studying other school subjects.
Skills and abilities:
Organization and conduct of the experiment.
Use of specialized literature.
Acquiring the ability to review collected material (report, presentation)
Design of work with drawings, diagrams, photographs.
Active participation in discussions of your work.
Research methods:
empirical (observation, experiment, measurement).
theoretical (logical stage of cognition).
Explanatory note.
“Numbers rule the world! Number is the power that reigns over gods and mortals!” - this is what the ancient Pythagoreans said. Is this basis of Pythagoras’ teaching still relevant today? When studying the science of numbers at school, we want to make sure that, indeed, the phenomena of the entire Universe are subject to certain numerical relationships, to find this invisible connection between mathematics and life!
Is it really in every flower,
Both in the molecule and in the galaxy,
Numerical patterns
This strict “dry” mathematics?
We turned to a modern source of information - the Internet and read about Fibonacci numbers, about magic numbers that are fraught with a great mystery. It turns out that these numbers can be found in sunflowers and pine cones, in the wings of dragonflies and starfish, in the rhythms of the human heart and in musical rhythms...
Why is this sequence of numbers so common in our world?
We wanted to know about the secrets of Fibonacci numbers. This research work was the result of our activities.
Hypothesis:
in the reality around us, everything is built according to amazingly harmonious laws with mathematical precision.
Everything in the world is thought out and calculated by our most important designer - Nature!
Introduction. History of the Fibonacci series.
Amazing numbers were discovered by the Italian medieval mathematician Leonardo of Pisa, better known as Fibonacci. Traveling around the East, he became acquainted with the achievements of Arab mathematics and contributed to their transfer to the West. In one of his works entitled “The Book of Calculations”, he presented to Europe one of greatest discoveries of all times and peoples - the decimal number system.
One day, he was racking his brains over solving a mathematical problem. He was trying to create a formula to describe the breeding sequence of rabbits.
The solution was a number series, each subsequent number of which is the sum of the two previous ones:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, ...
The numbers that form this sequence are called “Fibonacci numbers”, and the sequence itself is called the Fibonacci sequence.
"So what?" - you say, “Can we really come up with similar number series ourselves, increasing according to a given progression?” Indeed, when the Fibonacci series appeared, no one, including himself, had any idea how close he managed to come to solving one of the greatest mysteries of the universe!
Fibonacci led a reclusive lifestyle, spent a lot of time in nature, and while walking in the forest, he noticed that these numbers began to literally haunt him. Everywhere in nature he encountered these numbers again and again. For example, the petals and leaves of plants strictly fit into a given number series.
In Fibonacci numbers there is interesting feature: the quotient of dividing the subsequent Fibonacci number by the previous one, as the numbers themselves grow, tends to 1.618. It was this constant division number that was called the Divine proportion in the Middle Ages, and is now referred to as the golden section or golden proportion.
In algebra, this number is denoted by the Greek letter phi (Ф)
So, φ = 1.618
233 / 144 = 1,618
377 / 233 = 1,618
610 / 377 = 1,618
987 / 610 = 1,618
1597 / 987 = 1,618
2584 / 1597 = 1,618
No matter how many times we divide one by another, the number adjacent to it, we will always get 1.618. And if we do the opposite, that is, divide the smaller number by the larger one, we will get 0.618, this is the inverse of 1.618. also called the golden ratio.
The Fibonacci series could have remained only a mathematical incident, if not for the fact that all researchers of the golden division in the plant and animal world, not to mention art, invariably came to this series as an arithmetic expression of the law of the golden division.
Scientists, analyzing the further application of this number series to natural phenomena and processes, they discovered that these numbers are contained in literally all objects of living nature, in plants, animals and humans.
The amazing mathematical toy turned out to be a unique code embedded in all natural objects by the Creator of the Universe himself.
Let's look at examples where Fibonacci numbers occur in living and inanimate nature.
Fibonacci numbers in living nature.
If you look at the plants and trees around us, you can see how many leaves there are on each of them. From a distance, it seems that the branches and leaves on the plants are located randomly, in no particular order. However, in all plants, in a miraculous, mathematically precise way, which branch will grow from where, how the branches and leaves will be located near the stem or trunk. From the first day of its appearance, the plant exactly follows these laws in its development, that is, not a single leaf, not a single flower appears by chance. Even before its appearance, the plant is already precisely programmed. How many branches will there be on the future tree, where will the branches grow, how many leaves will there be on each branch, and how and in what order the leaves will be arranged. The joint work of botanists and mathematicians has shed light on these amazing natural phenomena. It turned out that the Fibonacci series manifests itself in the arrangement of leaves on a branch (phylotaxis), in the number of revolutions on the stem, in the number of leaves in a cycle, and therefore, the law of the golden ratio also manifests itself.
If you set out to find numerical patterns in living nature, you will notice that these numbers are often found in various spiral forms, which are so rich in the plant world. For example, leaf cuttings are adjacent to the stem in a spiral that runs betweentwo adjacent leaves:full rotation - at the hazel tree,- by the oak tree, - at the poplar and pear trees,- at the willow.
The seeds of sunflower, Echinacea purpurea and many other plants are arranged in spirals, and the number of spirals in each direction is the Fibonacci number.
Sunflower, 21 and 34 spirals. Echinacea, 34 and 55 spirals.
The clear, symmetrical shape of flowers is also subject to a strict law.
For many flowers, the number of petals is precisely the numbers from the Fibonacci series. For example:
iris, 3p. buttercup, 5 lep. golden flower, 8 lep. delphinium,
13 lep.
chicory, 21lep. aster, 34 lep. daisies, 55 lep.
The Fibonacci series characterizes structural organization many living systems.
We have already said that the ratio of neighboring numbers in the Fibonacci series is the number φ = 1.618. It turns out that man himself is simply a storehouse of phi numbers.
The proportions of the various parts of our body are a number very close to the golden ratio. If these proportions coincide with the golden ratio formula, then the person’s appearance or body is considered ideally proportioned. The principle of calculating the gold measure on the human body can be depicted in the form of a diagram.
M/m=1.618
The first example of the golden ratio in the structure of the human body:
If we take the navel point as the center of the human body, and the distance between a person’s foot and the navel point as a unit of measurement, then a person’s height is equivalent to the number 1.618.
Human hand
It is enough just to bring your palm closer to you and look carefully at your index finger, and you will immediately find the formula of the golden ratio in it. Each finger of our hand consists of three phalanges.
The sum of the first two phalanges of the finger in relation to the entire length of the finger gives the number of the golden ratio (with the exception of the thumb).
In addition, the ratio between the middle finger and little finger is also equal to the golden ratio.
A person has 2 hands, the fingers on each hand consist of 3 phalanges (except for the thumb). There are 5 fingers on each hand, that is, 10 in total, but with the exception of two two-phalanx thumbs, only 8 fingers are created according to the principle of the golden ratio. Whereas all these numbers 2, 3, 5 and 8 are the numbers of the Fibonacci sequence.
Golden ratio in the structure of the human lungs
American physicist B.D. West and Dr. A.L. Goldberger, during physical and anatomical studies, established that the golden ratio also exists in the structure of the human lungs.
The peculiarity of the bronchi that make up the human lungs lies in their asymmetry. The bronchi consist of two main airways, one of which (the left) is longer and the other (the right) is shorter.
It was found that this asymmetry continues in the branches of the bronchi, in all the smaller respiratory tracts. Moreover, the ratio of the lengths of short and long bronchi is also the golden ratio and is equal to 1:1.618.
Artists, scientists, fashion designers, designers make their calculations, drawings or sketches based on the ratio of the golden ratio. They use measurements from the human body, which was also created according to the principle of the golden ratio. Before creating their masterpieces, Leonardo Da Vinci and Le Corbusier took the parameters of the human body, created according to the law of the Golden Proportion.
There is another, more prosaic application of the proportions of the human body. For example, using these relationships, crime analysts and archaeologists use fragments of parts of the human body to reconstruct the appearance of the whole.
Golden proportions in the structure of the DNA molecule.
All information about the physiological characteristics of living beings, be it a plant, an animal or a person, is stored in a microscopic DNA molecule, the structure of which also contains the law of the golden proportion. The DNA molecule consists of two vertically intertwined helices. The length of each of these spirals is 34 angstroms and the width is 21 angstroms. (1 angstrom is one hundred millionth of a centimeter).
So, 21 and 34 are numbers following each other in the sequence of Fibonacci numbers, that is, the ratio of the length and width of the logarithmic spiral of the DNA molecule carries the formula of the golden ratio 1:1.618.
Not only erect walkers, but also all swimming, crawling, flying and jumping creatures did not escape the fate of being subject to the number phi. The human heart muscle contracts to 0.618 of its volume. The structure of a snail shell corresponds to the Fibonacci proportions. And such examples can be found in abundance - if there was a desire to explore natural objects and processes. The world is so permeated with Fibonacci numbers that sometimes it seems that the Universe can only be explained by them.
Fibonacci spiral.
There is no other form in mathematics that has the same unique properties as the spiral, because
The structure of the spiral is based on the Golden Ratio rule!
To understand the mathematical construction of a spiral, let us repeat what the Golden Ratio is.
The golden ratio is such a proportional division of a segment into unequal parts, in which the entire segment is related to the larger part as the larger part itself is related to the smaller one, or, in other words, the smaller segment is related to the larger one as the larger one is to the whole.
That is (a+b) /a = a / b
A rectangle with exactly this aspect ratio came to be called the golden rectangle. Its long sides are in relation to its short sides in a ratio of 1.168:1.
The golden rectangle has many unusual properties. Cutting a square from a golden rectangle whose side is equal to the smaller side of the rectangle,
we will again get a smaller golden rectangle.
This process can be continued indefinitely. As we continue to cut off squares, we will end up with smaller and smaller golden rectangles. Moreover, they will be located in a logarithmic spiral, which is important in mathematical models of natural objects.
For example, the spiral shape can be seen in the arrangement of sunflower seeds, in pineapples, cacti, the structure of rose petals, and so on.
We are surprised and delighted by the spiral structure of shells.
In most snails that have shells, the shell grows in a spiral shape. However, there is no doubt that these unreasonable creatures not only have no idea about the spiral, but do not even have the simplest mathematical knowledge to create a spiral-shaped shell for themselves.
But then how were these unreasonable creatures able to determine and choose for themselves the ideal form of growth and existence in the form of a spiral shell? Could these living beings, whom scientists world calls primitive life forms, calculate that the spiral shape of a shell would be ideal for their existence?
Trying to explain the origin of such even the most primitive form of life by a random combination of certain natural circumstances is absurd, to say the least. It is clear that this project is a conscious creation.
Spirals also exist in humans. With the help of spirals we hear:
Also, in the human inner ear there is an organ called Cochlea (“Snail”), which performs the function of transmitting sound vibration. This bony structure is filled with fluid and created in the shape of a snail with golden proportions.
There are spirals on our palms and fingers:
In the animal kingdom we can also find many examples of spirals.
The horns and tusks of animals develop in a spiral shape, the claws of lions and the beaks of parrots are logarithmic shapes and resemble the shape of an axis that tends to turn into a spiral.
It’s interesting that a hurricane and a cyclone’s clouds are twisting like a spiral, and this is clearly visible from space:
In ocean and sea waves, the spiral can be mathematically represented on a graph with points 1,1,2,3,5,8,13,21,34 and 55.
Everyone will also recognize such an “everyday” and “prosaic” spiral.
After all, the water escapes from the bathroom in a spiral:
Yes, and we live in a spiral, because the galaxy is a spiral corresponding to the formula of the Golden Ratio!
So, we found out that if we take the Golden Rectangle and break it into smaller rectanglesin the exact Fibonacci sequence, and then divide each of them in such proportions again and again, you get a system called the Fibonacci spiral.
We discovered this spiral in the most unexpected objects and phenomena. Now it’s clear why the spiral is also called the “curve of life.”
The spiral has become a symbol of evolution, because everything develops in a spiral.
Fibonacci numbers in human inventions.
Having observed a law in nature expressed by the sequence of Fibonacci numbers, scientists and artists try to imitate it and embody this law in their creations.
The phi proportion allows you to create masterpieces of painting and correctly fit architectural structures into space.
Not only scientists, but also architects, designers and artists are amazed by this perfect spiral of the nautilus shell,
occupying the least space and providing the least heat loss. American and Thai architects, inspired by the example of the “chambered nautilus” in the matter of placing the maximum in the minimum space, are busy developing corresponding projects.
Since time immemorial, the Golden Ratio proportion has been considered the highest proportion of perfection, harmony and even divinity. The golden ratio can be found in sculptures and even in music. An example is the musical works of Mozart. Even stock exchange rates and the Hebrew alphabet contain a golden ratio.
But we want to focus on a unique example of creating an efficient solar installation. An American schoolboy from New York, Aidan Dwyer, put together his knowledge of trees and discovered that the efficiency of solar power plants can be increased by using mathematics. While on a winter walk, Dwyer wondered why trees needed such a “pattern” of branches and leaves. He knew that branches on trees are arranged according to the Fibonacci sequence, and leaves carry out photosynthesis.
At some point, the smart boy decided to check whether this position of the branches helps to collect more sunlight. Aidan built a pilot plant in his backyard using small solar panels instead of leaves and tested it in action. It turned out that compared to a conventional flat solar panel, its “tree” collects 20% more energy and operates efficiently for 2.5 hours longer.
Dwyer solar tree model and graphs made by a student.
“This installation also takes up less space than a flat panel, collects 50% more sun in winter even where it does not face south, and it does not accumulate as much snow. In addition, a tree-shaped design is much more suitable for the urban landscape,” notes the young inventor.
Aidan was recognized one of the best young naturalists of 2011. The 2011 Young Naturalist competition was hosted by the New York Museum of Natural History. Aidan has filed a provisional patent application for his invention.
Scientists continue to actively develop the theory of Fibonacci numbers and the golden ratio.
Yu. Matiyasevich solves Hilbert's 10th problem using Fibonacci numbers.
Elegant methods are emerging for solving a number of cybernetic problems (search theory, games, programming) using Fibonacci numbers and the golden ratio.
In the USA, even the Mathematical Fibonacci Association is being created, which has been publishing a special journal since 1963.
So, we see that the scope of the Fibonacci sequence of numbers is very multifaceted:
Observing the phenomena occurring in nature, scientists have made striking conclusions that the entire sequence of events occurring in life, revolutions, crashes, bankruptcies, periods of prosperity, laws and waves of development in the stock and foreign exchange markets, cycles family life, and so on, are organized on a time scale in the form of cycles, waves. These cycles and waves are also distributed according to the Fibonacci number series!
Based on this knowledge, a person will learn to predict and manage various events in the future.
4. Our research.
We continued our observations and studied the structure
pine cone
yarrow
mosquito
person
And we became convinced that in these objects, so different at first glance, the same numbers of the Fibonacci sequence were invisibly present.
So, step 1.
Let's take a pine cone:
Let's take a closer look at it:
We notice two series of Fibonacci spirals: one - clockwise, the other - counterclockwise, their number 8 and 13.
Step 2.
Let's take yarrow:
Let's carefully consider the structure of the stems and flowers:
Note that each new branch of the yarrow grows from the axil, and new branches grow from the new branch. By adding up the old and new branches, we found the Fibonacci number in each horizontal plane.
Step 3.
Do Fibonacci numbers appear in the morphology of various organisms? Consider the well-known mosquito:
We see: 3 pairs of legs, head 5 antennae, the abdomen is divided into 8 segments.
Conclusion:
In our research, we saw that in the plants around us, living organisms and even in the human structure, numbers from the Fibonacci sequence manifest themselves, which reflects the harmony of their structure.
The pine cone, the yarrow, the mosquito, and the human being are arranged with mathematical precision.
We were looking for an answer to the question: how does the Fibonacci series manifest itself in the reality around us? But, answering it, we received more and more questions.
Where did these numbers come from? Who is this architect of the universe who tried to make it ideal? Is the spiral curling or unwinding?
How amazing it is for a person to experience this world!!!
Having found the answer to one question, he gets the next one. If he solves it, he gets two new ones. Once he deals with them, three more will appear. Having solved them too, he will have five unsolved ones. Then eight, then thirteen, 21, 34, 55...
Do you recognize?
Conclusion.
by the creator himself into all objects
A unique code is provided
And the one who is friendly with mathematics,
He will know and understand!
We have studied and analyzed the manifestation of the Fibonacci sequence numbers in the reality around us. We also learned that the patterns of this number series, including the patterns of “Golden” symmetry, are manifested in the energy transitions of elementary particles, in planetary and cosmic systems, in the gene structures of living organisms.
We discovered a surprising mathematical relationship between the number of spirals in plants, the number of branches in any horizontal plane, and the numbers in the Fibonacci sequence. We saw how the morphology of various organisms also obeys this mysterious law. We also saw strict mathematics in the human structure. The human DNA molecule, in which the entire development program of a human being is encrypted, the respiratory system, the structure of the ear - everything obeys certain numerical relationships.
We learned that pine cones, snail shells, ocean waves, animal horns, cyclone clouds and galaxies all form logarithmic spirals. Even the human finger, which is composed of three phalanges in the Golden Ratio relative to each other, takes on a spiral shape when squeezed.
An eternity of time and light years of space separate the pine cone and the spiral galaxy, but the structure remains the same: coefficient 1,618 ! Perhaps this is the primary law governing natural phenomena.
Thus, our hypothesis about the existence of special numerical patterns that are responsible for harmony is confirmed.
Indeed, everything in the world is thought out and calculated by our most important designer - Nature!
We are convinced that Nature has its own laws, expressed using mathematics. And mathematics is a very important tool
to learn the secrets of nature.
List of literature and Internet sites:
1.
Vorobiev N. N. Fibonacci numbers. - M., Nauka, 1984.
2. Ghika M. Aesthetics of proportions in nature and art. - M., 1936.
3. Dmitriev A. Chaos, fractals and information. // Science and Life, No. 5, 2001.
4. Kashnitsky S. E. Harmony woven from paradoxes // Culture and
Life. - 1982.- No. 10.
5. Malay G. Harmony - the identity of paradoxes // MN. - 1982.- No. 19.
6. Sokolov A. Secrets of the golden section // Youth technology. - 1978.- No. 5.
7. Stakhov A.P. Codes of the golden proportion. - M., 1984.
8. Urmantsev Yu. A. Symmetry of nature and the nature of symmetry. - M., 1974.
9. Urmantsev Yu. A. Golden section // Nature. - 1968.- No. 11.
10. Shevelev I.Sh., Marutaev M.A., Shmelev I.P. Golden Ratio/Three
A look at the nature of harmony.-M., 1990.
11. Shubnikov A. V., Koptsik V. A. Symmetry in science and art. -M.:
Leonardo Fibonacci is one of the most famous mathematicians of the Middle Ages. One of his most important achievements is the number series, which defines the golden ratio and can be traced throughout the nature of our planet.
An amazing property of these numbers is that the sum of all previous numbers is equal to the next number (check it yourself):
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610… - Fibonacci series
It turns out that this sequence has many interesting properties from a mathematical point of view. Here's an example: you can split a line into two parts. The ratio of the smaller part of the line to the larger one will be equal to the ratio of the larger part to the entire line. This proportionality ratio, approximately 1.618, is known as the golden ratio.
The Fibonacci series could have remained only a mathematical incident, if not for the fact that all researchers of the golden ratio find this sequence in the entire plant and animal world. Here are some amazing examples:
The arrangement of leaves on a branch, sunflower seeds, pine cones manifests itself as the golden ratio. If you look at the leaves of such a plant from above, you will notice that they bloom in a spiral. The angles between adjacent leaves form a regular mathematical series known as the Fibonacci sequence. Thanks to this, each individual leaf growing on a tree receives the maximum available amount of heat and light.
At first glance, the lizard has proportions that are pleasing to our eyes - the length of its tail is related to the length of the rest of the body as 62 to 38.
The scientist Zeising did a tremendous amount of work to discover the golden ratio in the human body. He measured about two thousand human bodies. The division of the body by the navel point is the most important indicator of the golden ratio. The proportions of the male body fluctuate within the average ratio of 13:8 = 1.625 and are somewhat closer to the golden ratio than the proportions female body, in relation to which the average value of the proportion is expressed in the ratio 8: 5 = 1.6. The proportions of the golden ratio also appear in relation to other parts of the body - the length of the shoulder, forearm and hand, hand and fingers, etc.
During the Renaissance, it was believed that it was this proportion from the Fibonacci series, observed in architectural structures and other forms of art, that most pleasing to the eye. Here are some examples of the use of the golden ratio in art:
Portrait of Mona Lisa
The portrait of Monna Lisa has attracted the attention of researchers for many years, who discovered that the composition of the picture is based on golden triangles, which are parts of a regular star-shaped pentagon, which is built on the principles of the golden ratio.
Parferon
Golden proportions are present in the dimensions of the facade of the ancient Greek temple of the Parthenon. This ancient structure with its harmonious proportions gives us the same aesthetic pleasure as it did to our ancestors. Many art historians, who sought to uncover the secret of the powerful emotional impact that this building has on the viewer, sought and found the golden proportion in the relationships of its parts.
Raphael - "Massacre of the Babies"
The picture is built on a spiral that follows the proportions of the golden ratio. We do not know whether Raphael actually drew the golden spiral when creating the composition “Massacre of the Innocents” or only “felt” it.
Our world is wonderful and full of great surprises. An amazing thread of connection connects many everyday things for us. The golden ratio is legendary for the fact that it united seemingly two completely different branches of knowledge - mathematics, the queen of precision and order, and humanitarian aesthetics.
IN Lately, working in individual and group processes with people, I returned to thoughts about combining all processes (karmic, mental, physiological, spiritual, transformational, etc.) into one.
Friends behind the veil increasingly revealed the image of a multidimensional Man and the interconnection of everything in everything.
An inner urge prompted me to return to old studies with numbers and once again look through the book of Drunvalo Melchizedek " Ancient mystery flower of life."
At this time, the film "The Da Vinci Code" was shown in cinemas. It is not my intention to discuss the quality, value or truth of this film. But the moment with the code, when the numbers began to scroll rapidly, became one of the key moments in this film for me.
My intuition told me that it was worth paying attention to the Fibonacci number sequence and the Golden Ratio. If you look on the Internet to find something about Fibonacci, you will be bombarded with information. You will learn that this sequence has been known at all times. It is represented in nature and space, in technology and science, in architecture and painting, in music and proportions in the human body, in DNA and RNA. Many researchers of this sequence have come to the conclusion that key events in the life of a person, state, and civilization are also subject to the law of the golden ratio.
It seems that Man has been given a fundamental hint.
Then the thought arises that a Person can consciously apply the principle of the Golden Section to restore health and correct fate, i.e. streamlining ongoing processes in one’s own universe, expanding Consciousness, returning to Well-Being.
Let's remember the Fibonacci sequence together:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025…
Each subsequent number is formed by adding the two previous ones:
1+1=2, 1+2=3, 2+3=5, etc.
Now I propose to reduce each number in the series to one digit: 1, 1, 2, 3, 5, 8,
13=1+3(4), 21=2+1(3), 34=3+4(7), 55=5+5(1), 89= 8+9(8), 144=1+4+4(9)…
Here's what we got:
1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9…1, 1, 2…
a sequence of 24 numbers that repeats again from the 25th:
75025=7+5+0+2+5=19=1+0=1, 121393=1+2+1+3+9+3=19=1+0=1…
Doesn't it seem strange or natural to you that
- there are 24 hours in a day,
- space houses - 24,
- DNA strands - 24,
- 24 elders from the God-Star Sirius,
- The repeating sequence in the Fibonacci series is 24 digits.
If the resulting sequence is written as follows,
1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9
8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
then we will see that the 1st and 13th number of the sequence, the 2nd and 14th, the 3rd and 15th, the 4th and 16th... the 12th and 24th add up to 9 .
3 3 6 9 6 6 3 9
When testing these number series, we got:
- Child Principle;
- Fatherly Principle;
- Mother Principle;
- Principle of Unity.
Golden Ratio Matrix
1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9
1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9
2 2 4 6 1 7 8 6 5 2 7 9 7 7 5 3 8 2 1 3 4 7 2 9
4 4 8 3 2 5 7 3 1 4 5 9 5 5 1 6 7 4 2 6 8 5 4 9
3 3 6 9 6 6 3 9 3 3 6 9 6 6 3 9 3 3 6 9 6 6 3 9
1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9
8 8 7 6 4 1 5 6 2 8 1 9 1 1 2 3 5 8 4 3 7 1 8 9
8 8 7 6 4 1 5 6 2 8 1 9 1 1 2 3 5 8 4 3 7 1 8 9
8 8 7 6 4 1 5 6 2 8 1 9 1 1 2 3 5 8 4 3 7 1 8 9
7 7 5 3 8 2 1 3 4 7 2 9 2 2 4 6 1 7 8 6 5 2 7 9
4 4 8 3 2 5 7 3 1 4 5 9 5 5 1 6 7 4 2 6 8 5 4 9
1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9
5 5 1 6 7 4 2 6 8 5 4 9 4 4 8 3 2 5 7 3 1 4 5 9
6 6 3 9 3 3 6 9 6 6 3 9 3 3 6 9 6 6 3 9 3 3 6 9
2 2 4 6 1 7 8 6 5 2 7 9 7 7 5 3 8 2 1 3 4 7 2 9
8 8 7 6 4 1 5 6 2 8 1 9 1 1 2 3 5 8 4 3 7 1 8 9
1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
Practical application of the Fibonacci series
One of my friends expressed his intention to work individually with him on the topic of developing his capabilities and abilities.
Unexpectedly, at the very beginning, Sai Baba came into the process and invited me to follow him.
We began to rise up inside the Divine Monad of our friend and, leaving it through the Causal Body, we found ourselves in another reality at the level of the Cosmic House.
Those who have studied the works of Mark and Elizabeth Claire Prophets know the teaching about the Cosmic Clock that Mother Mary conveyed to them.
At the level of the Cosmic House, Yuri saw a circle with an inner center with 12 arrows.
The elder who met us at this level said that before us the Divine Clock and 12 hands represent 12 (24) Manifestations of Divine Aspects... (possibly Creators).
As for the Cosmic Clock, they were located under the Divine Clock according to the principle of the energy eight.
— In what mode are the Divine Clocks in relation to you?
— The clock hands are standing still, there is no movement.Now thoughts are coming to me that many eons ago I abandoned the Divine Consciousness and followed a different path, the path of the Magician. All my magical artifacts and amulets, which I have and have accumulated in me over many incarnations, at this level look like baby rattles. On the subtle plane, they represent an image of magical energy clothing.
— Completed.However, I bless my magical experience.Living this experience truly motivated me to return to the source, to wholeness.They offer me to take off my magical artifacts and stand in the center of the Clock.
— What needs to be done to activate the Divine Clock?
— Sai Baba appeared again and offers to express the intention to connect the Silver String with the Clock. He also says that you have some kind of number series. He is the key to activation. The image of Leonard da Vinci's Man appears before your mind's eye.
- 12 times.
“I ask you to God-center the entire process and direct the energy of the number series to activate the Divine Clock.
Read aloud 12 times
1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9…
In the process of reading, the hands on the Clock began to move.
Energy flowed along the silver string, connecting all levels of Yurina’s Monad, as well as earthly and heavenly energies...
The most unexpected thing in this process was that four Entities appeared on the Clock, which are some parts of the One Whole with Yura.
During communication, it became clear that once there was a division of the Central Soul, and each part chose its own area in the universe for implementation.
The decision was made to integrate, which happened at the Divine Hours center.
The result of this process was the creation of the Common Crystal at this level.
After this, I remembered that Sai Baba once spoke about a certain Plan, which involves first connecting two Essences into one, then four, and so on according to the binary principle.
Of course, this number series is not a panacea. This is just a tool that allows you to quickly carry out the necessary work with a person, to align him vertically with different levels of Being.
Fibonacci numbers are a numerical sequence where each subsequent member of the series is equal to the sum of the two previous ones, that is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 , 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368,.. 75025,.. 3478759200, 5628750625,.. 260993908980000,.. 4222970156496 25,.. 19581068021641812000,.. The complex and amazing properties of the Fibonacci series numbers were studied a wide variety of professional scientists and mathematics enthusiasts.
In 1997, several strange features of the series were described by researcher Vladimir Mikhailov, who was convinced that Nature (including Man) develops according to the laws that are embedded in this numerical sequence.
A remarkable property of the Fibonacci number series is that as the numbers of the series increase, the ratio of two neighboring members of this series asymptotically approaches the exact proportion of the Golden Ratio (1:1.618) - the basis of beauty and harmony in the nature around us, including in human relationships.
Note that Fibonacci himself opened his famous series while thinking about the problem of the number of rabbits that should be born from one pair within one year. It turned out that in each subsequent month after the second, the number of pairs of rabbits exactly follows the digital series that now bears his name. Therefore, it is no coincidence that man himself is structured according to the Fibonacci series. Each organ is arranged in accordance with internal or external duality.
Fibonacci numbers attracted mathematicians with their ability to appear in the most unexpected places. It has been noticed, for example, that the ratios of Fibonacci numbers, taken through one, correspond to the angle between adjacent leaves on a plant stem, more precisely, they say what fraction of a revolution this angle is: 1/2 - for elm and linden, 1/3 - for beech, 2/5 - for oak and apple trees, 3/8 - for poplar and roses, 5/13 - for willow and almonds, etc. You will find the same numbers when counting the seeds in the spirals of a sunflower, in the number of rays reflected from two mirrors, in the number of options for routes for a bee to crawl from one cell to another, in many mathematical games and tricks.
What is the difference between the golden ratio spirals and the Fibonacci spiral? The golden ratio spiral is ideal. It corresponds to the Primary Source of harmony. This spiral has neither beginning nor end. It is endless. The Fibonacci spiral has a beginning from which it begins to “unwind”. This is a very important property. It allows Nature, after the next closed cycle, to build a new spiral from scratch.
It should be said that the Fibonacci spiral can be double. There are numerous examples of these double helices found throughout the world. Thus, sunflower spirals always correlate with the Fibonacci series. Even in an ordinary pine cone you can see this double helix Fibonacci. The first spiral goes in one direction, the second in the other. If you count the number of scales in a spiral rotating in one direction and the number of scales in another spiral, you can see that these are always two consecutive numbers of the Fibonacci series. The number of these spirals is 8 and 13. In sunflowers there are pairs of spirals: 13 and 21, 21 and 34, 34 and 55, 55 and 89. And there are no deviations from these pairs!..
In humans, in the set of chromosomes of a somatic cell (there are 23 pairs of them), the source of hereditary diseases are 8, 13 and 21 pairs of chromosomes...
But why does this particular series play a decisive role in Nature? This question can be answered comprehensively by the concept of trinity, which determines the conditions for its self-preservation. If the “balance of interests” of the triad is violated by one of its “partners,” the “opinions” of the other two “partners” must be adjusted. The concept of trinity is especially evident in physics, where “almost” all elementary particles are built from quarks. If we remember that the ratios of the fractional charges of quark particles form a series, and these are the first terms of the Fibonacci series, which are necessary for the formation of other elementary particles.
It is possible that the Fibonacci spiral can play a decisive role in the formation of the pattern of limited and closed hierarchical spaces. Indeed, let’s imagine that at some stage of evolution the Fibonacci spiral reached perfection (it became indistinguishable from the golden ratio spiral) and for this reason the particle should be transformed into the next “category”.
These facts once again confirm that the law of duality gives not only qualitative, but also quantitative results. They make us think that the Macroworld and Microworld around us evolve according to the same laws - the laws of hierarchy, and that these laws are the same for living and inanimate matter.
All this indicates that the Fibonacci series of numbers represents some kind of encrypted law of nature.
The digital code of the development of civilization can be determined using various methods in numerology. For example, by reducing complex numbers to single digits (for example, 15 is 1+5=6, etc.). Carrying out a similar addition procedure with all the complex numbers of the Fibonacci series, Mikhailov received the following series of these numbers: 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 8, 1, 9, then everything repeats 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 4, 8, 8,.. and repeats again and again... This series also has the properties of the Fibonacci series, each infinitely subsequent term is equal to the sum of the previous ones. For example, the sum of the 13th and 14th terms is 15, i.e. 8 and 8=16, 16=1+6=7. It turns out that this series is periodic, with a period of 24 terms, after which the entire order of numbers is repeated. Having received this period, Mikhailov put forward an interesting assumption - is not a set of 24 digits a kind of digital code for the development of civilization? Published
P.S. And remember, just by changing your consciousness, we are changing the world together! © econet
