Divine harmony: what is the golden ratio in simple words. Secrets of the universe in numbers

A person distinguishes objects around him by shape. Interest in the form of an object may be dictated by vital necessity, or it may be caused by the beauty of the form. The form, which is based on a combination of symmetry and the golden section, contributes to the best visual perception and the appearance of a sense of beauty and harmony. The whole always consists of parts, parts of different sizes are in a certain relationship to each other and to the whole. The principle of the golden section is the highest manifestation of the structural and functional perfection of the whole and its parts in art, science, technology and nature.

Golden Ratio - Harmonic Proportion

In mathematics proportion(lat. proportio) call the equality of two relations:

a : b = c : d.

Line segment AB can be divided into two parts in the following ways:

into two equal parts AB : AC = AB : BC;
into two unequal parts in any ratio (such parts do not form proportions);
so when AB : AC = AC : BC.

The latter is the golden division or division of the segment in the extreme and average ratio.

The golden section is such a proportional division of a segment into unequal parts, in which the entire segment relates to the larger part in the same way as the larger part itself relates to the smaller one; or in other words, the smaller segment is related to the larger one as the larger one is to everything:

a : b = b : c
or
c : b = b : a.

Rice. one. Geometric representation of the golden ratio

Practical acquaintance with the golden ratio begins with dividing a straight line segment in the golden ratio using a compass and ruler.

Rice. 2.BC = 1/2 AB; CD = BC

From a point B a perpendicular is restored equal to half AB. Received point C connected by a line to a dot A. A segment is drawn on the resulting line BC, ending with a dot D. Line segment AD transferred to a straight line AB. The resulting point E divides the segment AB in the golden ratio.

Segments of the golden ratio are expressed by an infinite irrational fraction AE= 0.618... if AB take as a unit BE\u003d 0.382 ... For practical purposes, approximate values \u200b\u200bof 0.62 and 0.38 are often used. If the segment AB taken as 100 parts, then the largest part of the segment is 62, and the smaller is 38 parts.

The properties of the golden section are described by the equation:

x 2 – x – 1 = 0.

Solution to this equation:

The properties of the golden section created a romantic aura of mystery and almost mystical worship around this number.

The second golden ratio

The Bulgarian magazine "Fatherland" (No. 10, 1983) published an article by Tsvetan Tsekov-Karandash "On the second golden section", which follows from the main section and gives another ratio of 44: 56.

Such a proportion is found in architecture, and also takes place in the construction of compositions of images of an elongated horizontal format.

Rice. 3.

The division is carried out as follows. Line segment AB is divided according to the golden ratio. From a point C the perpendicular is restored CD. Radius AB there is a point D, which is connected by a line to a point A. Right angle ACD is divided in half. From a point C a line is drawn until it intersects with a line AD. Dot E divides the segment AD in relation to 56:44.

Rice. 4.

The figure shows the position of the line of the second golden section. It is located in the middle between the line of the golden section and middle line rectangle.

Golden Triangle

To find segments of the golden ratio of the ascending and descending series, you can use pentagram.

Rice. 5. Construction of a regular pentagon and pentagram

To build a pentagram, you need to build a regular pentagon. The method of its construction was developed by the German painter and graphic artist Albrecht Dürer (1471...1528). Let be O- the center of the circle A is a point on the circle and E- the middle of the segment OA. Perpendicular to Radius OA, restored at the point O, intersects the circle at a point D. Using a compass, set aside a segment on the diameter CE = ED. The length of a side of a regular pentagon inscribed in a circle is DC. Putting segments on the circle DC and get five points to draw a regular pentagon. We connect the corners of the pentagon through one diagonal and get a pentagram. All diagonals of the pentagon divide each other into segments connected by the golden ratio.

Each end of the pentagonal star is a golden triangle. Its sides form an angle of 36° at the apex, and the base laid on lateral side, divides it in proportion to the golden ratio.

Rice. 6. Construction of the golden triangle

We draw a straight line AB. from point A lay a segment on it three times O arbitrary value, through the resulting point P draw a perpendicular to the line AB, on the perpendicular to the right and left of the point P set aside segments O. Received points d and d 1 connect with straight lines to a point A. Line segment dd 1 set aside on the line Ad 1 , getting a point C. She split the line Ad 1 in proportion to the golden ratio. lines Ad 1 and dd 1 is used to build a "golden" rectangle.

History of the golden section

It is generally accepted that the concept of the golden division was introduced into scientific use by Pythagoras, ancient Greek philosopher and mathematician (VI century BC). There is an assumption that Pythagoras borrowed his knowledge of the golden division from the Egyptians and Babylonians. Indeed, the proportions of the pyramid of Cheops, temples, bas-reliefs, household items and decorations from the tomb indicate that the Egyptian masters used the ratios of the golden division when creating them. The French architect Le Corbusier found that in the relief from the temple of Pharaoh Seti I in Abydos and in the relief depicting Pharaoh Ramses, the proportions of the figures correspond to the values of the golden division. The architect Khesira, depicted on a relief of a wooden board from the tomb of his name, holds measuring instruments in his hands, in which the proportions of the golden division are fixed.

The Greeks were skilled geometers. They even taught arithmetic to their children with the help of geometric shapes. The square of Pythagoras and the diagonal of this square were the basis for constructing dynamic rectangles.

Rice. 7. Dynamic Rectangles

Plato (427...347 BC) also knew about the golden division. His dialogue "Timaeus" is devoted to the mathematical and aesthetic views of the school of Pythagoras and, in particular, to the issues of the golden division.

In the facade of the ancient Greek temple of the Parthenon there are golden proportions. During its excavations, compasses were found, which were used by architects and sculptors of the ancient world. The Pompeian compass (Museum in Naples) also contains the proportions of the golden division.

Rice. eight.

In what has come down to us ancient literature the golden division is first mentioned in Euclid's Elements. In the 2nd book of the "Beginnings" the geometric construction of the golden division is given. After Euclid, Hypsicles (2nd century BC), Pappus (3rd century AD) and others studied the golden division. medieval Europe they got acquainted with the golden division from the Arabic translations of the "Beginnings" of Euclid. The translator J. Campano from Navarre (3rd century) commented on the translation. The secrets of the golden division were jealously guarded, kept in strict secrecy. They were known only to the initiates.

In the Renaissance, interest in the golden division among scientists and artists increased in connection with its use both in geometry and in art, especially in architecture Leonardo da Vinci, an artist and scientist, saw that Italian artists had great empirical experience, but little knowledge . He conceived and began to write a book on geometry, but at that time a book by the monk Luca Pacioli appeared, and Leonardo abandoned his idea. According to contemporaries and historians of science, Luca Pacioli was a real luminary, the greatest mathematician in Italy between Fibonacci and Galileo. Luca Pacioli was a student of the painter Piero della Francesca, who wrote two books, one of which was called On Perspective in Painting. He is considered the creator of descriptive geometry.

Luca Pacioli was well aware of the importance of science for art. In 1496, at the invitation of Duke Moreau, he came to Milan, where he lectured on mathematics. Leonardo da Vinci also worked at the Moro court in Milan at that time. In 1509, Luca Pacioli's Divine Proportion was published in Venice, with brilliantly executed illustrations, which is why they are believed to have been made by Leonardo da Vinci. The book was an enthusiastic hymn to the golden ratio. Among the many advantages of the golden ratio, the monk Luca Pacioli did not fail to name its “divine essence” as an expression of the Divine Trinity - God the Father, God the Son and God the Holy Spirit (it was understood that the small segment is the personification of God the Son, the larger segment is God the Father, and the entire segment - God the Holy Spirit).

Electronic books:

Mario Livio.

AT recent times, working in individual and group processes with people, I returned to thoughts about the unification of all processes (karmic, mental, physiological, spiritual, transformational, etc.) into one.

Friends behind the veil more and more revealed the image of the multidimensional Man and the interconnection of everything in everything.

An inner impulse prompted me to return to the old studies with numbers and once again look through the book by Drunvalo Melchizedek " ancient secret flower of life."

At this time, the film "The Da Vinci Code" was shown in cinemas. I do not intend to discuss the quality, value and 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 what to pay attention to number sequence Fibonacci and the Golden Ratio. If you look on the Internet to find something about Fibonacci, you will be bombarded with information. You will find out that this sequence was 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 section.

It seems that the Human has been given a fundamental clue.

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 the ongoing processes in one's own universe, expanding the Consciousness, returning to the Welfare.

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 previous two:

1+1=2, 1+2=3, 2+3=5 etc.

Now I propose to bring each number of 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

in a day - 24 hours,
space houses - 24,
strands of DNA - 24,
24 elders from the God Star Sirius,
repeating sequence in the Fibonacci series - 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 numerical series, we got:

Child Principle;
Father Principle;
Mother Principle;
the principle of unity.

Matrix of the Golden Section

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

A friend of mine expressed his intention to work individually with him on the development of his abilities and abilities.

Suddenly, 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 a friend and, having left 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 Clair Prophetov know the teaching about the Cosmic Clock, which was passed on to them by Mother Mary.

At the level of the Space House, Yuri saw a circle with an inner center with 12 arrows.

The elder, who met us at this level, said that before us is the Divine Clock and 12 hands represent 12 (24) Manifestations of the Divine Aspects… (perhaps the Creators).

As for the Cosmic Clock, they were located under the Divine ones according to the principle of the energy eight.

- In what mode are the Divine Clocks in relation to you?

- The hands of the Clock are standing, there is no movement.Thoughts come to me now that many eons ago I abandoned the Divine Consciousness and went a different path, the path of a Magician. All my magical artifacts and amulets that have accumulated in me and in me over many incarnations look like baby rattles at this level. On the subtle plane, they represent an image of magical energy clothes.

- Completed.However, I bless my magical experience.Living this experience sincerely prompted me to return to the original source, to wholeness.I am offered 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 offered 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 the inner eye.

- 12 times.

“I ask you to God-center the whole process and direct the action of the energy of the number series to the activation of 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 went.

An energy went through the silver string, which connected all the levels of the Yurina Monad, as well as the earthly and heavenly energies…

The most unexpected thing in this process was that four Essences appeared on the Clock, which are some parts of the One Whole with Yura.

During the communication, it turned out that once there was a division of the Central Soul, and each part chose its own area in the universe for realization.

A decision was made to integrate, which happened in the center of the Divine Clock.

The result of this process was the creation of the Common Crystal at this level.

After that, I remembered that Sai Baba once spoke about a certain Plan, which involves first combining 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 perform the necessary work with a person, adjust him vertically with different levels Genesis.

Leonardo Fibonacci is one of the most famous mathematicians of the Middle Ages. One of his most important achievements is the number series, which determines the golden ratio and can be traced throughout the nature of our planet.

The amazing property of these numbers is that the sum of all the previous numbers is equal to the next number (check for 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 mathematically interesting properties. Here's an example: you can split a line in two. 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 factor, approximately equal to 1.618, is known as the golden ratio.

The Fibonacci series could have remained only a mathematical incident if it were not for the fact that all researchers of the golden section 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 a golden ratio. If you look at the leaves of such a plant from above, you can see 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.

In a lizard, at first glance, proportions that are pleasing to our eyes are captured - the length of its tail relates to the length of the rest of the body as 62 to 38.

The scientist Zeising did a tremendous job 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 approach the golden ratio somewhat closer than the proportions of the 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 section are also manifested in relation to other parts of the body - the length of the shoulder, forearm and hand, hand and fingers, etc.

In the Renaissance, it was believed that it was this proportion from the Fibonacci series, observed in architectural structures and other forms of art, 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 drawing is based on golden triangles, which are parts of a regular star-shaped pentagon, which is based 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 building with its harmonious proportions gives us the same aesthetic pleasure as our ancestors. Many art critics who sought to uncover the secret of that mighty emotional impact, which this building has on the viewer, they searched for and found the golden ratio in the ratios of its parts.

Raphael - Massacre of the Innocents

The picture is built on a spiral that respects the proportions of the golden section. We do not know whether Raphael actually painted 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 interconnection connects many things that are ordinary for us. The golden ratio is legendary in that it united seemingly two completely different branches of knowledge - mathematics, the queen of precision and order, and humanitarian aesthetics.

The surrounding world, starting with the smallest invisible particles, and ending with distant galaxies of boundless 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 that form its basis. This pattern has been displayed in mathematical form and is often found in human environment nature, once again excluding the possibility that it arose by chance.

Fibonacci numbers and their sequence

Fibonacci number sequence called 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 …

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

A series of Fibonacci numbers has its own interesting patterns:

In the Fibonacci series, each number divided by the next will show a value tending towards 0,618 . The farther 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 the number by the previous one, then the result of the division will tend to 1,618 . For example, the same numbers were used as mentioned above: 8/5=1,6 and 233/144=1,618 .
The number divided by the next one after it will show a value approaching 0,382 . And the farther from the beginning of the series the numbers are taken, the more precisely meaning ratios: 5/13=0,385 and 144/377=0,382 . Division of digits in reverse order will give a result 2,618 : 13/5=2,6 and 377/144=2,618 .

Using the above calculation methods and increasing the gaps between the numbers, you can display the following range 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 “golden section” and Fibonacci numbers are very clearly represented by the analogy with a segment. If segment AB is divided by point C in such a ratio that the condition is met:

AC / BC \u003d BC / AB, then it will be the "golden section"

READ ALSO THE FOLLOWING ARTICLES:

Surprisingly, it is this ratio that can be traced in the series of Fibonacci numbers. Taking a few numbers from the series, you can check by calculation that this is so. For example, such a sequence of Fibonacci numbers ... 55, 89, 144 ... Let the number 144 be the whole segment AB, which was mentioned above. Since 144 is the sum of the 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 \u003d 55 will be 0.382 of this whole, and BC \u003d 89 will be equal to 0.618.

Where are Fibonacci numbers found?

The regular sequence of Fibonacci numbers was known to the Greeks and Egyptians long before Leonardo Fibonacci himself. This number series acquired such a name after the famous mathematician ensured the wide distribution of this mathematical phenomenon in scientific ranks.

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 section" in their proportions. These are spiral curls of the shell, and the arrangement of sunflower seeds, cacti, pineapples.

The spiral, the proportions of the branches of which are subject to the laws of the "golden section", underlies the formation of a hurricane, the weaving of a web by a spider, the shape of many galaxies, the interweaving 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, before releasing a leaf, makes a release. After the first sheet is released, a second ejection occurs before the release of the second sheet, equal in strength to 0.62 of the conditionally accepted unit of force of the first ejection. The third outlier is 0.38 and the fourth is 0.24.

Also for the trader great importance has the fact that the price movement in the forex market is often subject to the patterns of golden Fibonacci numbers. Based on this sequence created whole line tools that a trader can use in his arsenal

Often used by traders, the instrument "" can accurately show the price movement targets, as well as the levels of its correction.

The golden ratio and the Fibonacci sequence numbers. June 14th, 2011

Some time ago, I promised to comment on Tolkachev's statement that St. Petersburg was built according to the principle of the Golden Section, and Moscow - according to the principle of symmetry, and that this is why the differences in the perception of these two cities are so palpable, and this is why a St. ”, And the Muscovite “gets sick with his head” when he comes to St. Petersburg. It takes some time to adjust to the city (as when flying to the states - you need to adjust over time).

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

Now the details:
The definition of ZS is the division of a segment into two parts in such a ratio that 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 principle of ZS, then with its height, say, 10 meters, the height of the drum with the dome will be 3.82 cm, and the height of the base of the building will be 6.18 cm. (It is clear that the numbers I took equal for clarity)

And what is the relationship between GL 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 3S.
So, 21:34 = 0.617, and 34:55 = 0.618.

That is, at the heart of the ZS are the numbers of the Fibonacci sequence.
This video once again clearly demonstrates this connection between the AP and the Fibonacci numbers

Where else do the AP principle and the Fibonacci sequence numbers meet?

Plant leaves are described by the Fibonacci sequence. sunflower seeds, Pine cones, flower petals, 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 seen in the proportions of the face.

Emil Rozenov studied the ZS in the music of the Baroque and Classicism eras using the works of Bach, Mozart, Beethoven as an example.

It is known that Sergei Eisenstein artificially built the film "Battleship Potemkin" according to the rules of the Legislative Assembly. He broke the tape into five parts. In the first three, the action develops on the ship. In the last two - in Odessa, where the uprising is unfolding. This transition to the city takes place exactly at the point of the golden ratio. Yes, and in each part there is a turning point, which occurs according to the law of the golden section. In the frame, scene, episode, there is a certain leap in the development of the theme: the plot, the mood. Eisenstein believed that, since such a transition is close to the golden section point, it is perceived as the most natural and natural.

Many decorative elements, as well as fonts, are created using GS. For example, the font of A. Dürer (the letter “A” in the figure)

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 refer to the distance from the same belt to the top of the head, as the entire height of a person to the length from the belt to the feet.”

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

Strictly speaking, the star itself or the pentacle is the construction of the AP.

A series of Fibonacci numbers is visually modeled (materialized) in the form of a spiral

And in nature, the 3S 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
- A spider weaves a web in a spiral
- A hurricane spirals
- A frightened herd of reindeer scatters in a spiral.
- The DNA molecule is twisted in a double helix. The DNA molecule consists 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 the form of a spiral
- Spiral "cochlea in the inner ear"
- 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 on the principle of the Golden Section, which is why this proportion is more harmoniously perceived by the human eye. It does not require "fixing" or supplementing the resulting picture of the world.

Now about the golden section in architecture

The Pyramid of Cheops represents the proportions of the GS. (I like the photo - with the Sphinx littered with 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 facade of the ancient Greek temple of the Parthenon also has golden proportions.

Notredam de Paris Cathedral in Paris, France.

One of the outstanding buildings made according to the principle of the AP is the Smolny Cathedral in St. Petersburg. Two paths lead to the cathedral along the edges, and if you approach the cathedral along them, then it seems to rise in the air.

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

However, buildings that use the principles of symmetry prevail.
For example, the Kremlin and the Spasskaya Tower.

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

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

Thus, 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 GS is its dynamism and the desire to unfold, due to the sequence of Fibonacci numbers. Whereas symmetry, on the contrary, represents stability, stability and immobility.

In addition, the additional ZS introduces an abundance of water spaces into Peter's plan, spilling over the city and dictating the city's subordination to their bends. And Peter's scheme 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 a “headache” when visiting the capitals. The Pope relates this to the energies of cities:
St. Petersburg - has masculine and, accordingly, masculine energies,
Well, Moscow - respectively - female and has feminine energies.

So, the residents of the capitals, who have tuned in to their certain balance of feminine and masculine in their bodies, find it difficult to rebuild when visiting a neighboring city, and someone may have some difficulties with the perception of one or another energy, and therefore the neighboring city may not at all be in love!

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

Used resources.