Doman cards for free, pictures of geometric shapes, cards of geometric shapes, study geometric shapes. How compositions are made from geometric shapes An example of a composition inscribed in a balanced triangle

DRAWING AS REPRESENTED: COMPOSITION FROM GEOMETRIC BODIES. STEP-BY-STEP GUIDE. REVIEW

Volumetric composition of geometric bodies. How to draw?

A composition of geometric bodies is a group of bodies of a geometric nature, the proportions of which are regulated according to the table of modules cut into each other and thereby forming a single array. Often such a group is also called architectural drawing and architectural composition. Although the formation of the composition, like any other production, begins with a sketch idea - where you can determine the overall array and silhouette, front and background plans, the work must be "built" sequentially. In other words, to have as its beginning a compositional core, and only then, by means of the calculated sections, to “acquire” new volumes. In addition, this allows you to avoid accidental flaws - "unknown" sizes, too small indents, ridiculous cuts. Yes, we must immediately make a reservation that such topics raised by almost every drawing textbook as “Organization of the workplace”, “Varieties of paints, pencils and erasers”, and so on, will not be considered here.

Composition from geometric shapes, drawing

Before proceeding to the examination exercise - “Composition of three-dimensional geometric shapes”, you must obviously learn how to depict the geometric bodies themselves. And only after that you can go directly to the spatial composition of geometric bodies.

How to draw a cube correctly?

On the example of geometric bodies, it is easiest to master the basics of drawing: perspective, the formation of a volumetric-spatial design of an object, the patterns of chiaroscuro. The study of the construction of geometric bodies does not make it possible to be distracted by small parts, which means it allows you to better learn the basics of drawing. The image of three-dimensional geometric primitives contributes to a competent image and more complex geometric shapes. Depicting the observed object competently means showing the hidden structure of the object. But in order to achieve this, the existing tools, even leading universities, are not enough. So, on the left side, a cube is shown, checked by the "standard" method, widely used in most art schools, schools and universities. However, if you check such a cube using the same descriptive geometry, presenting it in a plan, it turns out that this is not a cube at all, but is some geometric body, with a certain angle, probably the position of the horizon line, and its vanishing points only reminiscent.

Cuba. Left is wrong, right is right

It is not enough to put a cube and ask to depict it. Most often, such a task leads to proportional and perspective errors, among which the most famous are: reverse perspective, partial replacement of the angular perspective by the frontal one, that is, the replacement of a perspective image by an axonometric one. There is no doubt that these errors are caused by a misunderstanding of the laws of perspective. Knowing the perspective helps not only to warn against blunders at the very first stages of building a form, but also stimulates you to analyze your work.

Perspective. Cubes in space

Geometric bodies

Here, combined orthogonal projections of geometric bodies are shown, namely: a cube, a ball, a tetrahedral prism, a cylinder, a hexagonal prism, a cone and a pyramid. In the upper left part of the figure, lateral projections of geometric bodies are shown, in the lower - a top view or plan. Such an image is also called a modular scheme, since it regulates the sizes of bodies in the depicted composition. So, it can be seen from the figure that at the base all geometric bodies have one module (the side of the square), and in height the cylinder, pyramid, cone, tetrahedral and hexagonal prisms are equal to 1.5 cube sizes.

Geometric bodies

Still life of geometric shapes - we go to the composition in stages

However, before moving on to the composition, a couple of still lifes consisting of geometric bodies should be completed. The exercise “Still life drawing from geometric bodies in orthogonal projections” will be even more useful. The exercise is quite difficult, which should be taken with due seriousness. Let's say more: without understanding linear perspective it will be even more difficult to master a still life according to orthogonal projections.

Still life of geometric bodies

Geometric body frames

Inserts of geometric bodies - this is such a mutual arrangement of geometric bodies, when one body partially enters another - it crashes. The study of frame variations will be useful for every draftsman, because it provokes the analysis of one form or another, architectural or living in equal measure. Any depicted object is always more useful and efficient to consider from the standpoint of geometric analysis. The tie-ins can be conditionally divided into simple and complex, but it should be noted that the so-called "simple tie-ins" require great responsibility in the approach to the exercise. That is, in order to make the cut-in exactly simple, you should decide in advance where you would like to place the cut-in body. by the most simple option there is such an arrangement when the body is displaced from the previous one in all three coordinates by half the size of the module (that is, half the side of the square). General principle search for all cuts is the construction of the cut body from its inner part, that is, the cut of the body, as well as its formation itself, begins with a section.

Section planes

Composition of geometric shapes, step-by-step exercise

It is widely believed that the arrangement of bodies in space through the “chaotic” imposition of their silhouettes on each other makes it easier and faster to form a composition. Perhaps this is what prompts many teachers to demand the presence of a plan and a facade in the conditions of assignments. So, at least, the exercise is already presented in the main architectural domestic universities.

Volumetric-spatial composition of geometric bodies considered in stages

Chiaroscuro

Chiaroscuro is the distribution of illumination observed on an object. In the figure, it manifests itself through tone. Tone is a visual means that allows you to convey natural relationships of light and shadows. It is relationships, since even such graphic materials, How charcoal pencil And White paper, are usually not able to accurately convey the depth of natural shadows and the brightness of natural light.

Basic concepts

Conclusion

It should be said that geometric precision is not inherent in the drawing; So, in specialized universities and schools, using a ruler in the classroom is strictly prohibited. Trying to correct the drawing with a ruler leads to even more errors. That's why it's hard to underestimate practical experience- since only experience can train the eye, consolidate skills and enhance artistic flair. At the same time, only with the help of sequential execution of the image of geometric bodies, their mutual inserts, acquaintance with perspective analysis, aerial perspective- it is possible to develop the necessary skills. In other words, the ability to depict simple geometric bodies, the ability to represent them in space, the ability to connect them with each other and, no less important, with orthogonal projections, opens up broad prospects for mastering more complex geometric shapes, whether they are household items or human figure and head architectural structures and details or cityscapes.

Types of composition Vertical composition gives work of art rush, upward movement or creates a feeling of constriction L.F. Zhegin Crowd e

Types of composition V. Surikov. Boyarynya Morozova Diagonal compositions convey the dynamics of the action, movement towards the viewer or away from him and cover large spaces

Concert "Spring" from the cycle "The Seasons" by Antonio Vivaldi part. "Spring is coming!" Spring is coming! And nature is full of joyful song. The sun and heat, streams murmur. And Zephyr spreads holiday news like magic. Suddenly I run into velvet clouds, Heavenly thunder sounds like a blessing. But the mighty whirlwind quickly dries up, And the chirping again floats in the blue space. 2 part. "Dream of a peasant" Flowers breathing, rustle of grasses, The nature of dreams is full. The shepherd is sleeping tired for the day, And the dog yapping almost audibly. 3 part. The "Pastoral Dance" of the Shepherd's bagpipe The sound is carried, buzzing over the meadows, And the nymphs dancing the magic circle of Spring are colored with marvelous rays. A.G. Venetsianov. Sleeping shepherd. 1780

Form - In the visual arts, form is the outline, appearance, contour of an object. The simplest forms approach the square, triangle, circle, "amoeba". the sum of techniques, expressive and visual means to create an image in any kind of art A. Giacometti. Spider A. Giacometti. Cat

The square is a finished, stable form that expresses affirmative images; it does not have movement or flight. The triangle is an active form that develops on the plane and in space, carries the possibility of movement, expresses the struggle of opposites, and can be aggressive. The circle is the most vivid expression of the idea of ​​nature (Earth, Sun, universe), therefore it is associated with the concepts of "good", "happiness", "life". The fluid form of the amoeba gives the images an unstable character, is associated with romance, melancholy, pessimism.

Line To enhance the artistic image of the form can be stylized or transformed. They emphasize or change character traits subject, and unnecessary details are discarded. Especially often these techniques are used in poster and book graphics and in animation, as well as in modern sculpture. has its own form, which expresses the image. It can be swift or viscous, smooth or angular, purposeful or chaotic, and thus forms various images.

This is the organization of the musical whole, the ways of development musical material, as well as genre designations that the authors give to their works, for example: song, romance, ballad, prelude, etc. Composition forms in music are based on the principles of repetition and contrast known to you. Distinguish two-part and three-part musical forms, variations, rondo, sonata form, etc. The scale of the idea of ​​a musical work determines its form-composition. Song genres are characterized by simple forms (couplet, couplet-variation); works of dance genres are often written in three-part form. And the dramaturgy of such genres as symphony, concerto, opera, ballet, requires more detailed forms, built on the juxtaposition and opposition of contrasting images.

Pick up two musical works With various form. Compare how the main musical idea develops and affirms in them. What modes of development prevail in each of these works. Pick up examples of works of painting, graphics or sculpture that have a certain character of form.

municipal autonomous educational institution

Perevozsky municipal district

Nizhny Novgorod region

« high school No. 2 of the city of Perevoza "

ResearchJob

Bymathematics

"Geometry in Painting"

Performed:

student 7 "A" class

Shimina Daria

Supervisor:

mathematic teacher

Klementieva M. N.

Transportation 2016

Content

Introduction. ...………………………………………………………………3

Main part. . . .……………………………………......................4-.13

1. The concept of geometric technique in painting.…………………… 4

2. Geometric painting. Drawing geometric bodies……….. 5

3.Geometric abstraction…………………………………………….....6

4. Cubism…………………………………………………………………. 7

5. Geometric painting by Richard Sarson …...................................8

6. Geometric painting by Simon Birch………………………………9

7. Paintings from straight lines Tadaomi Shibuya…………………………10

8.How to make a picture in the technique of geometric painting………..11-12

9.My paintings in the technique of geometric painting………………..13

Conclusion ….…………………………………………………………………………14

INTRODUCTION

Creativity and mathematics are to the same extent the creation of beauty, as the work of a painter or a poet - the totality of ideas, like the totality of colors and words, must have inner harmony.

Godfrey Hardy, English mathematician and philosopher.

I have a lot of interests. One of them is drawing. I love to draw nature, still lifes, people. And this works well for me! Recently, I was browsing the Internet for material for a lesson. visual arts and came across paintings of geometric shapes. I was very interested in this technique, and I decided to learn about it as much as possible. With the help of geometric shapes, you can draw portrait sketches, landscapes, ornaments, etc. At school, from all subjects I prefer geometry (we started studying it only this academic year).

In my research work, I tried to reflect the technique of geometric painting and show how closely geometry is related to art.

So,target my research work: learn the technique of geometric paintingand apply the learned material in practice.

Tasks:

Learn the technique of geometric painting;

draw a picture in the technique of geometric painting with your own hands.

Subject of study: mathematics.

Object of study: geometric drawing technique.

Main part. World of Figures

1. What is the geometric technique of painting.

Geometric painting technique is one of the earliest stages in the development of art Ancient Greece(IX-VIII centuries BC). This is manifested in the painting of utensils. The geometric style is characterized by a variety and clarity of patterns, their severity emphasizes the construction of a constructive object. The ornament is located in stripes and is obtained from broken lines, crosses, circles. In more late period development of ancient Greece, the image of the image of a man from geometric shapes appears.

2.Geometric painting. Drawing geometric bodies

In drawing geometric shapes, the main thing is to be able to imagine an object as voluminous and from different angles. It is better to start drawing simple geometric shapes or household items.

Such exercises help to acquire the necessary skills in the drawing and drawings of architectural structures.

The diagram below shows all the stages from the composition (the correct arrangement of objects in space) to the construction and shading of objects.

Stages of work:

Mark the location of objects on a piece of paper extreme points(composition).

Find the center of the figure, from where the construction begins;

Marking with dots;

Outline the lines of the future part, and then finish drawing;

Drawing shadows (light, shadow, penumbra, drop shadow, glare, reflex);

Create a whole picture.

The latter can be done with clear lines.

The first sketches on the sheet should be pale, and then more clear lines should be made. The eraser should be used extremely rarely - when the mark is made too clearly, but erroneously and will interfere with the further construction of the drawing. It is worth erasing erroneous marks only when the correct ones are found.

If you want to learn how to draw beautifully, then you should try to draw from memory or from nature. Before you draw a picture, you need to study and examine the subject from all sides and do it with different provisions sketch drawings that will help to better reflect the shape being drawn.

3.Geometric abstraction.

Geometric abstraction - form abstract art using geometric shapes combined into an abstract composition. Such a picture is created by combining a wide variety of geometric bodies, colored planes, broken and straight lines.

This art is popular throughoutXXcentury. By using this art you can share your thoughts, emotional state. It is not always possible to draw such a picture, since it is quite difficult to do this. As practice shows, according to psychologists, drawing such pictures can help solve some human problems.

4. Cubism.

Cubism - avant-garde direction in painting appeared at the beginningXXcentury. In this direction, many geometric shapes are used.

In 1912, a new direction was born in cubism. Art critics began to call it "synthetic cubism".

In the visual arts, three branches of this trend can be distinguished, which reflect different aesthetic concepts. Each of which can exist as a separate independent movement: Cezanne Cubism (1907-1909), Analytical Cubism (1909-1912) and Synthetic Cubism.

Artists and geometry

5.Geometric painting by Richard Sarson

"I want to play with forms always"
Adore..."

Richard Sarson is a graphic artist. He graduated from King's College London, received a bachelor's degree, and later a master's degree. The work of Richard Sarson fascinates with its unusualness. Everyone can see anything in them! It doesn't take much to create such a picture. Compasses, paper and ballpoint pens will help make your fantasies come true.

The drawing of his technique consists of many circles intersecting with each other. As the author says, he has such pictures, it turns out, at the call of his heart. All the artist's works have clear lines, and the creator of the works himself considers the main thing how his work will look as a whole, and not what it is created from. The artist's favorite figure is a circle. “It's incredible to draw a line and go back to where you started,” says Richard.
According to the artist, people think that drawing with ballpoint pens will be too rough. Therefore, in addition to drawings with a ballpoint pen, Richard tries three-dimensional drawings, creating them from threads stretched over pins. The amazingness of such works is that everyone can wind the ball back and correct the failed part of the work, and when creating a drawing from clear lines, one awkward movement can ruin the whole picture.

Forms are what I live by, Richard Sarson admits. He knows so much about them that he smells and tastes, the sharpness and smoothness of the lines with which he can convey what we cannot convey in words.

6. Geometric painting by Simon Birch

Everyone copes with a serious illness as best they can.

British artist Simon Birch was given a terrible diagnosis in 2007. After that, he began to create unusual paintings using geometric shapes.

Simon Birch was born in 1969 in the UK. At the end educational institution received a master's degree in fine arts from the Royal Melbourne Institute of Technology.

Simon paints on canvas armed with a brush and putty. His paintings are made with strange strokes, as if he is trying to brush off all his thoughts. Unusual artistic technique helped him maintain realism in his strange pictures. In the works, with the help of form and color, the image and emotions of a person are displayed.

The collection of colorful geometric paintings is called "Laughing With a Mouth Full of Blood". The name is not very pleasant, but the life of an artist is also not easy. Probably, his paintings serve as therapy and do not allow to lose heart.

7. Paintings from straight lines Tadaomi Shibuya

Straightforwardness is a character trait of honest and open people, as well as paintings created by a resident of Japan Tadaomi Shibuya.

It is very difficult to find a perfectly straight line in the world. Paintings by Tadaomi Shibuya, according to the artist, help to create harmony and balance.

They say that a picture made using geometric shapes can be used to judge the character of a person. But this does not mean that Tadaomi Shibuya is strict and boring.

Someone notes in the work of Tadaomi Shibuya not original forms and creative ideas, but the primitiveness and angularity of the execution of the born idea.

8.How to make a picture in the technique of geometric painting.

After reading the theory and getting to know this technique better, I suddenly wanted to create such a miracle myself. But it turned out to be not so easy! To begin with, I decided to make a picture according to the model. In order for everything to work out, it was necessary to calculate everything to the smallest detail. I could just take and copy, but you need to make sure that everything is removed. I had to calculate how many and what kind of geometric shapes I would need to create a picture according to all the rules and proportions.

To create such wonderful picture I needed a regular sheet of paper (I have A4), geometric shapes (and there are a lot of them in the world ... Everything around us is geometry), colored pencils (you can make such a picture from any material) and a little imagination (and I have a lot of it! ).

9.My paintings in the technique of geometric painting.

Conclusion

It seems to me that in the course of my research work I have collected and studied quite interesting stuff:

There is a style in painting that is closely related to geometry.

This style has been used since ancient times and was invented in ancient Greece.

I have come to know many artists who use this technique.

I created my paintings in the technique of geometric painting.

I did what I find very useful, which is: Created my painting in this wonderful technique. And most importantly, I fell in love with the subject of geometry even more! The material collected by me can be used on various activities by geometry. I think that my classmates will be interested to learn about this fascinating and informative technique, which serves to develop geometric thinking, and also allows you to display inner world and character of a person. For some, it may even become a hobby!