The energy of digital Fibonacci codes. Fibonacci number and the golden ratio in nature. Fibonacci numbers in nature

Ecology of life. Cognitive: Nature (including Man) develops according to the laws that are embedded in this numerical sequence...

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,.. 422297015649 625,.. 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 Fibonacci double spiral. 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 number series represents a certain 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 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 - Isn't a set of 24 digits peculiar? digital code development of civilization? published

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The world around us, from the smallest invisible particles to the distant galaxies of endless space, is fraught with many unsolved mysteries. However, the veil of mystery has already been lifted over some of them thanks to the inquisitive minds of a number of scientists.

One such example is « golden ratio» and Fibonacci numbers , which form its basis. This pattern is reflected in mathematical form and is often found in surrounding a person nature, once again eliminating the possibility that it arose as a result of chance.

Fibonacci numbers and their sequence

Fibonacci sequence of numbers is a series of numbers, each of which is the sum of the previous two:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 …

The peculiarity of this sequence is the numerical values that are obtained by dividing the numbers of this series by each other.

The Fibonacci number series has its own interesting patterns:

In the Fibonacci series of numbers, each number divided by the next will show a value tending to 0,618 . The further the numbers are from the beginning of the series, the more accurate the ratio will be. For example, the numbers taken at the beginning of the row 5 And 8 will show 0,625 (5/8=0,625 ). If we take the numbers 144 And 233 , then they will show the ratio 0.618 .
In turn, if in a series of Fibonacci numbers we divide a number by the previous one, then the result of the division will tend to 1,618 . For the example, the same numbers were used as discussed above: 8/5=1,6 And 233/144=1,618 .
A number divided by the next one after it will show a value approaching 0,382 . And the further the numbers are taken from the beginning of the series, the more accurate the value of the ratio: 5/13=0,385 And 144/377=0,382 . Dividing the numbers in reverse order will give the result 2,618 : 13/5=2,6 And 377/144=2,618 .

Using the calculation methods described above and increasing the gaps between the numbers, you can derive the following series of values: 4.235, 2.618, 1.618, 0.618, 0.382, 0.236, which is widely used in Fibonacci tools in the Forex market.

Golden ratio or Divine proportion

The analogy with a segment represents the “golden ratio” and Fibonacci numbers very clearly. If segment AB is divided by point C in such a ratio that the condition is met:

AC/BC=BC/AB, then it will be the “golden ratio”

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Surprisingly, this is precisely the relationship that can be traced in the Fibonacci series. By taking a few numbers from the series, you can check by calculation that this is so. For example, this sequence of Fibonacci numbers... 55, 89, 144 ... Let the number 144 be the integer segment AB mentioned above. Since 144 is the sum of two previous numbers, then 55+89=AC+BC=144.

Dividing the segments will show the following results:

AC/BC=55/89=0.618

BC/AB=89/144=0.618

If we take the segment AB as a whole, or as a unit, then AC=55 will be 0.382 of this whole, and BC=89 will be equal to 0.618.

Where do Fibonacci numbers occur?

The Greeks and Egyptians knew the regular sequence of Fibonacci numbers long before Leonardo Fibonacci himself. This is the name number series acquired after the famous mathematician provided widespread this mathematical phenomenon among scientists.

It is important to note that the golden Fibonacci numbers are not just science, but a mathematical representation of the world around us. Many natural phenomena, representatives of the flora and fauna have the “golden ratio” in their proportions. These are the spiral curls of the shell, and the arrangement of sunflower seeds, cacti, and pineapples.

The spiral, the proportions of the branches of which are subject to the laws of the “golden ratio,” underlies the formation of a hurricane, the weaving of a web by a spider, the shape of many galaxies, the intertwining of DNA molecules and many other phenomena.

The length of the lizard's tail to its body has a ratio of 62 to 38. The chicory shoot makes an ejection before releasing a leaf. After the first sheet is released, a second ejection occurs before the release of the second sheet, with a force equal to 0.62 of the conventional unit of force of the first ejection. The third outlier is 0.38, and the fourth is 0.24.

For a trader, it is also of great importance that the price movement in the Forex market is often subject to the pattern of golden Fibonacci numbers. Based on this sequence created a whole series tools that a trader can use in his arsenal

The “ ” tool, often used by traders, can show with high accuracy the targets of price movement, as well as its correction levels.

Fibonacci sequence, known to everyone from the film "The Da Vinci Code" - a series of numbers described in the form of a riddle by the Italian mathematician Leonardo of Pisa, better known by the nickname Fibonacci, in the 13th century. Briefly the essence of the riddle:

Someone placed a pair of rabbits in a certain enclosed space in order to find out how many pairs of rabbits would be born during the year, if the nature of rabbits is such that every month a pair of rabbits gives birth to another pair, and they become capable of producing offspring when they reach two months of age.

The result is a series of numbers like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 , where the number of pairs of rabbits in each of the twelve months is shown, separated by commas. It can be continued indefinitely. Its essence is that each next number is the sum of the previous two.

This series has several mathematical features that definitely need to be touched upon. It asymptotically (approaching slower and slower) tends to some constant ratio. However, this ratio is irrational, that is, it is a number with an infinite, unpredictable sequence of decimal digits in the fractional part. It is impossible to express it precisely.

Thus, the ratio of any member of a series to the one preceding it fluctuates around the number 1,618 , sometimes exceeding it, sometimes not achieving it. The ratio to the following similarly approaches the number 0,618 , which is inversely proportional 1,618 . If we divide the elements by one, we get numbers 2,618 And 0,382 , which are also inversely proportional. These are the so-called Fibonacci ratios.

What is all this for? This is how we approach one of the most mysterious natural phenomena. The savvy Leonardo essentially did not discover anything new, he simply reminded the world of such a phenomenon as Golden Ratio, which is not inferior in importance to the Pythagorean theorem.

We distinguish all the objects around us by their shape. We like some more, some less, some are completely off-putting. Sometimes interest can be dictated life situation, and sometimes the beauty of the observed object. Symmetrical and proportional shape, promotes the best visual perception and evokes a feeling of beauty and harmony. Holistic image always consists of parts of different sizes that are in a certain relationship with each other and the whole. Golden ratio- the highest manifestation of the perfection of the whole and its parts in science, art and nature.

If on simple example, then the Golden Section is the division of a segment into two parts in such a ratio that most relates to the smaller one as their sum (the entire segment) relates to the larger one.

If we take the entire segment c for 1 , then the segment a will be equal 0,618 , segment b - 0,382 , only in this way will the condition of the Golden Ratio be met (0,618/0,382=1,618 ; 1/0,618=1,618 ) . Attitude c To a equals 1,618 , A With To b 2,618 . These are the same Fibonacci ratios that are already familiar to us.

Of course there is a golden rectangle, a golden triangle and even a golden cuboid. Proportions human body in many respects close to the Golden Section.

Image: marcus-frings.de

But the fun begins when we combine the knowledge we have gained. The figure clearly shows the relationship between the Fibonacci sequence and the Golden Ratio. We start with two squares of the first size. Add a square of the second size on top. Draw a square next to it with a side equal to the sum of the sides of the previous two, third size. By analogy, a square of size five appears. And so on until you get tired, the main thing is that the length of the side of each next square is equal to the sum of the lengths of the sides of the two previous ones. We see a series of rectangles whose side lengths are Fibonacci numbers, and, oddly enough, they are called Fibonacci rectangles.

If we draw smooth lines through the corners of our squares, we will get nothing more than an Archimedes spiral, the increment of which is always uniform.

Doesn't remind you of anything?

Photo: ethanhein on Flickr

And not only in the shell of a mollusk you can find Archimedes’ spirals, but in many flowers and plants, they’re just not so obvious.

Aloe multifolia:

Photo: brewbooks on Flickr

Photo: beart.org.uk

Photo: esdrascalderan on Flickr

Photo: manj98 on Flickr

And now it’s time to remember the Golden Section! Are some of the most beautiful and harmonious creations of nature depicted in these photographs? And that's not all. If you look closely, you can find similar patterns in many forms.

Of course, the statement that all these phenomena are based on the Fibonacci sequence sounds too loud, but the trend is obvious. And besides, she herself is far from perfect, like everything in this world.

There is an assumption that the Fibonacci series is an attempt by nature to adapt to a more fundamental and perfect golden ratio logarithmic sequence, which is almost the same, only it starts from nowhere and goes to nowhere. Nature definitely needs some kind of whole beginning from which it can start; it cannot create something out of nothing. The ratios of the first terms of the Fibonacci sequence are far from the Golden Ratio. But the further we move along it, the more these deviations are smoothed out. To define any series, it is enough to know its three terms, coming one after another. But not for the golden sequence, two are enough for it, it is a geometric and arithmetic progression at the same time. One might think that it is the basis for all other sequences.

Each term of the golden logarithmic sequence is a power of the Golden Ratio ( z). Part of the series looks something like this: ... z -5 ; z -4 ; z -3 ; z -2 ; z -1 ; z 0 ; z 1 ; z 2 ; z 3 ; z 4 ; z 5... If we round the value of the Golden Ratio to three decimal places, we get z=1.618, then the series looks like this: ... 0,090 0,146; 0,236; 0,382; 0,618; 1; 1,618; 2,618; 4,236; 6,854; 11,090 ... Each next term can be obtained not only by multiplying the previous one by 1,618 , but also by adding the two previous ones. Thus, exponential growth is achieved by simply adding two adjacent elements. It's a series without beginning or end, and that's what the Fibonacci sequence tries to be like. Having a very definite beginning, she strives for the ideal, never achieving it. That's life.

And yet, in connection with everything we have seen and read, quite logical questions arise:
Where did these numbers come from? Who is this architect of the universe who tried to make it ideal? Was everything ever the way he wanted? And if so, why did it go wrong? Mutations? Free choice? What will happen next? Is the spiral curling or unwinding?

Having found the answer to one question, you will get the next one. If you solve it, you'll get two new ones. Once you deal with them, three more will appear. Having solved them too, you will have five unsolved ones. Then eight, then thirteen, 21, 34, 55...

Sources: ; ; ;

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 human life, states, civilizations 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 destiny, 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

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

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 moved.

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 the conversation it became clear that there had once been a separation 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 produce necessary work with a person, align him vertically with at different levels Genesis.

Golden ratio and Fibonacci sequence numbers. June 14th, 2011

Some time ago I promised to comment on Tolkachev’s statement that St. Petersburg is built according to the principle of the Golden Section, and Moscow is built according to the principle of symmetry, and that this is why the differences in the perception of these two cities are so noticeable, and this is why a St. Petersburger, coming to Moscow, “gets a headache” ”, and a Muscovite “gets a headache” when he comes to St. Petersburg. It takes some time to tune in to the city (like when flying to the states - it takes time to tune in).

The fact is that our eye looks - feeling the space with the help of certain eye movements - saccades (in translation - the clap of a sail). The eye makes a “clap” and sends a signal to the brain “adhesion to the surface has occurred. Everything is fine. Information such and such." And over the course of life, the eye gets used to a certain rhythm of these saccades. And when this rhythm changes dramatically (from a city landscape to a forest, from the Golden Section to symmetry), then some brain work is required to reconfigure.

Now the details:
The definition of GS is the division of a segment into two parts in such a ratio in which the larger part is related to the smaller one, as their sum (the entire segment) is to the larger one.

That is, if we take the entire segment c as 1, then segment a will be equal to 0.618, segment b - 0.382. Thus, if we take a building, for example, a temple built according to the 3S principle, then with its height, say, 10 meters, the height of the drum with the dome will be equal to 3.82 cm, and the height of the base of the structure will be 6.18 cm (it is clear that the numbers I took them flat for clarity)

What is the connection between ZS and Fibonacci numbers?

The Fibonacci sequence numbers are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597…

The pattern of numbers is that each subsequent number is equal to the sum of the two previous numbers.
0 + 1 = 1;
1 + 1 = 2;
2 + 3 = 5;
3 + 5 = 8;
5 + 8 = 13;
8 + 13 = 21, etc.,

and the ratio of adjacent numbers approaches the ratio of ZS.
So, 21: 34 = 0.617, and 34: 55 = 0.618.

That is, the GS is based on the numbers of the Fibonacci sequence.
This video once again clearly demonstrates this connection between GS and Fibonacci numbers

Where else are the 3S principle and Fibonacci sequence numbers found?

Plant leaves are described by the Fibonacci sequence. Sunflower grains, pine cones, flower petals, and pineapple cells are also arranged according to the Fibonacci sequence.

bird egg

The lengths of the phalanges of human fingers are approximately the same as the Fibonacci numbers. The golden ratio is visible in the proportions of the face.

Emil Rosenov studied the ES in the music of the Baroque and Classical eras using the examples of works by Bach, Mozart, and Beethoven.

It is known that Sergei Eisenstein artificially constructed the film “Battleship Potemkin” according to the rules of the Legislature. He broke the tape into five parts. Firstly three action develops on the ship. In the last two - in Odessa, where the uprising is unfolding. This transition to the city occurs exactly at the golden ratio point. And each part has its own fracture, which occurs according to the law of the golden ratio. In a frame, scene, episode there is a certain leap in the development of the theme: plot, mood. Eisenstein believed that since such a transition is close to the golden ratio point, it is perceived as the most logical and natural.

Many decorative elements, as well as fonts, were created using ZS. For example, the font of A. Durer (in the picture there is the letter “A”)

It is believed that the term “Golden Ratio” was introduced by Leonardo Da Vinci, who said, “let no one who is not a mathematician dare to read my works” and showed the proportions of the human body in his famous drawing “Vitruvian Man”. “If we tie a human figure - the most perfect creation of the Universe - with a belt and then measure the distance from the belt to the feet, then this value will relate to the distance from the same belt to the top of the head, just as the entire height of a person relates to the length from the waist to the feet.”

The famous portrait of Mona Lisa or Gioconda (1503) was created according to the principle of golden triangles.

As a matter of fact, the star or pentacle itself is a construction of the Earth.

The Fibonacci number series is visually modeled (materialized) in the form of a spiral

And in nature, the GS spiral looks like this:

At the same time, the spiral is observed everywhere(in nature and not only):
- Seeds in most plants are arranged in a spiral
- The spider weaves a web in a spiral
- A hurricane is spinning like a spiral
- A frightened herd of reindeer scatters in a spiral.
- The DNA molecule is twisted in a double helix. The DNA molecule is made up of two vertically intertwined helices, 34 angstroms long and 21 angstroms wide. The numbers 21 and 34 follow each other in the Fibonacci sequence.
- The embryo develops in a spiral shape
- Cochlear spiral in the inner ear
- The water goes down the drain in a spiral
- Spiral dynamics shows the development of a person’s personality and his values in a spiral.
- And of course, the Galaxy itself has the shape of a spiral

Thus, it can be argued that nature itself is built according to the principle of the Golden Section, which is why this proportion is more harmoniously perceived by the human eye. It does not require “correction” or addition to the resulting picture of the world.

Now about the Golden Ratio in architecture

The Cheops pyramid represents the proportions of the Earth. (I like the photo - with the Sphinx covered in sand).

According to Le Corbusier, in the relief from the temple of Pharaoh Seti I at Abydos and in the relief depicting Pharaoh Ramses, the proportions of the figures correspond to the golden ratio. The façade of the ancient Greek temple of the Parthenon also features golden proportions.

Notredame de Paris Cathedral in Paris, France.

One of the outstanding buildings made according to the GS principle is the Smolny Cathedral in St. Petersburg. There are two paths leading to the cathedral along the edges, and if you approach the cathedral along them, it seems to rise in the air.

In Moscow there are also buildings made using GS. For example, St. Basil's Cathedral

However, development using the principles of symmetry prevails.
For example, the Kremlin and the Spasskaya Tower.

The height of the walls of the Kremlin also nowhere reflects the principle of ZS regarding the height of towers, for example. Or take the Russia Hotel, or the Cosmos Hotel.

At the same time, buildings built according to the GS principle represent a larger percentage in St. Petersburg, and these are street buildings. Liteiny Avenue.

So the Golden Ratio uses a ratio of 1.68 and the symmetry is 50/50.
That is, symmetrical buildings are built on the principle of equality of sides.

Another important characteristic of the ES is its dynamism and tendency to unfold, due to the sequence of Fibonacci numbers. Whereas symmetry, on the contrary, represents stability, stability and immobility.

In addition, the additional WS introduces into the plan of St. Petersburg an abundance of water spaces, splashed throughout the city and dictating the city’s subordination to their bends. And Peter’s diagram itself resembles a spiral or an embryo at the same time.

The Pope, however, expressed a different version of why Muscovites and St. Petersburg residents have “headaches” when visiting the capitals. Dad relates this to the energies of cities:
St. Petersburg – has masculine and accordingly masculine energies,
Well, Moscow - accordingly - feminine and has feminine energies.

So, for residents of the capitals, who are attuned to their specific balance of feminine and masculine in their bodies, it is difficult to readjust when visiting a neighboring city, and some may have some difficulties with the perception of one or another energy and therefore the neighboring city may not be at all love!

This version is also confirmed by the fact that all Russian empresses ruled in St. Petersburg, while Moscow saw only male tsars!

Resources used.