Geometry was almost always present in art. Existing, however, in different eras, geometry in painting, sculpture and architecture took on different meanings. Sometimes it appeared in the role of perspective, being an instrument for transferring volume on a plane, and later flowed into a literal concept, representing geometric objects as objects of art. In paintings with abstraction, geometry becomes the main character of the plot, while in paintings of the Renaissance it is only responsible for the spatial image.
Concept of perspective
Perspective is a way of depicting objects on a certain plane, taking into account visual reductions in their values, as well as changes in borders, shapes and other relationships that are seen in nature. Thus, this is a distortion of the proportions of bodies and the geometry of the picture during their visual perception.
Types of perspective in painting
Geometry in painting and sculpture are fundamentally different from each other, although they go side by side, like science and art, and have been intertwined for many centuries. In the Renaissance, art provoked the study of geometry. Geometry in painting enriched art, introducing new opportunities and fundamentally excellent qualities. At present, we have the opportunity to look at it from a new perspective. Being a large branch of mathematics, geometry in painting is the connecting link that permeates the whole history.
There are three methods for reproducing three-dimensional space on a two-dimensional surface of a picture:
- perspective (direct and reverse);
- orthogonal projection method;
- axonometry.
History
These fundamental principles of geometry in painting were implemented at various stages in the development of artistic culture, when each of the methods found the most appropriate expression. For example, the system of orthogonal projections became the basis of the art of Ancient Egypt, while the axonometry, also called the parallel perspective, became characteristic of the images of the era of medieval Japan and China. The reverse perspective has become a typical method of depicting the icons of Ancient Russia and Byzantium, and the direct perspective became widespread during the Renaissance, becoming the basis of monumental painting of European and Russian art of the 17th-19th centuries.
The idea of orthogonal projections was suggested to man by nature: the shadow cast by an object is the simplest analogy of the image of a three-dimensional object on a two-dimensional plane. But this projection is not able to convey the depth of the real world, so in ancient Egypt the first attempts of artists to advance further in axonometry began to be noted.
Axonometry transmitted the frontal plane of the subject without any distortion. It could give an idea of the volume of the depicted space, but the depth itself remained an obscure quantity. Mathematics interprets this geometry in painting as a central projection with an infinitely distant center. Nevertheless, the axonometry method, which was also called the free perspective, has been known since ancient times. From the 2nd to the 18th centuries, the plans of settlements were presented in a similar way, as if from a bird's eye view.
The drawbacks of axonometry were offset by the Renaissance, when ideas about the future began to develop. Such a system has acquired a set of rules based on calculations. This method was notable for its complexity, but at the same time it accurately reproduced the surrounding world. The Renaissance perspective expanded the scope of the human worldview, opening up new opportunities and knowledge for people.
Perspective development
Axonometry replaced orthogonal projections, and that one gave way to perspective. The emergence of geometry in painting by stages took place gradually, in strict sequence. The complexity of the method determined its position in this scheme: the method of orthogonal projections as the most primitive took first place in the history of development. He helped reproduce the contours of real objects without distortion.
Each of the methods of geometry became an important step in the formation of painting. There was a search for the most advanced system for transmitting visual images.
Objective and subjective spaces
Man is surrounded by two geometric spaces. The first is real, objective space, the second is generated by the work of the brain and eye. People see and perceive it in their consciousness, therefore it was called the subjective or perceptual space.
The history of painting went from depicting actual space to visual, subjective. In the XIX-XX centuries, the creators intuitively approached the creation of a perceptual perspective, which was reflected in their works in the form of various deviations from the Renaissance system. The general theory of perspective, including both the renaissance and the perceptive, was created by academician B.V. Rauschenbach.
He found out that there can be no single perspective in the image of visible space, just as there are no perfect methods for representing three-dimensional space on the surface. An accurate image of three-dimensional space is not feasible in principle: with all his desire, an artist can give an approximate geometric picture of the real world. In accordance with his goals, the artist can choose one or another method that will help him most accurately express his idea. Therefore, it will be incorrect to reproach the ancient Egyptian master for excessive simplicity, the Japanese for lack of depth, the ancient Russian for distortion of perspective, while simultaneously elevating the creator of the Renaissance. However, the Renaissance artists can be reproached with excessive photographic.
Orthogonal painting of ancient Egypt
The whole philosophy of the ancient Egyptians is permeated by the idea of the eternal absolute of the pharaoh, revered as the son of God. This position could not but be reflected in the art and painting of ancient culture. Each object of the image was comprehended in isolation from the surrounding space, the creator delved into the essence of the object, discarding everything momentary and insignificant, leaving only eternal and genuine images, independent of time and space - nouns. They were compiled into whole messages and narrative paintings. Ancient Egyptian painting was closely intertwined with writing, the images were mixed with hieroglyphs.
To implement the idea of the eternal in a noun image, the method of orthogonal projections was used. The ancient Egyptian artists saw the only right way in this way: the only way the form can be captured without unnecessary distortion. They told the viewer information about the real world.
Since the artist did not have the opportunity to convey all three projections of the subject, he chose the most characteristic side of the subject: that is why when portraying animals the profile was chosen: it was so easy to convey the individual characteristics of the view, as well as depicting legs that could go depending on the position or stay alone. The chest and shoulders were portrayed turned towards the viewer. The defeated enemies were portrayed as if from above - for the most informative.
Ancient Egyptian creators created their works, relying not so much on vision as on speculation, it allowed the artist to combine several different points of view in one work. Speculation contributed to the development of a mathematical system of rules in the depiction of human figures, which were called canon. He confirmed the artist’s attitude to knowledge and power, being a symbol of dedication to the secrets of the priests. The stricter the framework of the canon, the more skill the artist required for the image.
The images were deliberately two-dimensional, but this did not bother the authors at all: the ancient Egyptians did not set themselves the task of displaying three-dimensional space, rather pursuing the goal of transmitting valuable information. If there is an action in the picture, the event did not develop in depth, but along the plane of the canvas, moving along the lines.
However, the problem of the image of space was gradually raised in the painting of Ancient Egypt. Sometimes the artist placed one figure behind another, but this technique was far from always successful. For example, in the image of Pharaoh Akhenaten about the wife sitting next to her, one could only guess from the image of her hand, which hugged her husband. The palm seemed to emerge from nowhere, and the second rested peacefully in the hand of the pharaoh.
But there were more successful examples of geometry in the paintings of artists, for example, when portraying archers. Each subsequent archer standing behind was depicted with a shift slightly up and to the right: this gave the impression of depth. From the point of view of geometry, this is already called frontal oblique axonometry.
The need to image volumetric space leads to the development of geometric systems in painting - axonometry. Although her beginnings began to be found in the painting of Ancient Egypt, she received real development later.
Parallel painting of the medieval east
Attempts to transmit depth on a plane began to be found in the paintings of Ancient Egypt, which pushed to create a new system - axonometry, which is also called a parallel perspective. This system was called by art critics a “fish bone” by analogy: it had an axis of descent and gravitated towards a linear perspective, but never grew into it.
"Fish bone" was found not only in Ancient Egypt, but also in images of Ancient Rome and Ancient Greece. However, Rome soon fell, not having enough time to develop the geometry system in the paintings of artists, and axonometry found its development only for several centuries, finding its place in the painting of medieval China and Japan.
The culture and art of China were not constrained by religious dogmas: in these parts Taoism, Confucianism and Buddhism peacefully existed side by side. Against the background of cultural and philosophical teachings, two areas of art developed - secular and religious. The path of knowledge of the truth passed through the renunciation of worldly vanity, the appeal to nature for tranquility and spiritual purification. The geometry of the picture and visual perception were complex for both the viewer and the artist. The Chinese artist perceived nature and its image as a spiritual space in which the personality of the contemplator dissolved. That is why the landscape has become widespread.
Axonometry as a central projection with an infinitely remote design center was ideally suited to this philosophy of contemplation. The artist’s point of view seemed to go to infinity, dissolving in the space of nature: the artist became part of art itself. Axonometry knows neither the angle of view, nor vanishing points, nor even the horizon, because it seems to slip away from the observer, going up somewhere and dissolving in space and the contemplator. The art of the eastern landscape was a view from infinity, which passed through the picture and rushed further into infinity.
A parallel perspective is most indicative of Chinese painting in pictures with man-made structures - parallelepipeds of houses and other human structures. The axonometry of geometry in oil paintings is obvious, but here you can notice that the scenes of human life are seen by the artist as if from far away, from infinity, which symbolizes the tinyness of human concerns and problems: the world appears as an anthill.
Axonometry has three coordinates. If you choose such a point of view that the two axes will represent the frontal orthogonal projection, then distortions will be noticeable along the third coordinate. Such a projection is called front oblique axonometry, in which Chinese masters usually did. The distortion coefficient for the third coordinate is not fixed, so it is not possible to judge the depth by the first two coordinates. The fuzziness of depth is enhanced by the parallelism of lines that do not tend to one point as they move away from the observer. So in a parallel projection, two opposing principles arise: flat and deep. The picture has a deep origin, but in fact it is a flat cut moving in depth without metric contractions.
Oriental artists cleverly used this contradiction, turning it into a kind of compromise between flat (Ancient Egypt) and deep (Renaissance). This dialectic of opposing opposites conveniently fit into the ancient Chinese philosophy of Yin-Yang. Yang for the Chinese painter symbolized bright places in the picture: mountains, snow, clouds. Yin filled the dark areas: water and lowlands, where all sewage flocked. The black-and-white Chinese landscapes were executed not only masterfully, but also soulfully and thoughtfully.
As for Japanese art, it grows from ancient Chinese culture. But nevertheless, Japan, separated from the whole world by the seas, has preserved its original culture up to the present day. Throughout the history of Japanese art, painting did not know any drastic changes. The geometric basis was the same parallel perspective. This is especially significant in the works of the famous Katsushik Hokusai. His work became the pinnacle of the geometry of parallel projections in painting.
Linear Renaissance Perspective
The world began to change, and this could not but affect creativity: the old canons collapsed, new thinking came, empirical knowledge triumphed over visual experience. The geometric language of art has become perspective. Although the embryos of the new method were encountered in antiquity, only with the Renaissance this projection was fully developed.
The linear perspective is based on the laws of geometric optics, reflecting perceptual space in the picture. Vision becomes dominant over speculation. The prospect combined the two main features of a culture of rebirth: rationalism and empiricism.
The main tools in the hands of artists were the horizon line and vanishing point. The vanishing point is the main point in the picture and the center of the composition, and the parallel lines tending to it are designed to bring the viewer to its semantic source. The composition of the picture acquired strict vertical symmetry passing through the main point.
Renaissance artists sought not only to convey the depth of space, but also to calculate it. That is why in the paintings it was often possible to observe the squares of the floor or ceiling tiles, because they represented a coordinate system. Thus, architecture in painting became the architectonics of the picture.
Together with geometry, a new artistic thinking came into the art of the Renaissance. The Renaissance perspective has become a revolution in artistic thinking and understanding of art. The painting began to reflect a deep interest in science.
The inverse perspective of the painting of Ancient Russia
Due to the strict alignment of geometric rules, this option of perspective seemed the only right one of all possible. However, there was another perspective system - the opposite.
Old Russian painting, alas, almost did not reach our days. Drying oil, which was covered with painting for better preservation, tended to darken over time, so that over the centuries, it turned into a black impenetrable coating. Such blackened boards were either disposed of by rafting along rivers, or burned, or updated along barely readable contours.
This continued until the end of the last century, when another was discovered under one black layer, and after it a second, and third, and fourth, and fifth, until piercingly bright colors surfaced from the depths of centuries. This discovery marked the return from oblivion of an entire era of Russian culture.
Thanks to this look, a new perspective, different from the Renaissance, opened up, which art critics immediately dubbed the primitive, naive and unfaithful. Old Russian painting combined many contradictions, but it soon becomes clear that this is not a set of inconsistencies, but a different perspective system, which was called the opposite.
The sources of the opposite perspective are in Byzantine art, from which ancient Russian culture grew. , , .
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Modern Art
Currently, geometry in painting, sculpture and architecture has taken literal meaning. Times are changing, and in contemporary art, projections and perspectives no longer always have such great significance. Now geometry in painting is a style that has stood out in real realities.
Its rudiments arose as far back as 900-700. BC e. Art historians emphasize the protogeometric style. It was characteristic of various arts and crafts. But closer to the 20th century, geometry acquired a new meaning not only for painting, but also for art in general.
Geometry in painting does not have a name, at least, a single one that would suit every creator. Styles such as cubism, abstractionism, suprematism, futurism, and many others began to stand out, where geometry itself became a kind of art object. Figures in these styles of painting and sculpture have created a huge number of innovative subjects that excite the mind of the audience to this day. Controversial, but compositionally accurate and harmonious works of art inspire contemporaries to new creative achievements.
Among the famous artists with geometry in painting can be called, for example, Malevich, Kandinsky, Picasso and many others. Their work is known even to those who are new to art. Geometry in the painting of contemporary artists is much more pronounced than in the works of old masters, which makes such examples easy to remember. Recall, at least, the “Black Square”, discussions about which are still ongoing.
Manifestations of such creativity can be both paintings with an abstraction of geometry, where circles meet with triangles and lines, forming a single ensemble with a verified composition and specific meaning, and amazing sculptures consisting of simple figures, but in which you can read a deep understanding of the structure of the world and others items. Modern works are often veiled, but at the same time they look at the very essence, bringing out the original idea of the subject, sometimes even in the most unexpected form. Geometry in modern painting is no longer a tool for creating art, but the tool itself, the essence of the idea.
Previously, people studied the prospect and its varieties in order to come to the most complete and accurate image of the world. Now, geometry in painting in paintings has led people to a fundamentally new understanding of the world, its non-literal component. People looked at the pictures in a new way.
Geometry in the painting of contemporary artists is much more pronounced than in the works of old masters. Today, it is important for artists not to perfect the reproduction of the outer shell of three-dimensional objects in a plane, but to accurately convey the essence of objects using a minimum of means and a maximum of expression.
We can conclude: geometry in sculpture and painting is returning to its beginning. Once it was important for the creators to fix the idea of the depicted object, and only later they turned to the desire to depict the world as accurately as possible. Now the geometry of the picture and visual perception are returning to the beginning, when the accuracy and accuracy of perspective are not so important, as the clarity of thought is valuable.