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St. Petersburg at a geometry lesson Types of symmetry in architecture
Axial symmetry Two points are called symmetrical with respect to a line if this line passes through the middle of the segment connecting these points and is perpendicular to it. A B C D D c
Axial symmetry in the architecture of St. Petersburg
St. Isaac's Cathedral The largest Orthodox church St. Petersburg Built in 1818-1858 according to the design of O. Monferand. Height 101.5 m.
Catherine Palace in Pushkin Former imperial palace. Located in the city of Pushkin (formerly Tsarskoye Selo). The building was founded in 1717 by order of Catherine I. Represents an example of late Baroque. During the war, the palace was severely destroyed. Its restoration took many years.
Central symmetry Two points are said to be symmetrical about a given point if this point is the midpoint of the segment connecting the points. A B O
In 1798-1810, work was carried out on the construction of the granite embankments of the Moika, which were decorated with a cast iron fence with a clear pattern of geometric elements CENTRAL SYMMETRY IN THE FAMOUS GRIDS OF ST. PETERSBURG
Belinsky Bridge In the 18th century, 7 stone drawbridges of the same type were built on the Fontanka. Only two have survived in their original form. One of them is Simeonovsky Bridge (Belinsky Bridge)
Fragment of the Summer Garden lattice
MIRROR SYMMETRY Mirror symmetry (symmetry relative to the plane) is a mapping of space onto itself in which any point M goes into a point N that is symmetrical to it relative to the plane.
Palace and park ensemble of Oranienbaum
Mirror symmetry in the gardens and parks of St. Petersburg
In this photo you can see different types symmetry Marble Palace was built in 1768-1785 according to the design of A. Rinaldi and commissioned by Catherine II. The first building in St. Petersburg, the facades of which are lined with natural stone.
On the topic: methodological developments, presentations and notes
Summer practice for 8th grade Suvorov students "Symmetry in Moscow architecture"
The material consists of explanatory note, goals and objectives. And also daily practice planning...
Department of Education Vologda region
budget professional educational institution
Vologda region
"Kadui Energy College"
INDIVIDUAL PROJECT
IP. 02/23/03/2016.
Topic: Symmetry in architecture
Profession: Auto mechanic
Is done by a student
Group No. 171:
Garunov Nikolay Viktorovich
FULL NAME.
Checked:
Kormacheva E.E..
"___"____________ 2016
He defended his work with a rating of ________________
2016
Content
Introduction………………………………………………………………................................... ..........2
Symmetry. Types of symmetry……………………………..………........ 4-7
Symmetry in architecture…………………………………………….8-11
Symmetry in the architecture of buildings in Kaduy……… …...……………….......12
Conclusion……………………………………………………..………………..14
Literature………………………………………………………. ………….......15
Introduction.
"Symmetry is the idea by which man
for centuries tried to comprehend and create order,
beauty and perfection."
Hermann Weil.
The world in which we live is filled with the geometry of houses, shops and streets, mountains and fields, creations of nature and man. Symmetry is an amazing mathematical phenomenon. In ancient times, this word was used to mean “harmony”, “beauty”. Indeed, translated from Greek this word means “proportionality, uniformity in the arrangement of parts, proportionality.”
When we covered the topic “Symmetry” in mathematics lessons, very little time was allocated for it, but I thought this topic was interesting, and I decided to take it for research. I wanted to know more about this issue, because I have heard this term more than once on other subjects and in everyday life. When I started researching, I noticed that symmetry is not only a mathematical concept, it manifests itself as something beautiful in living and inanimate nature, as well as in human creations. Therefore, I set myself the following goals and objectives of the project.
Objective of the project: get acquainted with the main types of symmetry and consider the application of types of symmetry in practical life
Tasks:
Describe the types of symmetry.
Consider the application of the principles of symmetry in the architecture of Kaduy.
Use the results of the research to form a scientific worldview based on the principles of symmetry.
Object of study: architectural structures of Prokhladny.
Subject of study: symmetry and architecture.
The relevance of research: the concept of symmetry runs through the entire centuries-old history of human creativity. It is found already at the origins of human knowledge; it is widely used by all directions without exception modern science. The principles of symmetry play important role in physics and mathematics, chemistry and biology, technology and architecture, painting and sculpture, poetry and music. The laws of nature that govern the inexhaustible variety of phenomena are, in turn, subject to the principles of symmetry. Therefore, the problem of this study is relevant in modern conditions.
1 . Symmetry. Types of symmetry.
There is an old parable about Buridan's donkey. One philosopher, named Buridan, had a donkey. Once, while leaving for a long time, the philosopher placed two completely identical armfuls of hay in front of the donkey - one on the left and the other on the right. The donkey couldn't decide which armful to start with and died of hunger. The parable of the donkey is, of course, a joke. However, look at the picture of the balanced scales. Aren't the balance scales somewhat reminiscent of the parable of Buridan's donkey? Indeed, in both cases, left and right are so identical that it is impossible to give preference to one or the other. In other words, in both cases we are dealing with symmetry , manifested in complete equality, complete balance of left and right.
According to legend, the term"symmetry" invented by a sculptorPythagoras of Rhegium , who lived in Regulus. He defined deviation from symmetry by the term"asymmetry" .
Symmetry in geometry - property geometric shapes. Two points lying on the same perpendicular to a given plane (or line) on opposite sides and at the same distance from it are called symmetrical with respect to this plane (or line).
Types of symmetry.
Axial symmetry.
Transformation in which each point A of a figure (or body) is transformed into one symmetrical to it relative to some axis l point A" is called axial symmetry ( l - axis of symmetry) .
If point A lies on the axisl , then it is symmetrical to itself, i.e. A coincides with A " .
In particular, if, when transforming symmetry about the axisl figure Ftransforms into itself, then it is called symmetrical about the axisl , A axis l called the axis of symmetry.
Central symmetry.
A transformation that takes each point A of a figure (body) to point A " , symmetrical to it relative to the center O, is calledtransformation of central symmetry or simply central symmetry.
Point O is calledcenter of symmetry and is motionless. This transformation has no other fixed points.
If, when transforming central symmetry relative to the center O, the figureFtransforms into itself, then it is called symmetrical with respect to the center O. In this case, the center O is called the center of symmetry of the figureF.
Symmetry relative to the plane (mirror symmetry).
There is another type of symmetry in geometry -symmetry relative to the plane.
If a transformation of symmetry relative to a plane transforms a figure (body) into itself, then the figure is called symmetrical relative to the plane, and this plane is called the plane of symmetry of this figure.
In some sources, this symmetry is called mirror symmetry. And the mirror not only copies the object, but also swaps the parts of the object that are front and back in relation to the mirror. In comparison with the object itself, its mirror counterpart turns out to be turned along the direction perpendicular to the plane of the mirror.
Examples of figures - mirror reflections of one another - can be the right and left hand human, right and left screws, parts architectural forms, some natural crystals and ornaments, some insects.
Portable (broadcast) symmetry.
This type of symmetry consists in the fact that parts of the whole form are organized in such a way that each next one repeats the previous one and is separated from it by a certain interval in a certain direction. This interval is called the symmetry step. The straight line AB is called the translation axis, and the distanceA – elementary transfer or period .
Portable symmetry is usually used when constructing borders. In works of architectural art it can be seen in the ornaments or lattices that are used to decorate them. Portable symmetry is also used in the interiors of buildings.
2. Symmetry in architecture.
Architecture - this is the art of construction, the ability to design and create cities, residential buildings, public and industrial buildings, squares and streets, parks. In many cities around the world you can find churches, palaces and mansions, modern buildings theaters, libraries in front of which you will want to stop and take a closer look. This is because buildings and streets, squares and parks, rooms and halls with their beauty can excite the imagination and feelings of a person, like other works of art. Masterpieces of architecture are remembered as symbols of peoples and countries. The whole world knows the Kremlin and Red Square in Moscow, the Eiffel Tower in Paris, and the ancient Acropolis in Athens. However, unlike other arts, people not only contemplate works of architecture, but also constantly use them. Architecture surrounds us and forms a spatial environment for people's life and activities.
Even in ancient times, the tasks of architecture were determined by three qualities - usefulness, durability, beauty. The well-known human desire for beauty inspires creative imagination architect to search for more and more unusual architectural forms, uniqueness of appearance and brightness artistic image structures.
Each building makes its own impression: one has a solemn,
a festive appearance, another – strict, the third – lyrical. Architectural monuments belonging to different eras and countries differ from each otherBy appearance or in style, how the living conditions and artistic tastes of people of those times differed.
The impression of a building largely depends on the rhythm, i.e. from the clear distribution and repetition in a certain order of the volumes of buildings or individual architectural forms on a building (columns, windows, reliefs, etc.). The predominance of elements of vertical rhythm - columns, arches, openings - creates the impression of lightness and upward direction.
On the contrary, the horizontal rhythm - cornices, friezes, belts and - gives the building the impression of squatness and stability.
In architecture, as in other forms of art, there is the concept of style, i.e. historically established set of artistic means and techniques.
Most common in architecturemirror symmetry. Build subordinate to herki of Ancient Egypt and temples of ancient Greece,amphitheaters and triumphalancient Roman arches, Renaissance palaces and churches,as well as numerous buildings withtemporary architecture.
Each part in a symmetrical system exists as a double of its obligatory pair, located on the other sidethe axis of the axle, and thanks to this it can racebe seen only as part of the whole.
Central axial symmetry is less commonly usedcalled in the history of architecture. Submit to herantique round temples and builtpark pavilions imitate them Cent axial symmetry also determinesthe shape of some architectural details -for example columns and their capitals.
Other types of symmetry in architectureare used extremely rarely, but they can bothto bake practical and artistic purposesconformity of form.
To rarely used speciessymmetry also includes helical. Shehas long been used for building elementsnia - spiral staircases and ramps, twisted column trunks.
Dissymmetry.
Absolute symmetry in large and complex structures is, strictly speaking, impossible. Complexity functional systems causespartial deviations from the main one, I determinethe general nature of the composition of the symmetrical schemeWe. Disturbed, partially upset simwe call metricdissymmetry .
Dissymmetry is a widespread phenomenonstrange things in nature. She is characteristicand for humans. Man is dissymmetrical, notdespite the fact that the outlines of his body haveplane of symmetry. Skazyva dissymmetryis in better control of one of the hands, carriedmetric location of the heart and many othershy organs, in the structure of these organs.
Free locationparts within the symmetrical scheme of the usualbut for Russian folk architecture it givesspecial attractiveness and individualityinterest in his works.
Partially broken symmetry, I answerunderstanding the complexity of life processes and at the same timeat the same time serving as an artistic mediumin expressing this complexity, we often encounteris also expected in modern foreign architecture tour.
Asymmetry.
From a mathematical point of view concepts asymmetry is just the absence of symmetry.However, a broad category of compo techniquesposition is not at all covered by this negativedefinition. In architecture - symmetry and asymmetry - two opposing methodsregular organization of spatialforms. Subordinated to one's own innerlaws, asymmetry by no means exhaustsdue to the destruction of symmetry. Unity is the goal of building an asymmetrical system sothe same as symmetrical, however, it is achievedit is in a different way. Identity of parts and their locationsposition is replaced by visual balance.Asymmetrical compositions in progressdevelopment of architecture arose as the embodimentunderstanding complex combinations of life processesand conditions environment. Specificthe forms of such compositions grow like rethe result of a unique combination of factors. Asymmetry is therefore individual, while inherent in the very principle of symmetrycommonality, a sign that connects all structurestions having symmetry of this type.
Subordination of parts - the main environmentthe art of combining an asymmetrical composition.Subordination is manifested not only in relation tosizing, arranging silhouettes And pla istic accents, but in the direction of sisthemes of spaces and volumes for the main partsbuildings or ensembles whose location does not coincide with the geometric center.
Asymmetrical composition can warehousesbe made of symmetrical parts, connections betweenwhich do not obey lawssymmetry. Many natural forms also have this character - they are subject to symmetry.parts, the whole is asymmetrical (example - leavesand the tree as a whole).
Architecture – amazing area human activity. Science, technology, and art are closely intertwined and strictly balanced in it. Only a proportionate, harmonious combination of these principles makes a structure erected by man an architectural monument.
3.Symmetry in the architecture of buildings in Kaduy.
An example of an amazing combination of symmetry and dissymmetry is the Church of Philip of Irapa.Looking at the Church of Philip of Irapa, I mentally drew the axes of symmetry and measurement. The church has precise proportions, strict symmetry of the facades, and when looking at it, a feeling of clarity and balance is created.
Conclusion: In the appearance of the Church of Philip of Irapa, according to the architectural canons of the construction of Russian churches, the laws of symmetry were used.
In architecture, axes of symmetry are used as means of expressing architectural design. An example of the use of axial symmetry in architecture is a building kindergarten"Baby".
Dissymmetry is broken, partially upset symmetry. An example of dissymmetry is the station building, the Victoria swimming pool building, and the medical center building.
An example of asymmetry is the Country Club.
Conclusion.
In my work, I examined the architectural structures of the village of Kaduy and found that they showed different kinds symmetry.
Research has shown that all types of symmetry are used in the design and construction of architectural structures and the design of building facades.
Symmetry is opposed to chaos, disorder. She is present in our
life literally in everything, but we are so used to it that we don’t notice
this. But no matter how we treat her, she is in our lives, adding to
there is peace, tranquility and a state of something alien to the eye.
I believe that no matter how art develops in the future, the elements
symmetries in it will still prevail and improve.
Literature.
I'm exploring the world. Moscow monasteries and temples: encyclopedia. OOO
"Publishing house Astrel" 2006
Great Encyclopedia of Cyril and Methodius. Electronic edition.
L. Tarasov, This amazingly symmetrical world, “Enlightenment”, M., 1980.
I. F. Sharygin, L. N. Erganzhieva, Visual geometry, “MIROS”, 2000.
Presentation on geometry on the topic: “Symmetry in architecture and construction.” Completed by students of grades 9-1: Chekalkina Ekaterina and Sokolova Ksenia Teacher Pochetukhina E.A.
Definition of symmetry. SYMMETRY is a property of geometric figures. Two points lying on the same perpendicular to a given plane (or line) on opposite sides and at the same distance from it are called symmetrical with respect to this plane (or line). A figure is symmetrical relative to a straight line (axis of symmetry) or plane if its points in pairs have the specified property. A figure is symmetrical with respect to a point (center of symmetry) if its points lie in pairs on straight lines passing through the center of symmetry, on opposite sides and at equal distances from it.
Examples of symmetry in geometric shapes. Asymmetry is the absence of symmetry. Symmetry can be axial or central. Axial example: Central example:
The presence of symmetry. The image on a plane of objects in the world around us has an axis of symmetry or a center of symmetry. Many tree leaves and flower petals are symmetrical relative to the average stem.
We often encounter symmetry in art, technology, everyday life, furniture, chemistry, helical symmetry in nature... symmetry in architecture and construction. The presence of symmetry.
Symmetry in architecture. The main techniques when creating architectural compositions are the combination of different volumes - high and low, rectilinear and curvilinear, alternation of spaces - open and closed, symmetry and asymmetry of the building. During construction, architects first consider the symmetry of the building, since if there is a mistake, the object may collapse.
An example of symmetry in architecture. In the buildings, all structures are located strictly symmetrically.
Some styles of architecture. Gothic style Renaissance Classicism Next slide
Gothic style of architecture. In the Middle Ages arose Gothic style. Gothic buildings are distinguished by an abundance of openwork, like lace, decorations, sculptures, and ornaments, so both outside and inside they give the impression of lightness and airiness. Windows, portals, and vaults have a characteristic lancet shape. The facades of the buildings had mirror (axial) symmetry. back
Style – Renaissance. The architects of the Renaissance created a style - the Renaissance, in which they used the heritage of ancient art and Greek architectural orders. True, they used them in a new way, more freely, with a deviation from the ancient canons, in other proportions and sizes, in combination with other architectural elements. Renaissance buildings were strict in form, with clear, straight lines. The symmetry of the facades is preserved. back
Style – classicism. All buildings built in the classicist style have clear rectilinear forms and symmetrical compositions. Against the background of smooth walls, porticos and colonnades protrude, giving the buildings a solemn monumentality and splendor. Decorative decorations of bas-reliefs and statues enliven the appearance of the buildings. The masters of classicism deliberately borrowed techniques from antiquity and the Renaissance and used orders with antique proportions and details. back
An example of an amazing combination of symmetry and asymmetry is the Intercession Cathedral (St. Basil's Cathedral) on Red Square in Moscow. This composition consists of ten temples, each of which has central symmetry, but in general has neither mirror nor rotational symmetry. Symmetrical architectural details The cathedrals are spinning in their asymmetrical, disorderly dance around its central tent: they either rise, then fall, or seem to run into each other, or lag behind, creating the impression of joy and celebration. Without its amazing asymmetry, St. Basil's Cathedral would be simply unthinkable.
Symmetry can be called the key to success in construction. Almost all buildings in the world, in order to avoid destruction, are built exclusively symmetrically. This is why symmetry is so important in construction.
Sources of information: www.letopisi.ru www.google.ru www.simmetr-geom.com Tarasov L.V. – This amazingly symmetrical world.
Symmetry in architecture “Architecture has three main things: beauty, tranquility and strength of the building. To achieve this, knowledge of proportion, perspective, mechanics or physics in general serves as a guide, and the common leader of all of them is reason.” “Architecture has three main things: beauty, tranquility and strength of the building. To achieve this, knowledge of proportion, perspective, mechanics or physics in general serves as a guide, and the common leader of all of them is reason.” V. Bazhenov V. Bazhenov
Symmetry in architecture Symmetrical objects have high functionality in different directions. All this led a person to think about the degree of expediency: greater stability and equal, that in order for a structure to be beautiful it must be symmetrical. Symmetry was used in the construction of religious and domestic buildings in Ancient Egypt. But symmetry is most clearly manifested in ancient buildings Ancient Greece. From then to the present day, symmetry in the human mind has become an objective sign of beauty. Maintaining symmetry is the first rule of an architect when designing any structure. Architectural structures created by man are for the most part symmetrical. They are pleasing to the eye and people consider them beautiful. What is this connected with?
Geometry has two treasures: one of them is the Pythagorean theorem, the other is the division of a segment in the average and extreme ratio... The first can be compared with the measure of gold, the second is more reminiscent gem. I. Kepler Golden ratio Golden ratio is a law proportional connection the whole and the parts that make up the whole, when the whole relates to the larger part as the larger part relates to the smaller
Parthenon The sacred hill and temple of Divine Athena, the Magnificent Parthenon, Having buried the forgotten ruins, aims to the gods of Olympus. N. Vasyutinsky PARTHENON, the main temple of the Athenian Acropolis, dedicated to Athena Parthenos (i.e. the Virgin), the patron goddess of the city. Construction began in 447 BC, the consecration of the temple took place at the Panathenaic festival in 438 BC, but decoration (mainly sculptural work) continued until 432 BC. The Parthenon is a masterpiece ancient greek architecture and a symbol of the Greek genius.
The picture shows whole line patterns associated with the golden ratio. When looking at the Parthenon at the location of the monumental gate at the entrance to the city (propylaea), the ratio of the rock mass at the temple also corresponds to the golden ratio. Thus, the golden proportion was already used when creating the composition of the temples on the sacred hill. The Parthenon has 8 columns on the short sides and 17 on the long sides. The projections are made entirely of squares of Pentilean marble. Sculptures The ratio of the height of the building to its length is 0.618. Parthenon
The Pantheon is considered the most perfect of all classical monuments preserved in the Italian capital. For a long time It was believed that it was built in 27 AD, but excavations have shown that the Pantheon is a reconstructed structure from the time of Hadrian (1st century AD). In 609, the pagan Pantheon became a Christian temple of the Holy Virgin Mary. The internal diameter of the Pantheon and its height are 43 meters. The sky is visible through the hole in the dome. This creates an atmosphere of solemnity. Between the second and third chapels is Raphael's tomb. On the tombstone there is an inscription: “Here lies Raphael, who competed with Mother Nature herself, and she feared that he would surpass her in creativity.” Pantheon
Pyramid of Cheops Pyramid of Cheops The Egyptian Pyramid of Cheops is the oldest and at the same time the only wonder of the world that has survived to this day. It received its name from the name of its creator - Pharaoh Cheops (around BC). The height of the Cheops pyramid is meters (and initially it was even 147 meters). It is built from 2.3 million limestone blocks, which weigh an average of two and a half tons. The pyramid stands on a specially prepared plane, which gives a horizontal deviation of less than two centimeters. The base of the pyramid is square, and the length of one side is 227.5 meters. The faces of the pyramid are oriented to the cardinal points, and their angle of inclination to the base is 52 degrees.
This name comes from Latin word clafssicus, which means exemplary. The style itself developed in the 17th century in France, accepting the ancient heritage as the norm, as an ideal example in all types of arts - literature, painting, architecture, theatrical art. The architecture of Classicism is characterized by clarity and geometricism of forms, symmetry, logical layout and restrained decor. This style had a great influence on the formation of the appearance of our northern capital. Many palaces, squares and parks created by famous architects, founders of Russian Classicism - V.I. Bazhenov, K.I. Rossi, M.F. Kazakov, gave St. Petersburg the appearance of a majestic and completely European city. 1. Palace Square with the arch of the General Staff building - architect K.I. Rossi 2.Mikhailovsky Palace in St. Petersburg– architect Rossi K.I. Classicism
Senate Building The Senate building was built according to the design of the architect M.F. Kazakov in the years, interior decoration continued until 1790. The Round Hall of the Senate is rightfully considered one of the masterpieces of architecture. Contemporaries called it the Russian Pantheon. The hall with a diameter of 24.7 m and a height of 27 m with a Corinthian order colonnade along the perimeter is covered with a coffered dome, at the base of which there are 24 skylights. Sculptural thematic bas-reliefs decorate the walls between the columns and windows.
The building's plan is an isosceles triangle with a courtyard divided by additional buildings into three parts: a central pentagonal one and triangular side ones. The main axis of the building runs along the axis of the triangle, on which the Dome of the hall is located, oriented towards Red Square. It is at the same time the center of one of its compositional axes. All rooms of the Senate are connected to each other by a corridor running along the perimeter of the courtyard. Senate building
At the very end of Mokhovaya Street, on a hill rises a luxurious palace made of white stone, known in Moscow as the Pashkov House. The combination of ancient severity and solemnity with purely Moscow patterning makes it a masterpiece of original Russian classicism. The palace was built by one of the best Moscow architects Vasily Bazhenov in the years. commissioned by the wealthy landowner Pashkov. In 1812 the house was destroyed by fire. However, the architects, restoring the house according to drawings from the 18th century, managed to recreate it. Before the War of 1812, in the courtyard of the house there was a garden in which parrots, peacocks and other birds unknown to Muscovites lived. On Sundays this garden was open to everyone. One of the legends about the creation of the Pashkov House says that when Vasily Bazhenov was not allowed to build a palace comparable to the Louvre for Catherine II on the territory of the Kremlin, he, by order of a wealthy nobleman, captain-lieutenant of the Semenovsky Life Guards regiment Peter Pashkov, erected a palace opposite. Turning it back to the Kremlin. Pashkov House
In addition to symmetry in architecture, one can consider antisymmetry and dissymmetry. Antisymmetry is the opposite of symmetry, its absence. An example of antisymmetry in architecture is St. Basil's Cathedral in Moscow, where symmetry is completely absent in the structure as a whole. However, it is surprising that the individual parts of this cathedral are symmetrical and this creates its harmony. And the square in the twilight of the night stands full of yesterday's execution; There are traces of fresh torment all around: Where is the corpse, chopped up on a grand scale, Where is the pillar, where is the pitchfork; There are cooled cauldrons full of resin; Here is an overturned scaffold: Iron teeth stick out, With bones, piles of ashes smolder, On stakes, writhing, the dead are numb and black... (description of Red Square after a mass execution by order of Ivan the Terrible. A.S. Pushkin. Oprichnik) Asymmetry
The grandiose structure was planned to reflect the course of the war, the significance of the victory and the protection provided by heavenly forces to the king and the state. Ivan the Terrible wanted to embody his plan in architecture in extraordinary detail and vividly. Therefore, a temple appeared with a more complex structure than any other religious building in Rus'. It consists of nine churches, designed like towers and united by galleries that run along the lower tier. In accordance with the king's plan, each church is dedicated to one or another holy or Christian holiday. St. Basil's Cathedral
This bizarre composition of ten temples, each of which has central symmetry, has neither mirror nor rotational symmetry as a whole. The symmetrical architectural details of the cathedral swirl in their asymmetrical, chaotic dance around its central tent: they either rise, or fall, or seem to run into each other, or lag behind, creating the impression of joy and celebration. Without its amazing asymmetry, St. Basil's Cathedral is simply unthinkable! Studying it, scientists came to the conclusion that the golden ratio predominates in it. If we take the height of the cathedral as one, then the basic proportions that determine the division of the whole into parts form the golden ratio series: 1: j: j 2: j 3: j 4: j 5: j 6: j 7, where j =0.618 In this division and contains the main architectural idea of creating the cathedral, common for all eight domes, uniting them into one composition.
Dissymmetry is a partial lack of symmetry, a disorder of symmetry, expressed in the presence of some symmetrical properties and the absence of others. An example of dissymmetry in an architectural structure is the Catherine Palace in Tsarskoye Selo near St. Petersburg. Almost all the properties of symmetry are fully maintained in it, with the exception of one detail. The presence of the Palace Church upsets the symmetry of the building as a whole. If we do not take this church into account, then the Palace becomes symmetrical. Dissymmetry
In modern architecture, techniques of both antisymmetry and dissymmetry are increasingly used. These searches often lead to very interesting results. A new aesthetics of urban planning is emerging. Concluding our conversation, we can state that beauty is the unity of symmetry and dissymmetry. So, the “sphere of influence” of symmetry (and therefore its antipode, asymmetry) is truly limitless. Nature - science - art. Everywhere we see the confrontation, and often the unity of two great principles - symmetry and asymmetry, which largely determine the harmony of nature, the wisdom of science and the beauty of art. Conclusions:
Ministry of Education of the Irkutsk Region
"Irkutsk Aviation College"
(GBPOUIO "IAT")
Project
in the discipline "Mathematics"
on the topic “Symmetry in architecture”
Completed:
1st year students
Groups PKS-15-2
Sharipov D.A.
Tolmachev M.V.
Kryuchkov V.V.
Supervisor:
Maksimova R.P.
Irkutsk 2015
Goal of the work
Get to know the main typessymmetry.
Identify how symmetry is used in
architectural structures.
Tasks
Describe the types of symmetry.Consider examples.
Learn to distinguish types of symmetry in
architecture of my hometown.
Symmetry
We call the same thing symmetryarrangement of equal parts in relation to
planes or lines. Symmetry
structure is one of the reasons for it
active influence on perception.
Asymmetry
From the point of view of mathematical conceptsasymmetry is just the absence of symmetry.
In architecture - symmetry and asymmetry are two opposing methods of natural
organization of spatial form.
Asymmetry
Asymmetrical compositions in progressarchitectural developments arose as
embodiment of complex combinations of life
processes and environmental conditions.
Specific forms of such compositions
grow as a result of unique
combinations of factors. (Fig.1)
Fig.1
Dissymmetry
This is a partial lack of symmetry, itsa disorder expressed in the presence of some
symmetrical properties and the absence of others. (Fig.2)
Fig.2
Dissymmetry
Absolute symmetry in large and complexstructures, strictly speaking, is impossible.
Complexity of functional systems
causes partial deviations from the main one,
defining the character of the composition
symmetrical scheme.
The simplest types of symmetry
Mirror symmetry (Fig. 3), symmetryleft and right (Fig. 4)
Fig.3
Fig.4
Mirror symmetry
This is a mapping of space onto itself, within which any point Z goes to
symmetrical to it relative to the plane α
point Z1. (Fig.5)
Fig.5
Central symmetry
In addition to mirror symmetrycentral or
rotational symmetry. In this case
transition of parts to a new position and
the formation of the original figure occurs
when this figure is rotated by a certain
angle around a point that is usually
called the center of rotation.
Axial symmetry
Central axial symmetry issymmetry about the vertical axis,
line of intersection of two (or more
number) of vertical planes of symmetry.
(Fig.6)
Fig.6
Axis of symmetry
In orthogonal drawings, the planesymmetry is depicted by a line, so it
often called the axis of symmetry. (Fig.7)
Fig.7
Axis of symmetry
An imaginary line dividing the body intotwo equal halves.(Fig. 8)
Fig.8 The highest degree symmetry
has a ball in the center of which
an infinite set intersects
axes and planes of symmetry. (Fig.9)
Fig.9
The meaning of symmetry in architecture
Symmetrical objects have highdegree of expediency, because
symmetrical objects have more
stability and equal functionality
in different directions.
Symmetry was used to create
religious and domestic buildings since ancient times
times From then until now
symmetry in human consciousness has become
an objective sign of beauty. Fig.10
Fig.11
Symmetry in Old Russian buildings
There are many things in ancient Russian architectureexamples of intuitive or conscious
the use of symmetry, this and
bell towers (Fig. 12), guard towers
towers (Fig. 13). A clear imprint of symmetry
later buildings also bear on them:
stone Russian churches (Fig. 14),
palaces (Fig. 15). Fig.12
Fig.14
Fig.13
Fig.15
Architectural structures of the city of Irkutsk
Sports Palace “Trud” - Symmetrical (Fig. 16)Musical Theater named after. N.M. Zagursky -
Symmetrical (Fig. 17)
House of Music of Denis Matsuev – Disymmetrical
(Fig.18)
Fig.17
Fig.18
Fig.16
Conclusion
Architecture is an amazing fieldhuman activity. It's cramped
intertwined and strictly balanced science,
technique art. Only proportionate
the harmonious unity of these principles makes
man-made structure
architectural monument, not subject to
time, like literary monuments,
sculpture, music.