Mordovian ornament “Rosette” on a ceramic plate using the dot painting technique. Introduction to Mordovian folk ornament

Target: create conditions for joint activities of teachers.

Tasks:

• Give an idea of ​​the products of Mordovian decorative and applied art.
• Master the skills of painting a wooden board using Mordovian ornamental motifs.

Equipment:

• Tables and chairs according to the number of participants; elements of Mordovian patterns, stencils with Mordovian ornaments, gouache in white, red, black and yellow colors, brushes No. 1, blank boards for painting, pokes, napkins.

Progress of the master class:

In our preschool educational institution, much attention is paid to introducing children to the culture of the peoples of the Volga region.

Today I want to show you a master class on painting a wooden board based on the Mordovian ornament.

Mordovian decorative and applied art is one of the most important sources of formation of the spiritual sphere of adults and children.

I’ll tell you a little about the culture of the Mordovian people: “The Mordovian people are divided into two groups: Moksha and Erzya. Their language is different National costumes, customs, but they have one thing in common - they all love their Mordovian land and honor the customs of their ancestors. The ancestors of the Mordovians were famous for their hard work. Men were engaged in hunting, fishing, and farming. And women were skilled needlewomen and good housewives.

I suggest you become masters for a while and paint the boards with Mordovian ornaments.

I. introduction and updating the knowledge of master class participants.

— Dear guests, apprentice craftsmen, welcome to our workshop.

Ornament- a pattern built on rhythmic alternation and organized arrangement of elements.

A feature of the Mordovian embroidery ornament is uniformity of pattern composition(ornamental stripes built by transferring a symmetrical figure along a straight line) or rosettes built on the basis of geometric figures.

Ornament – ​​geometric. The main background features squares, stars, circles, dots and various geometric shapes.

The main element of the Mordovian ornament is a rhombus, a rhombus with diagonals, a rhombus with extended sides.

Symmetry- the basic principle of constructing an ornament.

The Mordovian ornament is characterized by such types of symmetry, such as border, rosette and grid.

Border- a linear ornament obtained by parallel transfer of a figure.

Socket— when constructing rosettes, only the plane of symmetry or only the axis of symmetry, or the axis and plane of symmetry can be used.

Most rosettes are built on the basis of a diamond with extended and curved sides, a diamond with three or more branches on each side of the lattice diamond.

Net— in Mordovian embroidery, the most common type of mesh is rhombic.

- Let's pay attention to color scheme.

— What colors can you identify in the Mordovian ornament? (white, red, black, green)

The Mordovian pattern contains all the colors of the rainbow, but most often red.

- Which elements you see? (“rhombus”, “cross”, “triangles”, “check marks”, “herringbone”, square with extended sides and corners, C-shaped element, triangle, circles, semi-eight-pointed star).

II. Application of acquired knowledge when performing creative work.

The teacher invites you to the table.

“I suggest you become masters for a while and paint the boards with Mordovian ornaments.”

- Sit comfortably and let's get started.

Progress:

1. In front of you are stencils of Mordovian ornament. Choose your favorite one. Place it in the center of the board and paint it with red paint using pokes.

2. Now let’s work out our ornament in detail. Using the end of the brush, trace the contours of the pattern. For this we need black and white.

4. Take brush No. 1. We outline the contours with black paint and paint geometric patterns.

5. For additional colors, enter yellow.

6. Decorate the top of the board in the same way.

7. Finish by tracing the contours using black paint.

8. We complement the ornament with patterns using two elements: a cross and a checkmark, we will draw them with the end of the brush. The cross is red and the checkmarks are black.

III. Summarizing.

- What wonderful boards you made. You are real masters!

“It’s not for nothing that they say: “Like the master, so is the work.”

When summing up the results, a blitz survey is conducted. Participants note a creative attitude, make suggestions for correcting errors, note successful results, and evaluate the level of implementation of practical work.

The famous Mordovian artist Andrei Aleshkin deciphered the meaning of embroidery on the national Mordovian costume. Knowing the language of symbols, a traditional folklore outfit can be read like a book, learning the life story of its owner. Individual signs can be called forgotten Mordovian “runes”.

Honored Artist of Russia and Mordovia Andrei Aleshkin revealed the secret of the half-forgotten symbolism of the Mordovian national ornament. Andrei Stepanovich’s attitude to this issue was special: he was born in Chelyabinsk, studied in Leningrad, but never forgot about his roots - his ancestors, who were Mordvins-Teryushans.

Having moved to Saransk and studying the Mordovian national culture, the artist made a discovery that, one might say, turned his life upside down: Mordovian embroidery and signs carved on wood, very similar to runes, can be read like letters of a forgotten alphabet. It’s just that these signs seemed to be hidden in national ornaments on clothes and ancient household items of the Mordovians.

Rezas, or runes, can still be found in old Mordovian cemeteries. These are generic signs, marks denoting property. Each genus has its own sign. The ancient Mordovians placed the same cuts, that is, signs on trees, in the forest, marking their sides, their trees for cutting. The same signs were used to mark wheels, chests, and other household utensils.

Andrei Stepanovich began collecting images of family signs, not yet really understanding what he was collecting. And then I remembered how one day I was walking with my grandmother, and she showed him the Mordovian family signs right in the sky - according to the outlines of the constellations. Each genus had its own constellation. Andrei Stepanovich understood: these heavenly “signs” were taken by his distant ancestors as the basis for the Mordovian runes.

However, as the artist admits, he could not find the key to the ornament until he became president of the International Foundation of Finno-Ugric Peoples. He had the opportunity to communicate with a variety of specialists in national culture. Andrei Aleshkin began to study Mordovian culture through the customs, rituals, and dances of related Finno-Ugric peoples.

Video

Video: Masusik1000 on YouTube

Mordovian dances.

That’s how I found out that the colored stripes on belts, for example, Mansi, are not just a pattern, but an encrypted story about the life of their owners. The white stripe is a birth, the red stripe is a holiday, the black stripe is someone’s death.

On a men's Mordovian wedding suit in the Erzya Museum you can see the simplest belt with three stripes: white in the center and red along the edges. Apparently, an ordinary village young man came to the master and ordered a belt, and he asked him to describe his life. She was not eventful, but happy: birth (white stripe in the center), then a wedding and a prosperous family life(red stripes).

But this is the simplest symbolism. In embroidery it is much more complicated. Elements of ornament that modern man perceived as circles, wavy lines or crosses, had a completely different meaning for the ancient Mordovians. Each sign was meaningful and carried information.

A popular solar sign in Mordovia in the form of an eight-pointed rosette is a symbol of the sun. It can be seen on the modern flag of the republic. The oldest sign of fertility is the agricultural symbol of a plowed field: a rhombus divided into four parts. Moreover, in the ornament on the girls’ clothes, the cells of the diamond remained empty. U married women Dots were placed in the center of the cells on the diamond: the field was “sown.” But a rhombus with extended sides, not divided inside, is a symbol of a fortified settlement: a fortified settlement. The tops of the diamond were often decorated with a “hook” resembling horse heads: this was supposed to indicate that the clan could field a large number of armed horsemen and was worth reckoning with. On the coat of arms of Mordovia you can see 7 such diamond signs: these are symbols of seven cities on the territory of the republic.

Each pattern in the ornament has a meaning. For example, according to the Mordovian bride’s costume, according to the embroidery on it knowledgeable person I could immediately determine what kind of family the girl was from, what village she was from, and whether her family was rich. Her outfit was decorated with embroidered signs - amulets against the evil eye and damage, the wishes of many children.

Andrey Aleshkin decorates his paintings with Mordovian rune signs. He is happy to share his joy and pride in his ancestors. As the artist says, only by feeling a kinship with them, by studying how and with what they lived, can one consider oneself a true son of one’s people.

Video

Video: paintings by A.S. Alyoshkina on YouTube

— Of course, a national ornament is an encrypted chronicle of a people, a reflection of its history and worldview. And the ornament can be “read”, spells, parting words, wishes can be encrypted in it. The version about the “runic” component of the ornament has every right to exist.

The traditions of the Finno-Ugric world, its interaction with the cultures of neighboring peoples, were manifested in the ornaments of the Mordovian costume. The image of the world was embodied in the sign system inherent only to the Mordovian people, in “runes”-patterns depicting horses, ducks, flowering branches, and trees. Often, on various objects, the ornament consists only of wavy lines or rosettes, squares, rhombuses, the origin of which goes back to ancient family signs. The circle was used as a symbol of the sun, moon, wheel, the triangle symbolized the feminine principle, the square - order, truth, justice, masculine principle.

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A.S. Aleshkin was born on February 10, 1959 in Chelyabinsk. Graduated from the Leningrad Art School named after V.A. Serov, Leningrad Institute of Painting, Sculpture and Architecture named after I.E. Repin, awarded a bronze medal of the Russian Academy of Arts. He holds the position of professor at the Department of Interior Art, Faculty of Architecture and Construction, Moscow State University named after N.P. Ogareva. Exhibitor of exhibitions at regional, Russian and international levels. The works are stored in the Mordovian Republican Museum fine arts named after S.D. Erzya, in private collections in Russia, Germany, Finland.

Mordovian embroiderers. Beginning of the 20th century Simbirsk province. Alatyr district

Folk embroidery is one of oldest species applied arts. But even today this type of creativity has not lost its relevance. We admire the skill and ability of needlewomen of the past to decorate rough linen fabric with stitches of bright threads, and we are delighted with the intricacy of embroidery patterns of national clothes. Each nation has its own unique design for embroidered clothing, its color, and technical features, reflecting tastes and ideals that have been formed over centuries. This is the wealth folk culture. This is a great opportunity to learn a lot of valuable things about each nation, just “pull the right thread.”

More than one generation of our contemporaries tried to master the skills of embroiderers from the Mordovian hinterland. But many secrets of unique art are hidden behind the threshold of time. How to unravel the mystery of the beauty and perfection of a homespun piece decorated with an intricate embroidered pattern?
In our manual, we decided to tell you how, stitch by stitch, you can learn the techniques of Moksha and Erzya embroidery, master counting when creating a geometric pattern, and solve the puzzle of the most economical or simple way to make patterns with complex filling. The pattern of any embroidery ornament is very complex, but the pattern was made up of a set of simple figures. How to find the original form of an ornamental motif?
Folk craftswomen knew where the beginning and end of the most intricate pattern were, and at the same time they chose the simplest ways to fill it out. A practical guide will help the master who turned to Mordovian embroidery patterns to learn the secrets of embroidery counting, the secrets of obtaining color and light and shade effects, on which the richness of the embroidered decor of the Mordovian folk costume is built.

History of Mordovian folk embroidery
The Mordovian people mastered the art of decorating their own clothes with embroidery in ancient times. Unfortunately, few fabrics have been preserved among the archaeological finds, therefore, it is not easy to form an idea of ​​the embroidery of the ancient period. The earth has preserved small fragments of fabrics from thousands of years ago - they are rough and loose, woven from wool yarn or threads from plant fibers. The old masters knew various weaving techniques, producing fabric with plain or twill weave threads, which diversified the structure and quality of homespun canvases. The color of clothes made from home fabrics corresponded to the color of natural materials: white and black sheep wool, grayish tones of plant fibers such as hemp and flax. For embroidery, threads dyed with vegetable dyes were used: a decoction of roots and herbs, buds, leaves, and tree bark. There is the simplest embroidery with red and black wool. With special diligence, ancient craftswomen decorated the edges of clothes; here, in addition to embroidery, woven or leather cords, braid, tin beads and small paste beads, and bronze plates were sewn on. It is likely that, based on the possibilities, at the same time women could use decoration with expensive materials, such as bronze jewelry, beads and beads, as well as create their imitation, which was done with embroidery.
As archaeological sites show, counted embroidery originated about a thousand years ago. The canvas for its execution was a home-woven canvas of plain weave. The embroiderer laid the main stitches along the lines of the fabric threads, obtaining straight (horizontal and vertical) seams.
The introduction of sewn elements into the costume, for example, sewing with tin beads, marked the beginning of working with fastened seams and oblique (diagonal) stitches. The imitation or reproduction of oblique stitches is preserved by the reliefs on the piercings of forehead crowns and breast decorations.

At the same time, embroidery acquires the function of indicating the purpose of clothing. In combination with jewelry, embroidery assumed a special magical role in clothing for performing rituals (initiation of adulthood, marriage, transition to the age of maturity and senility, performance of funeral rites). Of particular importance was a complex of signs that could show which clan or tribe a person belonged to.
The eternal ritual system of folk life has formed the order in embroidery on clothes. Embroidery was the criterion by which the entire rural community assessed the adherence and obedience to the laws of their ancestors, the skillful skill and hard work of the craftswoman.
In the XVIII-XX centuries. Embroidery was practiced in all Mordovian villages. From century to century its patterns became more complex, often borrowing from neighboring peoples.
For different items of clothing, canvases of different densities and weaves of threads were prepared. For onuch-foot wraps, which were worn with bast shoes, the twill weaving technique was used, with a bias cut. Such fabrics were thicker and wore out less. The most common method was plain weave. It was on linen that embroidery was done. Weekend clothes were made from the highest quality canvas: well-bleached, thin and dense.
Basics of Mordovian counted embroidery
The girl had to be able to embroider. The one who did not learn this was forced to order embroidered clothes from rural craftswomen. The family hid this fact so as not to disgrace their daughter. With special responsibility, the girls showed their skills as skilled embroiderers to others when they were preparing a wedding bedspread for one of their bridesmaids.
Purchased materials were expensive, so they were used only for decorating holiday and wedding shirts and hats.

It is not difficult to distinguish Erzya clothing from Moksha clothing by embroidery. Upon careful examination of the costumes of representatives of different regions, one can discover a noticeable difference both in the methods of decorating clothes with embroidery and in the manner of wearing them. It is no coincidence that researchers highlight the boundaries of the existence of similar types of costume, identifying groups that are related in culture. Each group of Mordovian costume had its own embroidery character traits, it is by this that one can determine the place of origin of clothing.
Moksha embroidery southern regions Mordovia - Ruzaevsky, Insarsky, Kadoshkinsky - differs from the embroidery of the costume of the Moksha people living in the protected northern regions - Temnikovsky and Elnikovsky. The embroidery of the clothes of the peasants, who since ancient times settled in the lands now located in the southwest of the republic within the modern Torbeevsky and Zubovo-Polyansky districts, stands out with special features. The embroidery of the Erzya costume is not inferior in its diversity, especially since, unlike the Mokshans, the places of residence of the Erzya are located at a considerable distance from each other. Erzya districts are part of Mordovia, Chuvashia, Tataria, Nizhny Novgorod, Penza, Saratov, Ulyanovsk, Samara, and Orenburg regions. Embroidery keeps many secrets related to the history of people's lives.

Secrets of folk craftsmanship
To learn the secrets of folk craftsmanship, you need to carefully examine at least one detail of authentic folk clothing. Before the shirt was sewn, the craftswoman decorated its details with embroidery. In the sections of the cut panels, the front and back halves were determined; they were distinguished by the nature of the embroidery. All patterns in the finished shirt had to match the design.
Typically, dense embroidered fragments of worn-out clothing were used for the pocket.
When working on embroidery or sewing clothes, a skilled needlewoman made straight lines, stitches that corresponded to the structure of the fabric and its density.
Let's look at fragments of finishing on Erzya and Moksha shirts. The embroiderers here each showed in their own way an excellent ability to draw ornamental patterns and combine various seams in their work.
Thanks to the introduction of seams of different techniques into the finishing of clothing, embroiderers achieved an amazing effect: the seams began to play like the cutting of gems, then became like the sparkle of silk, then acquired a soft velvety quality. On the surface of the embroidery, our eye distinguishes, in addition to color, a relief pattern made up of stitches, standing out against the background of the linen surface of the canvas.
A pattern of black or dark blue threads lay like the finest lace on Moksha clothing, and spread like red carpets on the white canvas of an elegant Erzya shirt.
Along with monochromatic painting and typography, there were multi-color embroideries made using counted satin stitch. There were many versions of this embroidery. In the Erzya costume, narrow stripes were filled with counted satin stitch, reminiscent of braid woven on planks. A simple pattern of zigzags or small diamonds was built on the contrast of a red background and a dark green or black pattern. The introduction of gold thread into the decoration enhanced the coloristic effects.
The Moksha counting surface was very unique. In finishing Moksha shirts you can find many options for working with this technique. Geometric or highly geometric patterns floral ornament The colorful half-rosettes on the hems and shoulders of the shirts were filled with counted satin stitch.
The technique of colored pereviti found a unique application in Erzya clothing. Mordovian weave resembles a wide hem, which was made on fabric drawn in one direction (along the warp or along the weft).
Weaving over a sparse mesh gave the effect of openwork stitching with complex geometric patterns. This technique, like other embroidery techniques among the Mordovian people, had its own national characteristics.
The simplest technique, the oblique stitch, was used by Mordovian embroiderers to begin and complete the finishing of clothing with embroidery. Based on the oblique stitch, the technique of the Mordovian cross was developed, when the second row is laid along the oblique stitch with a counter slope, enhancing the relief of the line.

In order to comprehend national embroidery, it is necessary, first of all, to study the technical techniques of making Mordovian folk stitches. To obtain a pattern, the craftswoman had to count how many threads needed to be lifted onto the needle and how many to skip.
Seams that are made along the surface of the entire fabric are usually called blind. If the fabric was thinned out to create a mesh or strip of loose threads, the seams on such a basis were called through or stitched.
Since ancient times, experienced embroiderers have cared not only about how the embroidery looks from the front side, but also from the back side.
When sewing one-sidedly, the pattern is obtained only on the front side, on the wrong side - we see sparse stitches. Mordovian embroiderers, working in the technique of counted satin stitch, laying stitches tightly without gaps on the front side, counted on the reverse side.
We decorated and completed the work with auxiliary seams: connecting, edge, fastening, decorating, camouflage. For these purposes, Mordovian women more often used braid woven on fingers or on planks, and wove ribbons with a braided or embedded pattern. Borrowing the experience of needlework from the peoples who lived nearby, they imitated some weaving techniques with embroidery.
Seam painting in the form of longitudinal patterns was done on Moksha shirts using black or dark blue threads. The wool for embroidery was selected from fine-wooled young sheep with a bright black natural color. But especially popular were oriental dyes, such as indigo, which made it possible to dye threads blue-black or dark blue. The pattern embroidered with such threads was especially clear on the white surface of the canvas. Due to the high cost of overseas dyes, Moksha women have their own fashion for tracing embroidery with an ink pencil or impregnating it with blue.
The needle picks up and passes the required number of threads of fabric. In this case, one stitch falls on the front side, the other on the wrong side. Gradually the entire ornamental composition is revealed. Under the stitch in the set lies odd number threads: 5, 3, 1.
It is easier to keep track of the pattern if you first make a grid of equal stitches repeated after a certain number of rows.

An embroidery border made using the set technique can usually be found on the edges of clothes: the hem, sleeves, along the neckline. The ornamentation of shoulder embroideries was particularly complex, where a rhombus filled with a pattern was made in a set. On ritual clothing of the 18th century, such embroidery could completely cover the back.
Original color scheme distinguishes embroidery from Mokshans, who effectively combine red and black (dark blue) colors when working with these stitches.
Counted stitch is a blind one-sided seam. The drawing is not revealed immediately, but in separate motifs.
Counted stitch has a number of varieties:
A simple “brick” stitch is performed with an even count of fabric threads, single or paired small parallel horizontal or vertical stitches without gaps in the canvas. The next stitch moves halfway from the axis of the previous one, like brickwork. Small inclined stitches are formed from the reverse side.
The bias stitch is made with inclined stitches according to the pattern of the ornament. Small straight stitches are formed from the reverse side. When performing, the needle is led from the edge of the pattern to the right by 4-6 threads and upward by 2-4 threads of the fabric. On the wrong side, a horizontal stitch is made from right to left using 2-4 threads of fabric. The second knit stitch is made 2-4 threads of fabric above the first, etc. The second half of the ornament is made in mirror image.
From the reverse side, small frequent vertical or slightly inclined stitches are obtained. To fill large areas, rows of bias stitch are pressed closely together to create a smooth, grainy surface.

Mordovian cross

A cross stitch consisting of two oblique intersecting stitches. In Mordovian embroidery, cross stitch was used to obtain a high relief of the bias stitch. Rows of cross stitch were laid side by side, creating a ribbed surface.
The loose (remaining) threads of the fabric are combined into bundles with embroidery thread. To create a pattern, Erzyan women twisted two bundles at a time, moving the working thread in a figure of eight in three turns, then shifting the work by one bundle, grabbing a new column, and repeating the move in a figure of eight.
To obtain dense lines of a pattern that have the appearance of an unsparse, whole fabric, use the stlan technique, which is performed with threads in the color of the fabric. The stitches cover the gaps of the mesh.
An inexhaustible source of inspiration.
Preserving the richest traditions of Mordovian folk embroidery is one of the most difficult tasks of our time. Folk embroidery is an excellent example for creating modern works arts and crafts. Students of children's art schools master folk embroidery techniques. Professional craftsmen work in the interaction of folk traditions and modernity, preserving the richness and diversity of Moksha and Erzya costumes. At local industrial and consumer service enterprises, such as the Mordovian Patterns factory, the Stamo, Umarina, and Silhouette ateliers, artists are working on orders to recreate traditional Mordovian costume complexes for the stage. So that factory products with machine embroidery gain impact folk art, artists have to painstakingly study the origins of folk embroidery.

A fragment of the finishing of the hem of a Moksha shirt using seams, painted with ink outline. 30s XX century Penza region, Belinsky district

With. Bolshaya Elkhovka

Introduction……………………………………………………………………………………………………………5

Chapter 1. Symmetry is the fundamental principle of the structure of the world………………………...6

Chapter 2. Ornamental motifs of Mordovian embroidery

2.1. Ornament is an imprint of the soul of the people…………………………………………….11

2.2. Geometry in the ornament of Mordovian embroidery……………………………………..13

Chapter 3. Compositional features patterns on Mordovian shirts………………………...17

Conclusion……………………………………………………………………………….19

Terminological dictionary………………………………………………………………………………..20

References……………………………………………………………………………….21

1. Introduction

By studying mathematics, we discover more and more new components of beauty, getting closer to understanding, and subsequently to the creation of beauty and harmony.

Harmony (from the Greek harmonia) means “coherence, proportionality, unity of parts and the whole, determining the internal and external form of an object, event, phenomenon, and their perfection.” Externally, harmony can manifest itself in melody, rhythm, symmetry, proportionality. The last two characteristics relate primarily to mathematics. After all, mathematics is not only harmonious system laws, theorems and problems, but also a unique means of understanding beauty. And beauty is multifaceted and many-sided. It expresses the highest expediency of the structure of the world, confirms the universality of mathematical laws that operate equally effectively in crystals and living organisms, in the atom and in the Universe, in works of art and scientific discoveries. Truly:

The law of harmony reigns in everything,

And in the world everything is rhythm, chord and tone.

J. Dryden

Over the course of many centuries, the folk artistic skills of the Mordovian people have been honed. The history of the Mordovians is reflected in decorative - applied arts, the ancient traditions of which were vividly embodied in beadwork, artistic woodworking, patterned weaving, and appliqué. But the most striking and expressive was the embroidery. Her originality and high artistic merit attracted my attention.

The relevance of research is due to consideration of the composition of the ornamental motif of the composition in Mordovian patterns from the point of view of mathematics.

Goal of the work - explore geometric patterns in Mordovian embroidery patterns

Tasks:

1. Identify types of symmetry in the ornamental forms of Mordovian patterns

2. Characterize the compositional features of the patterns

3. Consider the location of the ornament on the Mordovian costumes

Object of study: embroidery on Mordovian costumes

Subject of study: geometry of embroidery patterns

Chapter 1. Symmetry is the fundamental principle of the structure of the world

Beauty and harmony are closely related to symmetry, this was noticed by ancient architects and artists. The word symmetry comes from a Greek word that means “same measure.”

Symmetry is one of the widespread and ubiquitous phenomena. Its universality serves effective tool knowledge of nature. Symmetry in nature is a consequence of the need to maintain stability. Behind the visible symmetry of external forms lies the invisible internal symmetry of the structure, the spatial arrangement of elements that guarantees balance. We can say that symmetry is a manifestation of matter’s desire for reliability and strength. Indeed, symmetrical forms are the most resistant to various types of influences, since they ensure the repeatability of successful forms.

However, nature would be weak and mediocre if it only duplicated itself all the time. Even to repeat her creations, she chooses different paths, which is especially clearly seen in different types of symmetry.

Symmetry is diverse. The immutability of certain objects can be observed in relation to various operations - rotations, reflections, translations.

We will call the symmetry of a figure any transformation that transforms the figure into itself, i.e., ensuring its self-alignment.

First, let's list the familiar types of symmetry. These include three types: symmetry about a point (central symmetry), symmetry about a line (axial symmetry) and symmetry about a plane.

Symmetry about a point (central symmetry):

Symmetry about a straight line (axial symmetry):

Symmetry relative to the plane (mirror symmetry) – is a mapping of space onto itself in which any point becomes symmetrical

point relative to the plane

Every person has at least an intuitive idea of ​​symmetry. Is there symmetry in everything in life?

Indeed, it is enough to look around to be convinced that this is so: fish and birds, animals and insects, monkey and man, flowers and leaves, mushrooms and algae - there is symmetry in everything in life ! What is symmetry?

Greek word συμμετριά mean joint measure, proportionality. The original concept of geometric symmetry as the proportionality of the parts of the whole, as the harmony of the proportions of the whole, acquired a universal meaning over time and was recognized as the universal idea of ​​​​invariance (i.e., immutability) with respect to transformations.

So, a geometric object is considered symmetrical if something can be done to it, after which it will remain unchanged. For example, a five-pointed star, being

rotated by 72=(360: 5), will take its original position

Symmetry, perceived by a person as a pattern of structure, as an external manifestation of internal order, has aesthetic value and is perceived as beauty.

The art of ornament uses such types of geometric symmetry as

border, rosettes, nets.

BORDER- This is a periodically repeating pattern.

Borders are a type of portable symmetry, when each previous figure coincides with the next one when moving forward along the border at a constant interval (symmetry step).

Any border can be combined with itself by parallel transfer. When drawing borders, in addition to parallel translation, symmetry relative to a straight line and central symmetry are used.

Total exists 7 types of borders

have only the symmetry of parallel translation relative to some axis

. ports are constructed not only using parallel transfer, but also rotational symmetry

Border elements

have mirror symmetry about the vertical axis

Border elements have mirror symmetry relative to the horizontal axis

Elements of borders have mirror symmetry relative to vertical and horizontal

Border elements, in addition to sliding reflection, have mirror symmetry

| Border elements have sliding reflection symmetry relative to the translation axis

Sockets

are obtained by rotating the figure around the vertical axis of symmetry by 360: n

(n = 2,3,4, ...) i.e. it has rotational symmetry of the nth order

Mesh ornaments

In the art of ornamentation, filling a plane with identical rectilinear figures is often used. In mathematics, such tiling is called - mesh ornaments. It is known that only two kinds of figures are different parallelograms(including rectangles, squares and diamonds) and hexagons with pairwise parallel sides fill the plane completely, without gaps or overlaps, using only translations, maintaining orientation. Depending on what types of symmetry are inherent in a particular element that is endlessly repeated in an ornament, such ornaments are divided into 17 groups.

The figure shows ornamental symmetry, which is based on one of five possible flat gratings, which are based on a regular triangle, square, rectangle, parallelogram and regular hexagon.

Chapter 2. Ornamental motifs of Mordovian embroidery

2.1. Ornament is an imprint of the soul of the people

“The good thing about ornament is that it preserves traces of its origin, like an enacted piece of nature, animal, plant, steppe, Scythian, Egyptian - whatever, national or barbarian - it is always speaking, seeing, active.”

O. Mandelstam

Ornament is called a pattern built by alternating in a certain order or, as they say, the rhythm of some patterns or lines. The word "ornament", from the Latin "ornamentum", means decoration

Ornament is one of the oldest types visual arts a person, which in the distant past carried symbolic and magical meaning, iconicity. in those days when people switched to a sedentary lifestyle and began to make tools and household items. The desire to decorate your home is common to people of any era. And yet, in ancient applied art, the magical element prevailed over the aesthetic, acting as a talisman against the elements and evil forces.

Apparently, the very first ornament adorned a vessel made of clay, when the invention of the potter's wheel was still far away. And such an ornament consisted of a series of simple dents made on the neck with a finger at approximately equal distances from each other; naturally, these dents could not make the vessel more convenient to use. However, they made it more interesting (pleasant to the eye) and, most importantly, “protected” it from the penetration of evil spirits through the neck.

Ancient man endowed his ideas about the structure of the world with certain signs. For example, a circle is the sun, a square is the earth, a triangle is mountains, a swastika is the movement of the sun, a spiral is development, movement, etc., but they, in all likelihood, did not yet have decorative qualities for objects (they were often covered with ornaments hidden from human eye parts of objects - bottoms, reverse sides.

But the early decorative and ornamental elements may not have had a semantic meaning, but were only abstract signs in which they expressed a sense of rhythm, form, order, and symmetry. Researchers of the ornament believe that it arose already in the Upper Paleolithic era (15-10 thousand years BC). Based on non-pictorial symbolism, the design was almost exclusively geometric, consisting of strict forms of circle, semicircle, oval, spiral, square, rhombus, triangle, cross and their various combinations. Zigzags, strokes, stripes, “Christmas tree” patterns, and braided (“rope”) patterns were used in decoration. Ornament as an independent piece of art does not exist, but sometimes it can become the basis for shaping a product.

Ornament is always associated with the shape, scale, material of the product, its practical purpose and artistic figurative meaning. Ornament is capable of expressing a wide variety of sensations: restraint and solemnity, lightness, grace and smoothness, internal tension or calm, free movement. His emotional expressiveness is endless. The ornament always reflects the character and cultural characteristics of the people who created it, as well as the era in which it arose in folk art, where the ornament found its greatest distribution, stable forms and principles of ornament construction gradually took shape, which largely determined the national artistic traditions different nations. Each era, each national culture has developed its own system of ornamentation - motifs, shapes, location on the surface to be decorated. Therefore, it is often possible to determine by the ornament to what time and to what country a particular work of art belongs.

1. It usually consists of repeating elements-motifs, which are the basis of the ornament. A certain combination of motifs creates an artistic image.

2. The pattern can be repeating (rapport) and closed (in a circle, in a square).

The ornament can be multi-colored (polychrome) or single-colored (monochrome).

Types of ornaments: geometric, plant, zoomorphic, anthropomorphic.

2.2. Geometry in the ornament of Mordovian embroidery

Decor mathematics, stitch geometry -

Simplicity and perfection are woven with a red thread,

Both in repose and in sulgamo

Symmetry pattern

Rhombus, square, rectangle

They decorate your panhar.

The moral and aesthetic ideals of the Mordovians were expressed in folk art. The artistic taste of the Mordovian people was formed taking into account the traditions of the Finno-Ugric peoples and the interaction of the cultures of neighboring peoples, primarily Russian. The multicolored ornaments helped us awaken this dormant memory. In each national ornament, the patterns were not random, but deeply symbolic.

Well-known researcher of the ethnography of the peoples of the Volga region at the end of the 19th and beginning of the 20th centuries

wrote about the Mordovian costume:

“Thanks to the original arrangement of the stripes, this shirt bears some resemblance to the outerwear - the “dolmatic” of the Byzantine kings, and the mass of wool spent on embroidery gives it significant heaviness and solemnity.”

Every person feels part of something: a family, society, and even the Universe. In addition, each of us feels that we belong to one or another ethnic group.

The centuries-old history of each nation shapes its life ideals. From generation to generation over the centuries, folk symbols and symbolic fixations of the surrounding world were formed based on the correspondence between the natural and the human.

In Mordovian patterns, the predominant ornamental motifs are geometric patterns, among which more than two dozen groups are distinguished by their nature and complexity. The main ones among them are zigzags, squares, rhombuses, triangles, horn-shaped patterns, crosses, eight-pointed stars, elongated hexagons, complex rosettes built on the basis of a rhombus or on the basis of regular octagons and hexagons.

In folk art, where ornament was most widespread, stable forms and principles of ornament construction gradually emerged, which largely determined the national artistic traditions of different peoples. Each era, each national culture has developed its own system of ornamentation - motifs, shapes, location on the surface to be decorated.

Therefore, it is often possible to determine by the ornament to what time and to what country a particular work of art belongs.

The initial option for obtaining patterns is net, built on the basis of a rhombus with extended and curved sides.

Another very common type of symmetry in Mordovian ornament is border. Borders from the simplest shapes (inclined straight segments, rhombuses, zigzags, etc.), placed between two horizontal or vertical parallel straight lines, were used for almost all parts of Mordovian clothing and headdresses.

Socket, as a type of symmetry, it has found wide application in the ornament of Mordovian embroidery. It is the compositional center of shoulder embroideries. Most sockets are built on a diamond base.

Mordovian ornament is admired both in Russia and abroad. Lately Erzya and Moksha embroidery is of interest to ethnographers. Mordovian ornament

This is a most complex plastic system, everything in it is harmonious, verified, precisely calculated

Chapter 3. Compositional features of patterns on Mordovian shirts

Since ancient times, Mordovia has been famous for its colorful national costumes.

The beauty of the clothes lies in the embroidery with which they were decorated.

Primary colors are red, green, yellow.

The patterns were decorated with black or blue edging.

Compositional arrangement of embroideries on Moksha and Erzya women's shirts

determined by the cut of clothing. In the patterns on clothes, we could discern generic signs - “cuts”, similar to ancient runes - signs of the runic writing of the ancient Scandinavians and Germans.

When decorating clothes, folk craftswomen for centuries selected the best ornamental patterns and carried the national wealth of embroidery traditions from generation to generation.

Features of the shirt (panar) of the Mordovians - Moksha

A characteristic feature of the cut of the shirt (panhard) is a rectangular panel. A piece of canvas, folded in half along the weft, makes up the front and back of the shirt. The sides are made from two shorter canvases sewn to the central panel below the sleeves. The sleeves, sewn to the central panel, are expanded with triangular wedges. Chest neckline - triangular shape

The geometric patterns are based on a rhombus. Ornamental borders border the edges of the hem, sleeves, and collar. The wood pattern often formed the basis of borders on the hems and cuffs of shirts. Once upon a time, its color and technical techniques were close to those of Erzya. But time has brought multicolor to traditional embroidery. Despite the fact that Moksha embroidery is small and does not cover significant areas of the canvas due to the special construction of the ornament, it is perceived as carpet. The ornament is characterized by a geometric character. The ornament consists of stripes, diamonds, squares, rosettes, triangles, etc.

Features of the Mordovian shirt - Erzi

The shirt is the main component of a woman's costume. Cut the shirt into a tunic shape. Her body consists of two rectangular panels in the center along the seam, two cuts. One is deep triangular for the head, the other is on the hem, necessary when walking. Straight sleeves. Square gussets are sewn under the sleeves.

Analyzing the embroidery from the point of view of geometry, we see that at the collar, in the area of ​​​​the collarbone, a rhombus was usually made - “selme”. A special ornament bordered the slit at the hem. Small triangles were embroidered at the junction of the canvas panels on the sides or at the base of the longitudinal stripes at the back. But in general, the embroidered ornament of the Erzya shirt is simple. Typically it includes point compositions, straight and broken lines. The patterns show rhombuses, rhombuses with inscribed squares.

The richness of geometric motifs in the ornamental forms of Mordovian patterns has aroused and will continue to arouse interest. New ornamental compositions, made in compliance with techniques characteristic of national embroidery, are widely used in the embroidery of modern products. Ornamental motifs that previously had symbolic meaning, turn into purely decorative forms.

Conclusion

This work examines the geometry of patterns that predominate in the ornament of Mordovian embroidery. As a result of the study, we see that:

1. The complexity of ornamental forms is subject to the laws of symmetry.

2. The predominant ornamental motifs are geometric patterns: squares, rhombuses, triangles, eight-pointed stars, elongated hexagons, complex rosettes built on the basis of a rhombus or on the basis of regular octagons and hexagons.

3.The Mordovian embroidery ornament is characterized by such types of symmetry as border, mesh, rosette.

4. The basis of the patterns on the Mordovian shirt - moksha - is a geometric pattern - a rhombus.

5. The pattern on the shirt - erzi includes dotted compositions, straight and broken lines. The patterns show rhombuses, rhombuses with inscribed squares.

The tasks posed in this work are completely solved.

Terminological dictionary

BORDER– periodically repeating pattern

SQUARE - a rectangle with all sides equal

ORNAMENT- a pattern built by alternating in a certain order

drawings or lines

RECTANGLE - parallelogram with all right angles

SOCKET- This is a round ornament found in embroidery and wood carvings.

RHOMB – parallelogram with all sides equal

MESH ORNAMENT - filling the plane with identical rectilinear lines

figures

Bibliography

1. Balashov: Historical and cultural essays. Saransk. Mordovian book publishing house, 1995.

3. Mordovian folk art

4.., Surina folk costume, 1990, Mordovian book publishing house

5. Luzgin of Mordovia. Saransk. Mord. book from - to 1993

Time: 2 hours

Equipment:

For the teacher - presentation, sketches of embroidery patterns, embroidery samples.

For students - workbook

Type: combined

Goals and objectives:

1. Cultivating emotional responsiveness to the beauty of folk art.

2. Familiarization with the composition of Mordovian embroidery: ornamental motifs, color scheme, arrangement of patterns in the suit. Acquaintance with the features of Erzya embroidery.

3. Development of a culture of relationships, interest and love for national roots.

Progress of the lesson:

1. Organizing time.Slide 1

Greetings. Checking students' readiness for the lesson.

I want to start our lesson with lines from the Mordovian poet Pyotr Gaini.

My native land is Mordovian land!

I compose my songs for you.

I love your wild fields

Sura and Moksha are pure streams,

I love the simplicity of your outfits,

Your rituals, your sonorous language,

Your tales make a bold dream,

Which I have been accustomed to listening to since childhood.

2. Communicate the topic, objectives and content of the lesson.

The topic of the lesson is: “Mordovian patterns.” Today you will get acquainted with the constituent elements of Mordovian patterns, their names and learn to decipher their meaning. Slide 2

3. Learning new material.

How it developed artistic creativity Mordovian people. Mordovian patterns were replenished and modified thanks to the communication of the Mordovian people with neighboring peoples. Over time, a symbolic system was formed, inherent only to the Mordovian ornament, Mordovian embroidery.

The Mordovian patterns that decorated clothes are closely related to the religion of the Mordovian people. Therefore, in the Mordovian embroidery ornament you can see flowering tree branches, bright sun giving its warmth to the earth and people, animals and birds, deep rivers, green forests, endless meadows covered with flowers, ripe juicy fruits that the Mordovian land so generously shares.

Ornament - a pattern built on rhythmic alternation and organized arrangement of elements.

There are the followingtypes of ornaments :

1. Geometric(consists of circles, dots, lines, diamonds, stars, lines, etc.)

2. Vegetable(made up of stylized leaves, flowers, fruits, branches, etc.)

3. Zoomorphic(depicts stylized figures or parts of figures of real and fantastic animals)

4. Anthropomorphic(male and female stylized figures or parts of a person’s face and body are used as motifs)

In Mordovian embroidery, the predominant motifs are geometric, but there are also two categories of motifs: images of birds and trees. The main Mordovian patterns are: rhombuses, squares, triangles, zigzags, horn-shaped patterns, crosses, eight-pointed stars, elongated hexagons, S-shaped figures. Now we will take a closer look at some of them.

Mordovian patterns.

1) Square or most often rhombus is the main element of the embroidery ornament. This is a universal symbol that has several meanings, and the most important of them is abundance and fertility. Slides 3-6

2) Zigzag. Can be considered a symbol of water. Since ancient times, people have revered water sources: springs, rivers, lakes, seas. Many peoples of the world have widespread myths that everything in the world came from water, which is the fundamental principle of all things. In Mordovian myths, water (Ineved, i.e. big, great water) is also the primary element of the universe, it corresponds to the beginning of the world. According to the Mordovians, the Great Water was also a kind of barrier separating the world of the living from other world, where the dead and supernatural creatures live. Slides7-9

3) Eight-pointed star. Symbolized the sun. In the myths and rituals of the Mordovian people, the remnants of the former religious perception of fire are clearly visible, that is, the attitude towards it as something supernatural, influencing human life in a special way. In ancient times, people considered the flame to be a product of the heavenly body, probably due to the fact that they first learned to use the “heavenly” fire that arose as a result of a lightning strike. In addition, there was much in common between the flames of a fire and the sun. They had a beneficial effect (they warmed, illuminated), but they could also burn, burn houses, crops, and lightning (a product of heavenly fire) could kill a person or animal. Slides 10-12

4) Horn-shaped patterns. Symbolized trees and grass. In spells and prayers of the Mordovians, the tree deities Chuvton-ava and Chuvton-paz were often mentioned; they meant the patrons of the living tree. Healers turned to them when healing the sick. Most likely, such ideas arose on the basis of the primary deification of the trees themselves, which among many peoples served as symbols of fertility, health and wealth. In Mordovian mythology, such veneration of trees was expressed in the image of the so-called world tree or tree of life, which is an apple tree, oak or birch. It is described as the largest tree of the forest, distinguished by its height, thickness, branching and splendor. Slides 13-17

5) S -obvious figures. Symbolized waterfowl and horse's head. Slides 18-20

You already know that Mordovian patterns were mainly used to decorate clothes. And the patterns in this case served as amulets. The pagan Mordovians had many gods: the gods of fire - Tol-ava and Tol-atya, the sun goddess Chiava or Shiava, the gods of water - Ved-ava and Ved-atya, the guardian of the forest - Vir-ava, the guardian of the field - Paks-ava, the giver harvest - Norov-ava and many others. Decorating their clothes with patterns symbolizing fire, sun, water, plants, and fertility, people asked their gods for protection.

All Mordovian patterns are so closely intertwined that one and the same pattern can be attributed to two or more symbols.

PHYSICAL MINUTE

Starting position - standing directly behind the back of the chair, toes and heels closed, hands resting on the back of the chair. Slowly rise onto your fingers and maintain this position for a while. Lower your entire foot, transferring the weight of your body to outside feet.

Starting position - standing. Raise your left (right) leg. Unbend and bend (pull the toe down, toe towards you). The exercise is performed at a fast pace. Repeat 10-12 times with each leg.

Starting position: standing, raise your left (straight) leg. Perform circular movements with your feet.

Students fill out the table.

Table. Mordovian patterns.

It is also worth mentioning types of symmetry Mordovian embroidery:

a) Net.

b) Border.

c) Socket.Slides 22-27

All these types include a large number of patterns and their varieties.

Colors in Mordovian patterns also have symbolic meaning.

1) White color . Symbolizes abundance, goodness, goodness, life, purity, holiness, restraint, innocence.

2) Red color . It was one of the most common and beloved among the Mordovians, it had many symbolic meanings, denoting love, beauty, strength, courage, emotionality, health, warmth, victory.

3) Black color. His perception was negative or neutral.

4) Green color. This color was closely connected with the surrounding natural world, therefore it embodied youth and immaturity.

5) Yellow. Symbolized maturity, usefulness, value.

View slides with teacher comments. Slides28-31

4. Reinforcing the material covered.

Students complete individual assignments on the sheets of paper (see appendix).

5. Summarizing.

What is an ornament?

What types of symmetry do you know?

What colors are used to create Mordovian patterns?

What Mordovian patterns do you know?

Today in the lesson you got acquainted with simple Mordovian patterns and complex ornaments. You learned about the symbolism of Mordovian patterns and the symbolism of flowers that are used in embroidery.

6. Homework.

Grading.