Picture My day Geometric shapes. Research work in mathematics "Geometry in painting"

18.06.2019

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Very often in the world of artists there are paintings, largely different from oil and pastel canvases. They resemble drawings, patterns, sketches and are completely incomprehensible to a simple viewer. Now we will talk about the compositions of geometric shapes, we will discuss what they are, what load is carrying and why they are at all occupy such an honorable place in the art of drawing and painting.

Simple compositions

Each Master Brushes, who started his way from an art school, will answer you that the exact lines, and their combinations are the first thing to teach there. This is how our eyesight and brain are arranged that if you initially learn to harmoniously combine simple forms among themselves, it will further draw complex paintings easier. The compositions of geometric figures allow us to feel the balance of the paintings, to visually determine its center, calculate the drop in light, determine the properties of its components.

It is worth noting that, despite the clarity and direct images of such images, they are drawn exclusively by hand, without lines and other auxiliary items. The parameters of the figures are measured using proportions that can be located in a two-dimensional measurement (flat picture), and can go into perspective into a single point of departure of all lines.

Beginners artists paint compositions from geometric shapes in two dimensions. For such pictures, one of the parties is selected - a plan or facade. In the first case, all the figures are depicted in the "view from above", then the cone and the cylinder becomes around, Prism acquires the form of its base. If the figures are depicted in the facade, one of their sides is demonstrated, most often the front. In the picture we see triangles, squares, parallelograms, and so on.

Three-dimensional paintings

In order to develop and the feeling of perspective, artists learn to portray the compositions of the geometric figures of the volume, which go into perspective. This image is considered three-dimensional, and in order to transfer it to paper, you need to imagine everything clearly. Similar drawing techniques are relevant in construction and architectural universities, they are used as exercises. However, students often from these "picturesque etudes" do real drawing incredible shapes of figures, cutting compositions with planes and semi-positions, depicting pictures in the section.

In general, it can be said that clarity, linearity is the main properties that any composition of geometric shapes possesses. The drawing at the same time can be static or dynamic - it depends on the type of figures depicted and on their location. If the picture is predominantly cones, triangled prisms, balls, then it seems to be "flies" - it is definitely dynamics. Cylinders, squares, tetrahedral prisms relate to statics.

Examples in painting

Geometric forms found their place in painting, along with romanticism and other destinations. A vivid example of this is the artist Juan Gras and his most famous picture "Man in a cafe", which, like a mosaic, consists of triangles, squares and circles. Another abstract composition of geometric figures - Pierrot canvas, artist B. Kubist. Bright, clear and very peculiar picture.

Types of composition The vertical composition gives the artistic product of the plowing, movement up or creates a feeling of suturing L.F. Zhgin Crowd E.

Types of composition of V. Surikov. Fewing Morozova Diagonal compositions transmit the dynamics of action, movement on the viewer or from it and covers large spaces

Concert "Spring" from the cycle "Seasons" Antonio Vivaldi part. "Spring is shaking!" Spring is getting better! And the joyful song is full of nature. Sun and warm, murmur streams. And the festive marshmallows will distribute, accurately magic. Suddenly the velvet clouds raid, as the Blagovest sounds heavenly thunder. But quickly runs up the whirlwind of mighty, and twitter again floats in the blue space. 2 part. "Dream of the peasant" flowers of the breath, herbs rustling, full of nature. Sleeping a shepherd for the day of the charter, and the dog is a little heard. 3 part. "Dance-pastoral" shepherd violin sound is spread, buzzing over the meadows, and the nymph dancing the magic circle of spring is bloomed with wonderful rays. A.G.Vetsianov. Sleeping a shepherd. 1780.

Form - In Fine Art, the form is the outline, outdoor view, the contour of the subject. The simplest forms are approaching the square, triangle, circle, "Amebe". The amount of receptions, expressive and visual means to create an image in any form of art A. Dzhacometti. Spider A. Dzhacometti. Cat

The square is complete, a steady form expresses asserting images, it is not peculiar to movement, flight. The triangle is active, developing on the plane and in space, the form carries the possibility of movement, expresses the struggle of opposites, may be aggressive. The circle is the most vivid expression of the idea of \u200b\u200bnature (land, sun, universe), therefore associates with the concepts of "good", "happiness", "life". The flowing form of amoeba gives images an unstable character, associated with romanticity, melancholy, pessimism.

Line to enhance the artistic image of the form can be stylized or transformed. They emphasize or change the characteristic features of the subject, and unnecessary parts are discarded. Especially often these techniques are used in poster and book graphics and in animation, as well as in modern sculpture. It has its own form that expresses the image. It can be rapid or tight, smooth or angular, purposeful or chaotic and thereby forms various images.

This is the organization of musical whole, methods for the development of musical material, as well as genre designations that authors give their works, for example: a song, romance, ballad, prelude, and other formulations in music are based on the principles of repetition and contrast. There are two-part and three-part musical forms, variations, rondo, a sounding form, etc. The scale of the idea of \u200b\u200bthe musical product determines its composition formulation. For song genres, simple forms are characteristic (bought, bureaucratic variations); The works of dance genres are often written in a three-part form. And the dramaturgy of such genres, as a symphony, concert, opera, ballet, requires more detailed forms built on comparison and contrasting contrasting images.

Choose two musical works with various shapes. Compare how the main musical thought is developing and approved. What methods of development prevail in each of these works. Choose examples of painting, graphics or sculptures that have a certain nature of the form.

In the first grades of geometry in the 10th grade, the basics of stereometry are laid, the guys get acquainted with spatial figures. As impossible spatial figures, I led them an example of optical illusions - shapes that seemed by the usual projection of a three-dimensional object, but with a more detailed study, contradictory compounds of the elements of the figure are viewed, the illusion of the impossibility of its existence in three-dimensional space is created. The guys have shown genuinely, I invite you to plunge into the world of mathematical illusions.

Many will say that mathematics (geometry) - discipline analytic, visual art - emotional, and somehow it happened that mathematics and painting are considered to be so different, almost opposite and mutually exclusive. Modern figures rarely enjoy the image of a geometric perspective to display the realism of the three-dimensional scene on canvas or sheet of paper. But there are also artists who have mathematics with its unprecedented opportunities are in the spotlight, and the most frequent methods are the image of polyhedra, tessellations, impossible figures, mebius tapes, unusual perspectives, fractals.

The Dutch artist Maurice Escher (1898-1972) can be considered the founder of mathematical art, its work is a source of inspiration for many followers. Escher created unique and charming work, in which a wide range of mathematical ideas are used and shown, and all sorts of splits of the plane, mosaic, polyhedra and logic of three-dimensional space are most interesting for studying the ideas of Escher.

So, I invite you to the world of optical illusions

The absurd similarity of Cuba

Try, climb the stairs to the upper floor at such a cross-arrangement of columns. Does not work? Why? On the floor of the lower platform, then inside the Belvedere, there is a staircase for which two climbs. However, reaching the top platform, they will turn out again outside, under the open sky, and again they will have to enter the Belvedere.

Falls or swears up this waterfall? Falling water leads to a motion of the mill wheel and flows over the inclined up (?) Zigzag chute between the two towers, returning to the point where the waterfall begins again. It seems that both towers of the same height; Nevertheless, the one is the right, turns out to be a floor lower than the tower on the left.

At the top and bottom (High and Low), 1947. Lithograph.

And in this house you would like to live? Two identical floors, but each opens with an observer from different points: the lower part - the scene he sees, standing on the ground, that is, on the platform laid out by tiles. Raising the eyes up, it will see the same tiled floor, repeated as the ceiling in the center of the composition, but at the same time serves as a floor for the top scene. Tile is repeated again, this time as a real ceiling.

Thus, you can safely combine geometry and painting, which makes many modern artists,creating paintings in the style of Escher and in its own style.Mathematical art flourishes today, followers operate in various directions, including sculpture, drawing on flat and three-dimensional surfaces, lithography and computer graphics. We'll see?

Where does this door lead? And what can be installed in such a showcase?

Incredible Tower

Unusual window

Here is the world of mathematical art!

Pictures of Site.

Simultaneously with the study of colors, the child can start showing cards geometric shapes. On our site you can download them for free.

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Print cards on tight paper or cardboard on 2, 4 or 6 pieces on 1 sheet. To conduct classes on the methods of Domana Cards are ready, you can show them to the baby and call the name of the picture.

Successes and new discoveries to your baby!

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Educational cards according to the method of Glen Domana with pictures of flat geometric shapes for children

Educational cards Geometric shapes according to the method of Glen Domana with pictures of flat geometric shapes for children

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I think that mathematical calculations do not matter for artistic art. But it is not. The reflection of the world around us than more or less and is visual art, is associated with the reproduction of geometric shapes and their proportions.

Sometimes these proportions are deliberately violated, optical illusions are created. Master in this area can be called Maunitsa Escher. Dutch artist of the middle of the XX century, in the space of the drawings of which is possible. One form flows to another, the prospect does not converge at one point, the objects have no beginning, no end. This inconsistency of the laws of nature and logic fascinates viewers who are trying to find the solve graphic paintings by the artist.

The world of avant-garde

Presenting art in a new way, using his capabilities as they did not do before them, the painters of the avant-garde direction (FR. avant-Garde. - Going ahead) tried to decompose the objective world into the components of its elements. They represented a feeling through shaped and color associations. From this it turned out that geometric shapes in paintings paintings were often expressed as a form and content.

An example may be creativity Vasily Vasilyevich Kandinsky. The Russian painter, representative of the forefront of the first half of the 20th century, makes the abstraction of his paintings by itself. Theoretically, the ideas of Kandinsky are substantiated by the creation next to the "real world" of the world of abstractions, externally, there is nothing in common with reality. This is a new system subject to its own laws.

In painting, his important role is played by the feeling, the artist's paintings are very musical, although they do not have sounds. The basis of his paintings is an emotional splash, the figures are subject to this movement, they follow the emotion. Kandinsky wrote that the circle, which so often becomes centrally his painting of the 20s. May be called "romantic". This romance is deep and contradictory as a fire burning in ice.

The geometry of the creator of the Black Square

Suprematism ("Excellence") - the avant-garde direction, the invention of which belongs Kazimir Malevich. His education refer to the creation time " Black square"(1915). The artist represented that in his work he came to the basis of art and stepped over him, stepped into the plane, where there is no form, there is nothing. The geometric shape in the author's paintings of this period is given by itself, without any contexts and specific values.

« White on white"1918, where a white square figure is depicted on white canvas - care to even greater freeness. Malevich sought in these paintings to reduce all previous art. Decade after the style of K. Malevich suffers changes. The artist passes towards the direction later called "Russian non-oofimatism". Here, colors and figures express certain thoughts, describe specific events.

« Athletes"1932 - the picture is completely symmetrical. In the foreground, the impersonal figures of athletes built preferably from the vertical lines, which in the background are replaced with horizontal contrasting with them. Colors crossed together on both plans.