Golden ratio in painting and architecture. Golden ratio” in fine arts. The golden ratio in I. I. Shishkin’s painting “Pine Grove”

The one-third rule, or the golden ratio. This rule was derived by Leonardo Da Vinci and is one of the most important. The most important element of the image is located at a distance of approximately 1/3 of the height or width of the frame from its border. Divide the frame into nine equal squares. The points of intersection of the lines are the “golden ratio”.

Photo by Andrey Popov

Another diagram confirming the “golden ratio” is shown below. Let's draw a diagonal of the photo, then from the free corner we lower a line to this diagonal at a right angle. This way our photo will be divided into three right triangles. The diagram can be rotated any way you like, but the most important parts of the plot should be located in these triangles.

Here is a drawing illustrating two “golden ratio” schemes at once.

A person distinguishes objects around him by their shape. Interest in the shape of an object can be dictated by vital necessity, or it can be caused by the beauty of the shape. The form, the construction of which is based on a combination of symmetry and the golden ratio, contributes to the best visual perception and the appearance of a feeling 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 ratio is the highest manifestation of the structural and functional perfection of the whole and its parts in art, science, technology and nature. Back in the Renaissance, artists discovered that any picture has certain points that involuntarily attract our attention, the so-called visual centers. In this case, it does not matter what format the picture has - horizontal or vertical. There are only four such points, and they are located at a distance of 3/8 and 5/8 from the corresponding edges of the plane.

This discovery was called the “golden ratio” of the painting by artists of that time. Therefore, in order to draw attention to the main element of the photograph, it is necessary to combine this element with one of the visual centers.
The properties of the golden ratio have created a romantic aura of mystery and almost mystical worship around this number.

History of the golden ratio
It is generally accepted that the concept of the golden division was introduced into scientific use by Pythagoras, an 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 Cheops pyramid, temples, bas-reliefs, household items and jewelry from the tomb of Tutankhamun indicate that Egyptian craftsmen 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 Hesira, depicted on a relief of a wooden board from a tomb named after him, holds in his hands measuring instruments in which the proportions of the golden division are recorded. The Greeks were skilled geometers. They even taught arithmetic to their children using geometric figures. The Pythagorean square and the diagonal of this square were the basis for constructing 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 Pythagorean school and, in particular, to the issues of the golden division. The facade of the ancient Greek temple of the Parthenon contains golden proportions. During its excavations, compasses were discovered that were used by architects and sculptors of the ancient world. The Pompeian compass (museum in Naples) also contains the proportions of the golden division. In the ancient literature that has come down to us, the golden division was first mentioned in Euclid’s Elements. In the 2nd book of “Principles” the geometric construction of the golden division is given. After Euclid, the study of the golden division was carried out by Hypsicles (II century BC), Pappus (III century AD), and others. In medieval Europe, with the golden division We met through Arabic translations of Euclid’s Elements. The translator J. Campano from Navarre (III century) made comments on the translation. The secrets of the golden division were jealously guarded and kept in strict secrecy. They were known only to initiates.

During the Renaissance, interest in the golden division increased among scientists and artists due to its use in both geometry and art, especially in architecture. Leonardo da Vinci, an artist and scientist, saw that Italian artists had a lot of 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 of Italy in the period between Fibonacci and Galileo. Luca Pacioli was a student of the artist Piero della Franceschi, who wrote two books, one of which was called “On Perspective in Painting.” He is considered the creator of descriptive geometry.

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

Leonardo da Vinci also paid a lot of attention to the study of the golden division. He made sections of a stereometric body formed by regular pentagons, and each time he obtained rectangles with aspect ratios in the golden division. Therefore, he gave this division the name golden ratio. So it still remains as the most popular.

At the same time, in the north of Europe, in Germany, Albrecht Dürer was working on the same problems. He sketches the introduction to the first version of the treatise on proportions. Dürer writes. “It is necessary that someone who knows how to do something should teach it to others who need it. This is what I set out to do.”

Judging by one of Dürer's letters, he met with Luca Pacioli while in Italy. Albrecht Durer develops in detail the theory of proportions of the human body. Dürer assigned an important place in his system of relationships to the golden section. A person’s height is divided in golden proportions by the line of the belt, as well as by a line drawn through the tips of the middle fingers of the lowered hands, the lower part of the face by the mouth, etc. Dürer's proportional compass is well known.

Great astronomer of the 16th century. Johannes Kepler called the golden ratio one of the treasures of geometry. He was the first to draw attention to the importance of the golden proportion for botany (plant growth and their structure).

Kepler called the golden proportion self-continuing. “It is structured in such a way,” he wrote, “that the two lowest terms of this never-ending proportion add up to the third term, and any two last terms, if added together, give the next term, and the same proportion is maintained until infinity."

The construction of a series of segments of the golden proportion can be done both in the direction of increase (increasing series) and in the direction of decrease (descending series).

If on a straight line of arbitrary length, put aside segment m, put aside segment M next to it.

In subsequent centuries, the rule of the golden proportion turned into an academic canon, and when, over time, the struggle against academic routine began in art, in the heat of the struggle “they threw out the baby with the bathwater.” The golden ratio was “discovered” again in the middle of the 19th century. In 1855, the German researcher of the golden ratio, Professor Zeising, published his work “Aesthetic Research”. What happened to Zeising was exactly what should inevitably happen to a researcher who considers a phenomenon as such, without connection with other phenomena. He absolutized the proportion of the golden section, declaring it universal for all phenomena of nature and art. Zeising had numerous followers, but there were also opponents who declared his teaching on proportions “mathematical aesthetics.”

Zeising tested the validity of his theory on Greek statues. He developed the proportions of Apollo Belvedere in the most detail. Greek vases, architectural structures of various eras, plants, animals, bird eggs, musical tones, and poetic meters were studied. Zeising gave a definition to the golden ratio and showed how it is expressed in straight line segments and in numbers. When the numbers expressing the lengths of the segments were obtained, Zeising saw that they constituted a Fibonacci series, which could be continued indefinitely in one direction or the other. His next book was titled “The Golden Division as a Basic Morphological Law in Nature and Art.” In 1876, a small book, almost a brochure, was published in Russia outlining this work of Zeising. The author took refuge under the initials Yu.F.V. This edition does not mention a single work of painting.
Golden proportions in parts of the human body

The golden ratio is a mathematical formula, the result of complex calculations made by ancient Greek scientists. The uniqueness and divine nature of the golden ratio is explained by the fact that its use brings an invisible but subconsciously perceptible order to science, music, architecture and even nature.

Golden ratio- this is such a proportional harmonic 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. It is the highest manifestation of the structural and functional perfection of the whole and its parts in art, science, technology and even in nature.

Proportions golden ratio look like this

It is believed that the concept golden ratio"discovered by the ancient Greek philosopher and mathematician Pythagoras. Although, there is an opinion that he finalized the research of more ancient scientists - the Babylonians or Egyptians. This is evidenced by the ideal proportions of the Cheops pyramid and many surviving Egyptian temples correspond golden ratio.

Special attention to the rule golden ratio artists of the Renaissance turned to the heritage of the ancient Greeks. The very concept of this harmonic proportion is “ golden ratio"- belongs to Leonardo da Vinci. In his works its use is quite obvious.

For example, the well-known work “The Last Supper” is an example of use golden ratio.

"The Last Supper" by da Vinci

According to the 19th century French architect Viollet-le-Duc, a form that cannot be explained will never be beautiful.

Vertical golden ratio can also be seen in the painting “Trinity” by Andrei Rublev.

Golden ratio. Rublev "Trinity"

Repeating equal quantities, alternating equal and unequal quantities in proportions golden ratio, artists create a particular rhythm in their paintings, evoke a particular mood in the viewer and involve him in viewing the image. At such moments, a person, even one who is not experienced in art, subconsciously understands that he somehow likes the picture, that it is pleasant to look at.

Line intersections golden ratio form four points on the plane, the so-called visual centers, which are located at a distance of 3/8 and 5/8 from the edges of the picture. It is at these points that it is most advantageous to place the key figures of the picture. This has to do with how the human eye works, how the brain works and our perception.

For example, in Alexander Ivanov’s painting “The Appearance of Christ to the People” the lines golden ratio intersect clearly on the figure of Christ in the distance. And although the figures in the foreground are much larger in size and drawn out more clearly, it is the blurred figure of Christ that attracts the eye, because it is placed in the visual center.

Golden ratio. Alexander Ivanov. "The Appearance of Christ to the People"

The artist Nikolai Krymov wrote: “They say: art is not science, not mathematics, that it is creativity, mood, and that nothing in art can be explained - look and admire. In my opinion this is not the case. Art is explicable and very logical, you can and should know about it, it is mathematical... You can prove exactly why a painting is good and why it is bad.”

In the visual arts, a simplified rule is more often used golden ratio- the so-called “rule of thirds”, when the picture is conventionally divided into three equal parts vertically and horizontally, forming four key points.

Russian artist Vasily Surikov in his monumental work “Boyaryna Morozova” used one of these four points, placing the head and right hand of the main character of the canvas in the upper left part of the picture. Thus, all points, as well as all lines and views in the picture are directed towards that point.

Now try to identify the points yourself golden ratio in the following pictures.

Konstantin Vasiliev’s work “At the Window” is quite simple for this task. Lines golden ratio they converge exactly on the heroine’s face, in her eyes, which forces the viewer to plunge into thoughts about her experiences.

Golden ratio. Konstantin Vasiliev. "Near the window"

Or another example of focusing our attention is the painting “Luisa San Felice in Captivity” by Giovacchino Tom. Again, it is easy to see that here the lines golden ratio intersect on the heroine's face.

Golden ratio. Giovacchino Tom."Louise San Felice in Captivity"

Now you will probably try to recognize divine harmony golden ratio in every picture you see.

Back in the Renaissance, artists discovered that any picture has certain points that involuntarily attract our attention, the so-called visual centers. In this case, it does not matter what format the picture has - horizontal or vertical. There are only four such points, and they are located at a distance of 3/8 and 5/8 from the corresponding edges of the plane. This discovery was called by artists the “golden ratio” of the painting.

Leonardo da Vinci was the first to consciously use the golden ratio proportions in art.

The pentagram symbol helped artists in defining the space of a painting, for example, in the arrangement of human figures. The “golden” spiral was used for the same purposes. Michelangelo's Holy Family is an example of how the five-pointed star served this purpose.

The portrait of Monna Lisa (La Gioconda) 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.

“The Last Supper” is Leonardo’s most mature and complete work. In this painting, the master avoids everything that could obscure the main course of the action he depicts; he achieves a rare convincingness of the compositional solution. In the center he places the figure of Christ, highlighting it with the opening of the door. He deliberately moves the apostles away from Christ in order to further emphasize his place in the composition. Finally, for the same purpose, he forces all perspective lines to converge at a point directly above the head of Christ. Leonardo divides his students into four symmetrical groups, full of life and movement. He makes the table small, and the refectory - strict and simple. This gives him the opportunity to focus the viewer’s attention on figures with enormous plastic power.

Golden spiral in Raphael's painting "Massacre of the Innocents"

In contrast to the golden ratio, the feeling of dynamics and excitement is manifested, perhaps, most strongly in another simple geometric figure - a spiral. The multi-figure composition, executed in 1509 - 1510 by Raphael, when the famous painter created his frescoes in the Vatican, is precisely distinguished by the dynamism and drama of the plot. Raphael never brought his plan to completion, however, his sketch was engraved by the unknown Italian graphic artist Marcantinio Raimondi, who, based on this sketch, created the engraving “Massacre of the Innocents”.

The presence of F in “The Flagellation of Christ” by Piero della Francesca and in “The Birth of Venus” by Sandro Botticelli is one of the secrets of these extraordinarily beautiful paintings.

Golden Proportions in the linear construction of the image on the icon “The Descent into Hell” by Dionysius and the workshop (XVI century)

Symmetry and golden proportions in the linear space of “Trinity” by Andrei Rublev.

Abstract artists also started with geometry, and the golden ratio appears in many compositions. For example, “Suprematist composition” 1915. Kazimir Malevich.

Golden ratio in painting

Landscape artists know from experience that half the surface of the canvas cannot be allocated to the sky or to the ground and water. It’s better to take either more sky or more land, then the landscape looks better. .

F.V.Kovalev. Golden ratio in painting

• #1

  land_driver (Wednesday, 03 February 2016 13:37)

  Who seeks will always find!

• #2

  I knew you'd like it

• #3

  land_driver (Wednesday, 03 February 2016 18:54)

  I especially liked the last section - “what do all the considered examples of the use of the golden ratio in painting prove? Absolutely nothing.”
  - What is this film about?
  - It’s nothing...

• #4

  Exposure of favorite myths often causes painful reactions.

• #5

  Elena (Friday, 12 February 2016 17:36)

  I read it with mixed feelings... On the one hand, you can’t argue. On the other hand, there is an obvious option to “check harmony with algebra,” and for some reason this offends. I’ll think about it, thanks for the reason to practice thinking.

• #6

  land_driver (Friday, 12 February 2016 18:03)

  It's always interesting to watch those who expose and those who try to refute those who expose

• #7

  Elena: Still, the words of Pushkin’s Salieri refer to music. And in music, as in Architecture, “algebra” is present from the very beginning. Another question is how significant this role is. This is written in detail in the article “The Golden Ratio and Pythagoras” on this site. Painting is a completely different matter. The laws of perspective, as we know, are not at all necessary in painting. Just like the laws of reflection and refraction of light. (We will not argue that only realistic painting is possible). All that remains, perhaps, is color theory.
  land_driver: It’s much more interesting to participate than just watch.

• #8

  Maxim Boyko (Monday, 15 February 2016 16:36)

  I didn’t understand much, since I’m far from a photographer. But it was interesting to read.

• #9

  land_driver (Tuesday, 16 February 2016 12:11)

  Connecting mathematics with music is like nothing at all

• #10

  Valera (Tuesday, 16 February 2016 16:51)

  Knowledge is bricks that need to be assembled in the right order. A masterpiece is possible everywhere...

• #11

  Hope (Wednesday, 17 February 2016 04:25)

  As they say, you can’t argue with mathematics. It is present everywhere - in life, in music, and in painting. Logically, all creative people should feel mathematics in their gut.

• #12

  Maxim: Interesting - not bad at all. Thank you.
  Land_driver: After Pythagoras, it’s certainly easy.
  Valera: Valera is poetic even in prose
  Nadezhda: David Hilbert once said about his student who gave up mathematics and became a poet: “He had too little imagination for mathematics.”

• #13

  Vitaly (Wednesday, 17 February 2016 20:46)

  Good practical advice about dividing the canvas into two unequal parts!
  I took this rule as a basis when I first became interested in photography, completely intuitively.
  And I realized that this was indeed the case, looking at my first surviving photos (early 60s of the last century :)).

• #14

  Marina (Thursday, 18 February 2016 10:38)

  Amazing article - very warm. I have heard about the golden ratio many times and wondered what the essence of this concept is. Your explanation is interesting.

• #15

  land_driver (Friday, 19 February 2016 12:09)

  As for “little imagination” - this is a well-known dispute between physicists and lyricists. It will never stop

• #16

  land_driver (Saturday, 20 February 2016 19:23)

  Today on Tverskaya, right on the street on the façade of a building, we saw a painting that completely contradicts all the rules, including the golden ratio - the horizon line divides the painting exactly in half, and a significant figure is located exactly in the center of the canvas. It's on the opposite side of the street somewhere opposite the Actor Gallery

• #17

  valera (Saturday, 20 February 2016 19:29)

  Since there is only enough imagination for poetry, this leads...

• #18

  Alexander (Sunday, 21 February 2016 17:04)

  I could not even imagine that in those days many artists studied painting so much that methods of the golden section were developed. And in general, if you think about it, painting is a kind of science; in order to paint a beautiful picture, you need to know so much and at the same time understand it well.
  P.S. - to be honest, like many other readers of your blog, I’m not well versed in many of the topics that you write on your blog, since speaking is not my element, so excuse me if I write a blizzard in some of the comments, misunderstanding you;) Yours is complicated topic for blogging and you are doing a good job, I rarely meet webmasters like you.

• #19

  The point is not a dispute between physicists and lyricists, but the fact that all human abilities are connected with each other, physics with lyricism, science with art, knowledge with intuition. Leonardo da Vinci is a brilliant example. And if someone deliberately limits the development of one of these parts, he becomes “crippled.” The greatest breakthroughs of the human spirit have always occurred at the borders of regions, as well as the greatest mistakes and delusions. In particular, those associated with the golden ratio. Mathematicians and artists simply did not understand each other.

• #20

  land_driver (Thursday, 25 February 2016 13:03)

  How can you consciously limit yourself in development? Like, I will deliberately not study mathematics, even though I want it and need it? It seems to me that if a person is lazy, then nothing can be done about it

• #24

  If everything that is on the ground is more interesting - flowers, streams, a river, a path, etc., and the sky is boring, gray, uniform, then it is more interesting when there is more land in the frame. If the sky is “magical”, if there are some extraordinary clouds in the sky, or a rainbow, or crazy colors, or against the sky there are tall trees, beautiful buildings, but nothing on the ground, then it is more interesting when there is more sky in the frame.

• #25

  For rest - cross-section, for dynamics - peddling....

• #26

  Lyudmila (Tuesday, 10 October 2017 21:30)

  I saw a medical center with the name Golden Ratio, now I think what the meaning of the name is, in the divine proportion of what to what? I only have associations with a scalpel...

• #27

  land_driver (Saturday, 14 October 2017 21:31)

  This is for sure, when I see a photo divided in half by the horizon line, I immediately feel somehow sad. I just want to cut something off - top or bottom

• #28

  Eh, it’s been a while since there have been new exciting articles on this wonderful site.

• #29

  Thank you from the bottom of my heart for the article! Since childhood, I could not understand what the golden ratio is, because all the literature that I came across on this subject gave examples of paintings that very vaguely fit into the rules. I wondered why, if proportion is one very clear constant, there are other proportions where the rectangle is divided not into a square and a rectangle, but into a rectangle and a RECTANGLE. What kind of liberties are these? How does this rule work then? Where is the smooth, beautiful square? And here the face is cut off along the line, the details have moved beyond the edges of the division! Why? – I asked. I also noticed that the situation was aggravated not only by researchers who were wishful thinking, but also by ordinary people who put “snail” on everything, even where it clearly doesn’t fit. It’s as if they themselves don’t understand what the meaning of the golden ratio is, and instead of explaining their examples they say: “Well, you can see it!” In geometry nothing is visible, everything must be calculated and proven :) You are the only author of all the ones I’ve read who not only clearly explained how geometry can work in painting, but also dispelled my bitter thoughts: it’s not me who doesn’t see a clear golden ratio in paintings and with my little mind I can’t understand the meaning of the rule, there is no golden ratio!! In mathematics there is, but in paintings - very rarely :) Thank you very much!

Conclusion

Votive reliefs

Grave reliefs

Reliefs

Attic funerary steles of the early 6th century were decorated with the likeness of an Egyptian capital with petals, which was carved in stone and painted. From 550 to 530 this motif is replaced by a double scroll shape resembling the head of a harp. A capital of a similar shape could be crowned with the figure of a sphinx or gorgon.

In Ionia, figurative images are not usually found on tombstones. Samian steles are often topped with a palmette.

If we consider later figurative images, the most characteristic images of Attica are a naked youth with a disk or staff, a warrior and an old man in a cloak and hat, leaning on a stick and accompanied by a dog. Thus, the gravestone sculpture represented the three ages of human life.

Steles with a wider pictorial field could include two figures: for example, a handshake between a standing man and woman. This gesture - dexiosis - has become one of the most common motives.

Many Athenian steles were part of the so-called “Themistocles Wall”, built after the departure of the Persians, into which, according to Thucydides, funerary monuments were built. Some steles retain the names of the authors, who were already mentioned above. There is, for example, the signature of Aristocles. The inscriptions were usually placed on the trunk of the stele or on its base.

In some cases, the stele may not have a funerary, but a votive character, when a miniature adorant is depicted next to the main figure. Sometimes the monument had a double function, such as the stele from Laconia dedicated to Chilo, the famous Greek legislator, who was ranked among the seven sages of antiquity and given honors on a par with mythological heroes.

Most Greek plastic art comes from sanctuaries under state protection. The dating of the works remains very approximate. There are several exact dates: this is the time of the creation of the treasury of the Sifnosians in Delphi, the dates of the Persian invasion of Athens and the time of the creation of Themistocles’ Wall with its funeral steles. Some statues can be dated based on pottery.

Our information about artists is extremely scarce. Ancient authors mythologize the first sculptors, linking their activities with the legendary Daedalus and his students. Apparently, the artist’s real income came from working in ceramics; real respect is for practical and theoretical works on architecture (it is known, for example, that Theodore of Samos, being not only a sculptor, but also an architect, wrote books). Sculptors were clearly valued lower than poets, but the presence of their signatures on the works speaks of a developed author’s self-awareness.

Archaic plastic art was created like poetry: it had to be “read” “line by line,” collecting disparate parts into a single whole. Only later was the language of realistic art developed, which became the basis for the greatest achievements of Greek classical sculpture.

Attention! When studying the topic “Archaic sculpture of Greece” based on the book by I. Boardman, it is necessary to find all the necessary illustrations of surviving monuments mentioned in the text.

Questions about the text:

1. The concept of daedalic art.

2. Techniques, proportions, production, purpose of kouros. Name specific statues.

3. Images of the core. Features of the garment, purpose. Kory of Chios, Athens.

4. Sculptural decoration of the ancient temple of Athena on the Acropolis under Peisistratus.

5. Specifics of the archaic pediment composition. Typical images. Pediment with o. Kerkyra.

6. Treasury of the Sifnians at Delphi.

7. Authors and their works. Antenor (Tyrannobusters), Archermus of Chios (Delos, Athens), Aristion from Paros (Thrasiclea), Faidimos (Moschophoros), Endois - “disciple of Daedalus” (head of Raye, seated Athena from the Athenian Acropolis).

[*] Protom (Greek) – the front part of the body.

Back in the Renaissance, artists discovered that any picture has certain points that involuntarily attract our attention, the so-called visual centers. In this case, it does not matter what format the picture has - horizontal or vertical. There are only four such points; they divide the image size horizontally and vertically in the golden ratio, i.e. they are located at a distance of approximately 3/8 and 5/8 from the corresponding edges of the plane (Fig. 8).

Figure 8. Visual centers of the picture

This discovery was called the “golden ratio” of the painting by artists of that time. Therefore, in order to draw attention to the main element of the photograph, it is necessary to combine this element with one of the visual centers.

1.7.1.Golden ratio in Leonardo da Vinci’s painting “La Gioconda”

The portrait of Mona Lisa is attractive because the composition of the drawing is built on “golden triangles” (more precisely, on triangles that are pieces of a regular star-shaped pentagon)

Leonardo da Vinci "La Gioconda"

1.7.2.Golden ratio in the paintings of Russian artists

N. Ge “Alexander Sergeevich Pushkin in the village of Mikhailovskoye”

In the film N.N. Ge “Alexander Sergeevich Pushkin in the village of Mikhailovskoye”, the figure of Pushkin is placed by the artist on the left on the line of the golden ratio. The head of a military man, listening with delight to the poet's reading, is on another vertical line of the golden ratio.

The talented Russian artist Konstantin Vasiliev, who passed away early, widely used the golden ratio in his work. While still a student at the Kazan Art School, he first heard about the “golden ratio”. And since then, when starting each of his works, he always began by mentally trying to determine on the canvas the main point where all the plot lines of the picture were supposed to be drawn together, as if to an invisible magnet. A striking example of a painting constructed “according to the golden ratio” is the painting “At the Window”.

K. Vasiliev “At the window”

Stasov in 1887 wrote about V.I. Surikov (Encyclopedia of Russian Painting - Moscow, 2002. - 351 p.): “...Surikov has now created such a picture (“Boyar Morozov”), which, in my opinion, is the first of all our paintings on subjects from Russian history... The power of truth, the power of historicity that Surikov’s new painting breathes with is amazing...”
And inextricably with this, this is the same Surikov (Encyclopedia of Russian Painting. – M., 2002 – 351 p.), who wrote about his stay at the Academy: “...most of all he was engaged in composition. There they called me a “composer”: I studied all the naturalness and beauty of composition. At home I set and solved problems for myself...” Surikov remained such a “composer” throughout his life. Any of his paintings is a living confirmation of this. And the most striking is “Boyarina Morozova”.
Here the combination of “naturalness” and beauty in the composition is perhaps most richly presented. But what is this combination of “naturalness and beauty” if not “organicity” in the sense as we talked about it above?
But where we are talking about organicity, look for the golden ratio in proportions!
The same Stasov wrote about “Boyarina Morozova” as about a “soloist” surrounded by a “choir”. The central “party” belongs to the boyar herself. Her role is given to the middle part of the picture. It is bound by the point of highest rise and the point of lowest decline of the plot of the picture. This is the rise of Morozova’s hand with the double-fingered sign of the cross as the highest point. And this is a hand helplessly extended to the same boyar, but this time - the hand of an old woman - a beggar wanderer, a hand from under which, along with the last hope of salvation, the end of the sledge slips out.
These are the two central dramatic points of the “role” of noblewoman Morozova: the “zero” point and the point of maximum takeoff.
The unity of the drama is, as it were, outlined by the fact that both of these points are chained to the decisive central diagonal, which determines the entire basic structure of the picture. They do not literally coincide with this diagonal, and this is precisely the difference between a living picture and a dead geometric scheme. But the aspiration towards this diagonal and connection with it is obvious.
Let's try to determine spatially what other decisive sections pass near these two points of the drama.
A little geometric drawing work will show us that both of these drama points include two vertical sections between them that extend 0.618... from each edge of the picture rectangle!

V.I. Surikov “Boyarina Morozova”

The “lowest point” completely coincides with section AB, located 0.618... from the left edge. What about the “highest point”? At first glance, we have an apparent contradiction: after all, section A1B1, spaced 0.618... from the right edge of the picture, does not pass through the hand, not even through the head or eye of the noblewoman, but ends up somewhere in front of the noblewoman’s mouth!

In the famous painting by I.I. Shishkin's "Ship Grove" clearly shows the motifs of the golden ratio. A brightly sunlit pine tree (standing in the foreground) divides the picture horizontally with the golden ratio. To the right of the pine tree is a sunlit hillock. It divides the picture vertically using the golden ratio. To the left of the main pine tree there are many pine trees - if you wish, you can successfully continue dividing the golden section horizontally on the left side of the picture. The presence in the picture of bright verticals and horizontals, dividing it in relation to the golden ratio, gives it a character of balance and calm in accordance with the artist’s intention.

I. I. Shishkin “Ship Grove”

We see the same principle in the painting by I.E. Repin "A.S. Pushkin at the act at the Lyceum on January 8, 1815."

The artist placed the figure of Pushkin on the right side of the picture along the line of the golden ratio. The left part of the picture, in turn, is also divided in proportion to the golden ratio: from Pushkin’s head to Derzhavin’s head and from it to the left edge of the picture. The distance from Derzhavin’s head to the right edge of the picture is divided into two equal parts by the golden section line running along the figure of Pushkin.