As you know, mathematics loves precision and brevity - it’s not for nothing that a single formula can verbal form occupy a paragraph, and sometimes an entire page of text. Thus, graphic elements, used throughout the world in science, are designed to increase the speed of writing and the compactness of data presentation. In addition, standardized graphic images can be recognized by a native speaker of any language who has basic knowledge in the relevant field.
The history of mathematical signs and symbols goes back many centuries - some of them were invented randomly and were intended to indicate other phenomena; others became the product of the activities of scientists who purposefully formed artificial language and guided solely by practical considerations.
Plus and minus
The history of the origin of symbols denoting the simplest arithmetic operations is not known for certain. However, there is a fairly plausible hypothesis for the origin of the plus sign, which looks like crossed horizontal and vertical lines. In accordance with it, the addition symbol originates in the Latin union et, which is translated into Russian as “and”. Gradually, in order to speed up the writing process, the word was shortened to a vertically oriented cross, resembling the letter t. The earliest reliable example of such a contraction dates back to the 14th century.
The generally accepted minus sign appeared, apparently, later. In the XIV and even XV centuries scientific literature a whole series of symbols were used to denote the subtraction operation, and only XVI century"plus" and "minus" in them modern form began to appear together in mathematical works.
Multiplication and division
Oddly enough, the mathematical signs and symbols for these two arithmetic operations are not fully standardized today. A popular symbol for multiplication is the diagonal cross proposed by the mathematician Oughtred in the 17th century, which can be seen, for example, on calculators. In mathematics lessons at school, the same operation is usually represented as a point - this method was proposed by Leibniz in the same century. Another representation method is an asterisk, which is most often used in computer representation of various calculations. It was proposed to use it in the same 17th century by Johann Rahn.
For the division operation, the slash sign (suggested by Oughtred) and horizontal line with dots above and below (the symbol was introduced by Johann Rahn). The first designation option is more popular, but the second is also quite common.
Mathematical signs and symbols and their meanings sometimes change over time. However, all three methods graphical representation multiplication, as well as both methods for division, are to one degree or another valid and relevant today.
Equality, identity, equivalence
As with many other mathematical signs and symbols, the designation of equality was originally verbal. For quite a long time, the generally accepted designation was the abbreviation ae from the Latin aequalis (“equal”). However, in the 16th century, a Welsh mathematician named Robert Record proposed two horizontal lines located one below the other as a symbol. As the scientist argued, it is impossible to think of anything more equal to each other than two parallel segments.
Despite the fact that a similar sign was used to indicate the parallelism of lines, new symbol equality gradually became widespread. By the way, such signs as “more” and “less”, depicting expanded different sides ticks appeared only in the 17th-18th centuries. Today they seem intuitive to any schoolchild.
Somewhat more complex signs equivalence (two wavy lines) and identity (three horizontal parallel lines) came into use only in the second half of the 19th century.
Sign of the unknown - “X”
The history of the emergence of mathematical signs and symbols is known and very interesting cases rethinking graphics as science develops. The sign for the unknown, called today “X,” originates in the Middle East at the dawn of the last millennium.
Back in the 10th century in the Arab world, famous at that time historical period by their scientists, the concept of the unknown was denoted by a word literally translated as “something” and beginning with the sound “Ш”. In order to save materials and time, the word in treatises began to be shortened to the first letter.
Many decades later, the written works of Arab scientists ended up in the cities of the Iberian Peninsula, in the territory of modern Spain. Scientific treatises began to be translated into national language, but a difficulty arose - in Spanish there is no phoneme “Ш”. Arabic loanwords starting with it were written according to special rule and were preceded by the letter X. Scientific language At that time there was Latin, in which the corresponding sign is called “X”.
Thus, a sign, which at first glance is only a randomly chosen symbol, has deep history and is originally a contraction of the Arabic word for “something.”
Designation of other unknowns
Unlike “X,” Y and Z, familiar to us from school, as well as a, b, c, have a much more prosaic origin story.
In the 17th century, Descartes published a book called Geometry. In this book, the author proposed standardizing symbols in equations: in accordance with his idea, the last three letters of the Latin alphabet (starting from “X”) began to denote unknown values, and the first three - known values.
Trigonometric terms
The history of such a word as “sine” is truly unusual.
The corresponding trigonometric functions were originally named in India. The word corresponding to the concept of sine literally meant “string”. During the heyday of Arabic science, Indian treatises were translated, and the concept, which had no analogue in Arabic, transcribed. By coincidence, what came out in the letter actually resembled existing word“hollow”, the semantics of which had nothing to do with the original term. As a result, when in the 12th century Arabic texts were translated into Latin, the word “sine” arose, meaning “hollow” and established as a new mathematical concept.
But the mathematical signs and symbols for tangent and cotangent have not yet been standardized - in some countries they are usually written as tg, and in others - as tan.
Some other signs
As can be seen from the examples described above, the emergence of mathematical signs and symbols largely occurred in the 16th-17th centuries. The same period saw the emergence of today's familiar forms of recording such concepts as percentage, square root, and degree.
Percentage, i.e. hundredth part, for a long time denoted as cto (short for Latin cento). It is believed that the sign that is generally accepted today appeared as a result of a typo about four hundred years ago. The resulting image was perceived as a successful way of reduction and took root.
The root sign was originally a stylized letter R (short for Latin word radix - “root”). Top line, under which the expression is written today, served as parentheses and was a separate symbol, separate from the root. Parentheses were invented later - they came into widespread circulation thanks to the work of Leibniz (1646-1716). Thanks to his work, the integral symbol was introduced into science, which looks like an elongated letter S - short for the word “sum”.
Finally, the sign for the operation of exponentiation was invented by Descartes and modified by Newton in the second half of the 17th century.
Later designations
Considering that the familiar graphic images of “plus” and “minus” were introduced into circulation only a few centuries ago, it does not seem surprising that mathematical signs and symbols denoting complex phenomena began to be used only in the century before last.
Thus, the factorial, which looks like an exclamation mark after a number or variable, appeared only at the beginning of the 19th century. Around the same time, the capital “P” to denote work and the limit symbol appeared.
It is somewhat strange that the signs for Pi and algebraic sum appeared only in the 18th century - later than, for example, the integral symbol, although intuitively it seems that they are more common. The graphical representation of the ratio of circumference to diameter comes from the first letter Greek words, meaning “circle” and “perimeter”. And the “sigma” sign for an algebraic sum was proposed by Euler in his last quarter XVIII centuries.
Names of symbols in different languages
As you know, the language of science in Europe for many centuries was Latin. Physical, medical and many other terms were often borrowed in the form of transcriptions, much less often - in the form of tracing paper. Thus, many mathematical signs and symbols in English are called almost the same as in Russian, French or German. How the point is more complicated phenomena, the higher the likelihood that different languages it will have the same name.
Computer notation of mathematical symbols
The simplest mathematical signs and symbols in Word are indicated by the usual key combination Shift+number from 0 to 9 in Russian or English layout. Separate keys are reserved for some commonly used signs: plus, minus, equal, slash.
If you want to use graphic images of an integral, an algebraic sum or product, Pi, etc., you need to open the “Insert” tab in Word and find one of two buttons: “Formula” or “Symbol”. In the first case, a constructor will open, allowing you to build an entire formula within one field, and in the second, a table of symbols will open, where you can find any mathematical symbols.
How to Remember Math Symbols
Unlike chemistry and physics, where the number of symbols to remember can exceed a hundred units, mathematics operates with a relatively small number of symbols. We learn the simplest of them in early childhood, learning to add and subtract, and only at the university in certain specialties do we get acquainted with a few complex ones mathematical signs and symbols. Pictures for children help in a matter of weeks to achieve instant recognition of the graphic image of the required operation; much more time may be needed to master the skill of performing these operations and understanding their essence.
Thus, the process of memorizing signs occurs automatically and does not require much effort.
In conclusion
The value of mathematical signs and symbols lies in the fact that they are easily understood by people who speak different languages and are native speakers of different cultures. For this reason, it is extremely useful to understand and be able to reproduce graphic images various phenomena and operations.
The high level of standardization of these signs determines their use in a wide variety of areas: in finance, information technology, engineering, etc. For anyone who wants to do business related to numbers and calculations, knowledge of mathematical signs and symbols and their meanings becomes a vital necessity.
Geometric symbols
The absolute symbolic language is the language of geometric figures...
Geometric figures are the concrete embodiment of numbers. Numbers belong to the world of principles, and they become geometric figures as they descend into the physical plane.
O. M. Aivankhov
Almost all geometric symbols consist of combinations of several geometric elements - simple components, each of which at the same time has its own special meaning, making its contribution to the overall composition.
“Geometric figures are like the frame of reality, while images still contain, so to speak, a little flesh, skin and muscles” (O. M. Aivankhov).
Geometric symbols are stable and are passed down from generation to generation without changes.
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Geometric symbols. Class of signs identical in shape geometric elements widely used in the mythological and religious spheres, as well as emblems and heraldry.
Geometric symbols
Swastika straight (left-handed)
Swastika as a solar symbol
A straight (left-sided) swastika is a cross with the ends curved to the left. Rotation is considered to occur clockwise (opinions sometimes differ in determining the direction of movement).
The straight swastika is a symbol of blessing, good omen, prosperity, good luck and aversion to misfortune, as well as a symbol of fertility, longevity, health and life. It is also a symbol of masculinity, spirituality, inhibiting the flow of lower (physical) forces and allowing higher energies to manifest themselves. divine nature.
Reverse swastika (right-handed)
Swastika on a Nazi war medal
The reverse (right-handed) swastika is a cross with the ends bent to the right. Rotation is considered to occur counterclockwise.
The reverse swastika is usually associated with the feminine principle. Sometimes it is associated with the launch of negative (physical) energies that block the passage to sublime powers of the spirit.
The Sumerian swastika, formed by four women and their hair, symbolizes the female generative force
Pentagram (pentacle): general meaning of the symbol
Pentagram sign
The pentagram, written in one line, is the most ancient of all the symbols that we possess. It had different interpretations in different historical times of mankind. It became the Sumerian and Egyptian star sign.
Later symbolism: five senses; masculine and feminine principles expressed by five points; harmony, health and mystical powers. The pentagram is also a symbol of the victory of the spiritual over the material, a symbol of security, protection, and a safe return home.
Pentagram as a magical symbol
Pentagrams of the White and Black Magicians
The pentacle, with one end up and two down, is a sign of white magic known as the "foot of the druid"; with one end down and two up, it represents the so-called “goat’s hoof” and the horns of the devil - a characteristic change in symbolism from a positive to a negative sign when it is turned over.
The White Magician's Pentagram is a symbol of magical influence and dominance disciplined Will over the phenomena of the world. The will of the Black Magician is directed towards destruction, towards refusal to perform a spiritual task, therefore the inverted pentagram is seen as a symbol of evil.
Pentagram as a symbol of a perfect person
Pentagram symbolizing perfect man
The pentagram, a five-pointed star, is a symbol of a perfect man standing on two legs with his arms spread apart. We can say that man is a living pentagram. This is true both physically and spiritually - man possesses and exhibits five virtues: love, wisdom, truth, justice and kindness.
Truth belongs to the spirit, love to the soul, wisdom to the intellect, kindness to the heart, justice to the will.
Double pentagram
Double Pentagram (Man and the Universe)
There is also a correspondence between the human body and the five elements (earth, water, air, fire and ether): will corresponds to earth, heart to water, intellect to air, soul to fire, spirit to ether. Thus, by his will, intellect, heart, soul, spirit, man is connected with the five elements working in the cosmos, and he can consciously work in harmony with them. This is precisely the meaning of the symbol of the double pentagram, in which the small one is inscribed in the large one: man (microcosm) lives and acts within the Universe (macrocosm).
Hexagram
Hexagram image
A hexagram is a figure composed of two polar triangles, a six-pointed star. It is a complex and seamless symmetrical shape in which six small individual triangles are grouped around a large central hexagon. The result is a star, although the original triangles retain their individuality. Since the upward-facing triangle is a heavenly symbol, and the downward-facing triangle is an earthly symbol, together they are a symbol of a person who unites these two worlds. It is a symbol of a perfect marriage that binds a man and a woman.
Seal of Solomon
Seal of Solomon, or Star of David
This is the famous magical seal of Solomon, or the Star of David. The upper triangle in her image is white, and the lower one is black. It symbolizes, first of all, the absolute law of analogy, expressed by the mystical formula: “What is below is similar to what is above.”
The Seal of Solomon is also a symbol of human evolution: one must learn not only to take, but also to give, absorb and radiate at the same time, radiate for the Earth, perceive from Heaven. We receive and are fulfilled only when we give to others. This is the perfect union of spirit and matter in man - the union of the solar plexus and the brain.
Five pointed star
Five pointed star
Star of Bethlehem
The five-pointed star has different interpretations, including symbolizing joy and happiness. It is also the emblem of the Semitic goddess Ishtar in her warlike incarnation, and in addition, the Star of Bethlehem. For Freemasons, the five-pointed star symbolizes the mystical center.
The Egyptians gave great importance five- and six-pointed stars, as is clear from the text preserved on the wall of the mortuary temple of Hatshepsut.
Seven pointed star
Seven-pointed star of magicians
Repeated in the seven-pointed star characteristic features five-pointed. The Gnostic star has seven rays.
Seven- and nine-pointed stars, drawn with one line, are mystical stars in astrology and magic.
The Star of Magi can be read in two ways: sequentially along the course of the rays (along the line of the star) and along the circumference. Along the rays are the planets that control the days of the week: Sun - Sunday, Moon - Monday, Mars - Tuesday, Mercury - Wednesday, Jupiter - Thursday, Venus - Friday, Saturn - Saturday.
Nine-pointed star
Nine-pointed star of magicians
Nine-pointed stars, like seven-pointed ones, if they are drawn with one line, are mystical stars in astrology and magic.
The nine-pointed star, composed of three triangles, symbolizes the Holy Spirit.
Monad
Four components of the monad
It is a magical symbol called the monad by John Dee (1527–1608), advisor and astrologer Queen of England Elizabeth I.
Dee presents the nature of magical symbols in terms of geometry and tests the monad in a number of theorems.
Dee explores the monad at such a deep level that he finds connections between his theory and Pythagorean harmony, biblical knowledge and mathematical proportions.
Spiral
Spiral structure Milky Way
Spiral shapes are found very often in nature, ranging from spiral galaxies and to whirlpools and tornadoes, from mollusk shells to patterns on human fingers, and even the DNA molecule is shaped like a double helix.
The spiral is a very complex and multi-valued symbol. But first of all, it is a symbol of the great creative (vital) force both at the cosmic level and at the microcosm level. The spiral is a symbol of time, cyclic rhythms, changes in the seasons of the year, birth and death, the phases of “aging” and “growth” of the Moon, as well as the Sun itself.
Tree of Life
The Tree of Life in the Human Being
Tree of Life
The Tree of Life does not belong to any culture - not even the Egyptians. It transcends races and religions. This image is an integral part of nature... Man himself is a miniature Tree of Life. He possessed immortality when connected to this tree. The Tree of Life can be thought of as the arteries of a great cosmic body. Through these arteries, as if through channels, flow the life-giving forces of the cosmos, which nourish all forms of existence, and the cosmic pulse of life beats in them. The Tree of Life is a separate section, part of the scheme of the universal code of life.
Sphere
Armillary sphere (engraving from the book of Tycho Brahe)
A symbol of fertility (like the circle), as well as integrity. IN Ancient Greece the sign of the sphere was a cross in a circle - an ancient emblem of power. A sphere composed of several metal rings, illustrating the cosmogonic theory of Ptolemy, who believed that the Earth was at the center of the Universe, is an ancient emblem of astronomy.
Platonic solids
Platonic solids inscribed in a sphere
The Platonic solids are five unique shapes. Long before Plato, Pythagoras used them, calling them ideal geometric bodies. Ancient alchemists and such great minds as Pythagoras believed that these bodies were associated with certain elements: cube (A) - earth, tetrahedron (B) - fire, octahedron (C) - air, icosahedron (D) - water, dodecahedron ( E) is ether, and the sphere is emptiness. These six elements are the building blocks of the universe. They create the qualities of the Universe.
Planet symbols
Planet symbols
Planets are represented by a combination of simplest geometric symbols. This is a circle, a cross, an arc.
Consider, for example, the symbol of Venus. The circle is located above the cross, which personifies a certain “spiritual attraction” that pulls the cross upward into the elevated areas belonging to the circle. The cross, subject to the laws of generation, decay and death, will find its redemption if it is raised within this great circle of spirituality. The symbol as a whole represents feminine in the world, which is trying to spiritualize and protect the sphere of the material.
Pyramid
Great Pyramids of Cheops, Khafre and Mikerin
The pyramid is a symbol of the hierarchy that exists in the Universe. In any area, the pyramid symbol can help to move from the lower plane of multiplicity and fragmentation to the higher plane of unity.
It is believed that the initiates chose the pyramid shape for their sanctuaries because they wanted the converging lines towards the Sun to teach humanity a lesson in unity.
Star tetrahedron
Star tetrahedron
A star tetrahedron is a figure consisting of two intersecting tetrahedra. This figure can also be perceived as a three-dimensional Star of David.
Tetrahedra appear as two opposing laws: the law of spirit (radiation, bestowal, selflessness, selflessness) and the law of matter (pulling in, cooling, freezing, paralysis). Only a person can consciously combine these two laws, since he is the connecting link between the world of spirit and the world of matter.
The star tetrahedron thus represents the two poles of creation in perfect balance.
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(MHC course - for students in grades 10 - 11)
Lesson format: lesson-lecture
Target: identify features structural analysis carried out on the basis of sign systems closely related to semiotics ( science of sign systems) and semantics ( science of meaning)
Tasks:
- Student comprehension during the analysis process work of art unity of form and meaning
- From the point of view of value orientations, to teach an understanding of the unity of the entire world artistic culture
- Develop a more tolerant and tolerant attitude towards the forms and values of foreign cultures.
Do not lay up for yourselves treasures on earth, where moth and rust destroy and where thieves break in and steal, but lay up for yourselves treasures in heaven, where neither moth nor rust destroys and where thieves do not break in and steal; for where your treasure is, there will your heart be also.
Visual range: Geometric Symbols Slideshow (See Slide Appendix)
Lesson progress
Codes can be very different: zoomorphic, plant, color, food, chemical, numerical, geometric. In any cultural “text” - literary, visual, ornamental - they carry their message, which can be parallel direct text. The chain can include any number of codes depending on the cultural tradition.
One of the most ancient and at the same time simplest, and therefore universal, is the code geometric symbols and numerical symbolism closely related to it.
POINT – Let's start with the simplest and at the same time the most difficult - from the POINT. In ancient times, the point symbolized the cosmogonic process (the creation of the world), its Beginning, Center and First Cause. The place where everything comes from and where everything returns.
The altar is the sacred point in the temple it is a place of sacrament. In the ancient Egyptian temple, this is an obelisk, marking the birth of the first ray, and later, a golden boat in which the miracle of “rejuvenation” of the Sun/Ra occurs.
The difference in the interpretation of the ways of comprehending the divine essence in Eastern and Western Christianity led to the creation of a radical various types temple. Eastern Church adheres to the idea of illumination in silent and passive contemplation, and as a result, a model of a centric, domed temple was developed, with space, as if descending from top to bottom, overshadowing the believers with divine light. The Western Church interpreted this process precisely as a process, as a Path, progression from darkness to light, from ignorance to knowledge true faith, and, accordingly, a solution was found in the form of a horizontally elongated basilica structure.
In mythology, the symbol “point/grain/seed” was embodied in the cult of fertility, the dying and resurrecting god of vegetation.
The deployment of a point on a plane and in space can take on different configurations. The simplest option– straight LINE- can turn into a ray of sun, an arrow, a spear (remember “The Tale of Igor’s Campaign” - Russian warriors “scattered arrows across the field”, “the winds, the grandchildren of Stribog, blow arrows from the sea”, “the rain comes with arrows”). Wavy and broken lines – ancient symbols moist, fruit-bearing soil and water. The undulation of movement united water, fire and snake in the minds of the ancients. As a result, lightning (a fiery serpent) was also depicted as a broken line, zigzag or meander.
The simplest types of meander were associated in the ancient Greek tradition with water, and the more complex ones were associated with the labyrinth of King Minos, the habitat of the Minotaur. ( Meander - a labyrinth without end and beginning, without a definite structure - similar to chaos).
Follow the chain of characters: point à line à wavy line / water à meander.
____________________________________________
(after discussion) Point ( opposition to chaos), line ( expansion of a point in space), wavy line/water ( water is similar to chaos due to the lack of structure and a certain shape ), meander/maze ( symbol of chaos); By following the chain, we can get an idea of the logic of mythological thinking, according to which, thanks to a phased replacement, the initial opposition is removed and any concept can turn into its opposite.
CIRCLE– has amazing property combine opposites on one side, it's finite(the limitation of that part of the plane that the circle cuts off from space), on the other hand, it is infinite, since Roundabout Circulation, forming it, is potentially infinite, it has no beginning or end.
The circle symbolizes the unity of the feminine and masculine: the circle itself is associated with the feminine, and its center with the masculine; dark part circle is " yin», feminine , A light – « yang», masculinity . A circle, divided into two parts, connects light and darkness, life and death, day and night, summer and winter, their endless succession in the natural cycle.
The circle is a symbol of unity, integrity and completeness, infinity and eternity, the highest divine perfection.
In many cultures, the Cosmos is represented in the form of a ball and its subject images (egg, turtle, disc).(Piero della Francesca . Madonna and Saints (Altarpiece of Montefeltro). OK. 1472-1474. Looking at this altar image, it is impossible not to experience a feeling of reverence. Strict proportionality of all parts, perfection geometric shapes and purity of color, combined, create a true masterpiece of religious painting. Symbolic egg. A snow-white egg hangs from the vaulted ceiling, shining brightly in the light. It seems to hang directly above the Madonna, and its shape echoes the oval of her head. The master, placing the egg between heaven and earth, created a visible image of the dual nature of Christ.)
Many cities, including Moscow, have radial ring structure, and the most ancient dwellings ( wigwam, igloo) repeat the circle of people sitting around the fire.
In the structure of ritual structures, the circle was most often used to indicate the ideal celestial sphere: in the Buddhist tradition, the seven heavens were depicted in the form of disks strung on the World Axis, a dome - everywhere means the sky, a round hole in the ceiling - the eye of the sky.
In the visual arts, the rondo form is rare and is used only during the classical periods. The semicircle of the arch over many Renaissance compositions, inside the picture, is completed to a full circle and symbolizes the celestial sphere.
SQUARE. The Neolithic era is associated with the emergence of a more defined symbol of space and time - SQUARE. In the configuration of a square, not only the center and periphery are significant, but its sides and corners. A square is, first of all, a symbol of the earth: from a specific square or rectangular field to an image of the universe with a center designated by the World Tree and orientation along the four cardinal directions, where “small” world trees grow, winds, elements, and deities of the seasons live.
The model of the world, outlined in the form of a square, already has more detailed landmarks: top and bottom - in a vertical projection, right and left - in a horizontal one. The square was associated with the concepts of equality, simplicity, uniformity and order, that is, with an ideal, stable, statistical structure, which is the most suitable foundation for any sacred structure - a temple, a pyramid, a pagoda. In addition, any building with its foundation rests on the ground, it is, as it were, part of the earth and its roots, and, accordingly, this is symbolically fixed in a square or rectangular plan.
The altars of earth were always square in shape, unlike the altars of heaven, which were round.
The square associated masculinity, rightness, wisdom, truth, justice.
An example of a perfectly timed merger like mathematical formula, the composition of the painting and its symbolism is “The Baptism of Christ” by Piero Della Francesca. The composition consists of a circle (heaven) and a square (earth), which overlap each other by half and thereby symbolize the entry of the Spirit of God into the earthly flesh of Jesus during baptism, the unity of the divine and human beginnings in the Son of God, but with predominance earthly beginning until the resurrection - the figure of Christ occupies half the circle and the entire square. The Holy Spirit in the form of a dove is located in the center of the circle, as the focus of the heavenly spheres.
TRIANGLE. The concrete embodiment of this symbol are the images of the World Mountain and the pyramid - peculiar staircases to the sky.
A triangle consists of a horizontal base, an opposite vertex and the sides connecting them. Vertical height denotes creativity, strength and energy, life, triumph of the spiritual, vertical standing man, That horizontal personifies the passivity and inertia of matter. Sides of a triangle connect the horizontal of the base with the height and thereby, as it were, remove their opposition, life force and energy overcome passivity, creativity rises, breaks through inertia, spirit unites with matter, earth with sky.
Most significant for fine arts is a triangle in a square, meaning the divine in the human, the spiritual in the material, the heavenly in the earthly. Leonardo da Vinci masterfully mastered this form-symbol, an example of which is the composition “Madonna of the Rocks” ( triangle of figures guards the divine child), "La Gioconda" ( stable isosceles triangle half-figures as a symbol of inner spiritual harmony), "The Last Supper" ( equilateral triangle figures of Christ with arms outstretched towards people against the backdrop of a luminous rectangle of a window - a symbol of his divinity and future transfiguration).
CROSS– one of the most complex and polysemantic symbols. Its very configuration ( connection of vertical and horizontal, top and bottom) indicates its duality, a double function that evokes opposite feelings, and explains the combination in it of such opposite meanings as life, fertility, prosperity, addition ( remember the plus sign in mathematics), but at the same time torture, death, an instrument of torture, passion, as well as resurrection through death on the cross.
In folklore, a cross signifies a transition from one space to another - a place that is especially dangerous due to the loss of clear orientation. The crossroads of roads offer a choice: to the right is life, to the left is death, but it is impossible to determine where the right is and where the left is in the system of absolutely identical guidelines of the deceptive Fate.
In the vertical projection, the cross schematically coincides with both the World Tree and the figure of a man with arms outstretched to the sides, in a praying pose (as an option - “Oranta”).
The world tree connects all three levels of the world, ascent to the heavenly world.
In paganism, sacrifice was practiced on the World Tree - people still tie white and red ribbons on especially revered trees. Even God could be the “victim.” For the sake of gaining higher wisdom One, the head of the Scandinavian pantheon, sacrificed himself and hung pierced by a spear on the World Tree Ygdrasil for nine days. Suffering was one of the ways of communion with the deity.
Later, in Christianity, this mythology was rethought: the World Tree turned into an instrument of shameful execution, a sacred sacrifice into a shameful death, the Son of God was sacrificed, and, due to the principle of the unity of the Trinity, God himself, the sacrifice was brought not to God, but to atone for sins humanity. Thus, Christ’s sacrifice on the cross becomes a turning point in the relationship between God and man, and the cross becomes a kind of marker of this historical event.
Crucifix in Christian tradition replaced the cosmic World Tree. It united God and man in Christ, the holiness of heaven and the darkness of the underworld ( the cross at its base rests on Mount Golgotha with a cave symbolizing hell), the Fall and its atonement ( After the resurrection, Christ descended into hell and brought Adam and Eve out of it, since with his sacrifice he atoned for their original sin and thereby opened the way for humanity to spiritual salvation), life and death in resurrection, past and future (the descent of Christ into hell is a prototype of the second coming of Christ, the end of the world and the Last Judgment). The Crucifixion united the absolute of Eternity and the variability of historical time.
The cross is present in spatial structure any Christian temple, both vertically and horizontally. A peculiar “philosophy” of the cross is contained in a number of early Christian mosaics.
The cross had the magic of protection, so it was widely used in carving, sewing, and as an amulet.
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Task to choose from:
a) describe the main symbols of the geometric code
b) analyze your chosen work of painting from the point of view of the symbolism of the geometric code
