Individual project on the topic: Symmetry in architecture. Symmetry in architecture “Architecture has three main things: beauty, tranquility and strength of the building. To achieve this, knowledge is the guide. Download ppt "Symmetry in Ar"

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
PKS-15-2 groups
Sharipov D.A.
Tolmachev M.V.
Kryuchkov V.V.
Supervisor:
Maksimova R.P.
Irkutsk 2015

Objective

Get to know the main types
symmetry.
Reveal how symmetry is used in
architectural structures.

Tasks

Describe the types of symmetry.
Consider examples.
Learn to distinguish the types of symmetry in
architecture of the native city.

Symmetry

Symmetry is what we call the same
arrangement of equal parts in relation to
planes or lines. Symmetry
structure is one of the reasons for its
active influence on perception.

Asymmetry

In terms of mathematical concepts
asymmetry is just the absence of symmetry.
In architecture, symmetry and asymmetry are two opposite methods of regularity.
spatial organization.

Asymmetry

Asymmetric compositions in progress
development of architecture arose as
the 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, its
a disorder expressed in the presence of
symmetrical properties and the absence of others. (Fig.2)
Fig.2

Dissymmetry

Absolute symmetry in large and complex
structures, strictly speaking, is impossible.
Complexity of functional systems
causes partial deviations from the main,
character-defining composition
symmetrical layout.

The simplest types of symmetry

Mirror symmetry (Fig. 3), symmetry
left and right (fig.4)
Fig.3
Fig.4

Mirror symmetry

This is a mapping of space onto itself, with
where any point Z goes to
symmetrical to it with respect to the plane α
point Z1. (fig.5)
Fig.5

Central symmetry

In addition to mirror symmetry
considered central 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 normally
called the center of rotation.

Axial symmetry

Central axial symmetry is
symmetry about the vertical axis,
line of intersection of two (or more)
numbers) of vertical planes of symmetry.
(Fig.6)
Fig.6

Axis of symmetry

In orthogonal drawings, the plane
symmetry is represented by a line, so its
often referred to as the axis of symmetry. (Fig.7)
Fig.7

Axis of symmetry

An imaginary line dividing the body into
two equal halves. (Fig. 8)
Fig.8

The highest degree of symmetry
has a ball in the center of which
intersect an infinite number
axes and planes of symmetry. (Fig.9)
Fig.9

The Importance of Symmetry in Architecture

Symmetrical objects have a high
degree of expediency
symmetrical objects have more
stability and equal functionality
in different directions.
Symmetry was used to create
religious and domestic buildings from ancient
times. From then until now
symmetry in the human mind has become
objective sign of beauty.

Fig.10
Fig.11

Symmetry in ancient Russian buildings

In ancient Russian architecture there are many
examples of intuitive or conscious
use of symmetry, this and
bell towers (Fig. 12), watchtowers
towers (Fig. 13). A clear imprint of symmetry
bear on themselves and later buildings:
stone Russian temples (Fig. 14),
palaces (Fig. 15).

Fig.12
Fig.14
Fig.13
Fig.15

Architectural buildings of the city of Irkutsk

Palace of Sports "Trud" - Symmetrical (Fig.16)
Musical Theatre. N.M. Zagursky -
Symmetrical (Fig.17)
House of Music Denis Matsuev - Dissymmetric
(Fig.18)
Fig.17
Fig.18
Fig.16

Conclusion

Architecture is an amazing field
human activity. It's tight in her
intertwined and strictly balanced science,
technique art. Only proportionate
the harmonious unity of these principles makes
man-made structure
monument of architecture, not subject to
time, like monuments of literature,
sculpture, music.

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 shapes. Two points lying on the same perpendicular to a given plane (or line) on different sides and at the same distance from it are called symmetrical with respect to this plane (or line). A figure is symmetrical with respect to a line (axis of symmetry) or a 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 lack of symmetry. Symmetry is axial and central. Axial example: Central example:

The presence of symmetry. The image on the plane of objects of the world around us has an axis of symmetry or a center of symmetry. Many tree leaves, flower petals are symmetrical about the middle stem.

We often encounter symmetry in art, technology, everyday life, furniture, chemistry, screw symmetry in nature ... symmetry in architecture and construction. The presence of symmetry.

Symmetry in architecture. The main techniques in creating architectural compositions are the combination of different volumes - high and low, rectilinear and curvilinear, the alternation of spaces - open and closed, the symmetry and asymmetry of the building. During construction, first of all, architects consider the symmetry of the building, since in case of an error the object may collapse.

An example of symmetry in architecture. In 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, the Gothic style arose. Gothic buildings are distinguished by an abundance of openwork, like lace, ornaments, sculptures, ornaments, therefore, both outside and inside, they give the impression of lightness and airiness. Windows, portals, vaults have a characteristic lancet shape. The facades of the buildings had a 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, Greek architectural orders. True, they applied them in a new way, more freely, with a departure from the ancient canons, in other proportions and sizes, in combination with other architectural elements. Renaissance buildings were austere in form, with clear, straight lines. The symmetry of the facades is preserved. back

Style - classicism. All buildings built in the style of classicism have clear rectilinear forms and symmetrical compositions. Against the background of smooth walls, porticos and colonnades protrude, which give the buildings a solemn monumentality and splendor. Decorative decoration of bas-reliefs and statues enliven the appearance of buildings. The masters of classicism consciously borrowed the techniques of antiquity and the renaissance, applied 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 a central symmetry, in general it has neither mirror nor rotational symmetry. The symmetrical architectural details of the cathedral whirl in their asymmetrical, chaotic dance around its central tent: they either rise, or fall, or, as it were, run into each other, or lag behind, creating an 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 LV - This amazingly symmetrical world.

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Slides captions:

St. Petersburg at a geometry lesson Types of symmetry in architecture

Axial symmetry Two points are said to be symmetrical with respect to a line if this line passes through the midpoint 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 in St. Petersburg. It was built in 1818-1858 according to the project of O. Montferan. Height 101.5 m.

Catherine's 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 the late Baroque. During the war, the palace was badly damaged. Its restoration took many years.

Central symmetry Two points are said to be symmetric with respect to 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 GRATES OF ST.

Belinsky Bridge In the 18th century, 7 stone drawbridges of the same type were built on the Fontanka. Only two of them have survived in their original form. One of them is Simeonovsky Bridge (Belinsky Bridge)

Fragment of the lattice of the Summer Garden

MIRROR SYMMETRY Mirror symmetry (symmetry with respect to the plane) is such a mapping of space onto itself, in which any point M passes into a point N symmetrical to it with respect to the plane.

Palace and Park Ensemble of Oranienbaum

Mirror symmetry in the gardens and parks of St. Petersburg

In this picture you can see different types of symmetry. The Marble Palace was built in 1768-1785 according to the project of A. Rinaldi, 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 of Suvorov students of the 8th grade "Symmetry in the architecture of Moscow"

The material consists of an explanatory note, goals and objectives. As well as daily practice planning....

Department of Education of the Vologda Region

budgetary professional educational institution

Vologda region

"Kadui Energy College"

INDIVIDUAL PROJECT

IP. 23.02.03.2016.

Topic: Symmetry in architecture

Profession: Auto mechanic

Is done by a student

group #171:

Garunov Nikolai Viktorovich

FULL NAME.

Checked:

Kormacheva E.E..

"___" ____________ 2016

Defended the work with an assessment of ________________

2016

Content

Introduction ………………………………………………........................... ..........2

Symmetry. Types of symmetry………………………………..………........ 4-7

Symmetry in architecture ……………………………………………… .8-11

Symmetry in the architecture of buildings in Kaduy settlement……… …...……………….......12

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

Literature………………………………………………………. ………….......fifteen

Introduction.

“Symmetry is the idea by which man

for centuries tried to comprehend and create order,

beauty and perfection.

Herman Weil.

The world we live in 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 in the meaning of "harmony", "beauty". Indeed, in translation from Greek, this word means "proportionality, uniformity in the arrangement of parts, proportionality."

When we took the topic “Symmetry” in mathematics lessons, very little time was allotted for it, but this topic seemed interesting to me, and I decided to take it for research. I wanted to learn more on this issue, because I have heard this term more than once on other objects and in everyday life. Having started the research, 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 the 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 village.

Use the results of the study 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 areas of modern science without exception. The principles of symmetry play an important role in physics and mathematics, chemistry and biology, engineering and architecture, painting and sculpture, poetry and music. The laws of nature that govern the inexhaustible in its diversity of the picture of phenomena, in turn, obey the principles of symmetry. Therefore, the problem of this study is relevant in modern conditions.

1 . Symmetry. Symmetry types.

There is an old parable about Buridan's donkey. One philosopher named Buridan had a donkey. One day, leaving for a long time, the philosopher placed in front of the donkey two absolutely identical armfuls of hay - one on the left and the other on the right. The donkey could not decide which armful to start with, and starved to death. The parable of the donkey is, of course, a joke. However, take a look at the image of the balanced scales. Don't the balance of the scales remind one of the parable of Buridan's donkey? Indeed, in both cases, left and right are so much alike that neither one nor the other can be preferred. 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 the sculptorPythagoras Regius , who lived in the city of Regul. Deviation from symmetry he defined by the term"asymmetry" .

Symmetry in geometry is a property of geometric shapes. Two points lying on the same perpendicular to a given plane (or line) on different sides and at the same distance from it are called symmetrical with respect to this plane (or line).

Symmetry types.

Axial symmetry.

A transformation in which each point A of a figure (or body) is transformed into a symmetrical one with respect 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 during the transformation of symmetry about the axisl figure Ftransforms into itself, then it is called symmetric with respect to the axisl , a axis l called the axis of symmetry.

central symmetry.

Transformation that translates each point A of the figure (body) into point A " , symmetrical to it about the center O, is calledcentral symmetry transformation or simply central symmetry.

Point O is calledcenter of symmetry and is immovable. This transformation has no other fixed points.

If, during the transformation of central symmetry about 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 about the plane (mirror symmetry).

In geometry, there is another kind of symmetry -symmetry about the plane.

If a symmetry transformation with respect to a plane transforms a figure (body) into itself, then the figure is called symmetric with respect to the plane, and the given plane is called the plane of symmetry of this figure.

In some sources, this symmetry is called mirror. And the mirror not only copies the object, but also swaps the front and back parts of the object with respect to the mirror. In comparison with the object itself, its trans-mirror twin turns out to be inverted along the direction perpendicular to the plane of the mirror.

Examples of figures - mirror reflections of one another - can serve as the right and left hand of a person, right and left screws, parts of architectural forms, some natural crystals and ornaments, some insects.

Portable (broadcast) symmetry.

This kind of symmetry consists in the fact that the parts of the whole form are organized in such a way that each next 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 carry or period .

Portable symmetry is usually used when building 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 building, the ability to design and create cities, residential buildings, public and industrial buildings, squares and streets, parks. In many cities of the world you can find churches, palaces and mansions, modern theater buildings, libraries in front of which you want to stop and take a closer look at them. 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, 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 the life and activities of people.

Even in ancient times, the tasks of architecture were determined by three qualities - usefulness, strength, beauty. The well-known human desire for beauty inspires the creative imagination of the architect to search for ever new unusual architectural forms, the uniqueness of the appearance and the brightness of the artistic image of the building.

Each building makes its own impression: one has a solemn,

festive appearance, another - strict, the third - lyrical. Architectural monuments belonging to different eras and countries differ from each otherin appearance or 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 a clear distribution and repetition in a certain order of the volumes of buildings or individual architectural forms on the building (columns, windows, reliefs, etc.). The predominance of elements of vertical rhythm - columns, arches, openings - creates the impression of lightness, upward aspiration.

On the contrary, the horizontal rhythm - cornices, friezes, belts and - gives the building the impression of squatness, stability.

In architecture, as in other forms of art, there is a concept of style, i.e. historically established set of artistic means and techniques.

Most common in architecturemirror symmetry. She is subordinate to buildki of ancient Egypt and the temples of ancient Greece,amphitheaters and triumphalnye arches of the Romans, palaces and churches of the Renaissance,as well as numerous buildings withtemporary architecture.

Each detail in a symmetrical system exists as a twin of its obligatory pair, located on the other side.ron axis, and thanks to this it can raceviewed as part of the whole.

Center-axial symmetry is less commonly usedwas called in the history of architecture. obey hernena ancient round temples and builtin imitation of them park pavilions Cent axial symmetry also determinesthe shape of some architectural details -such as columns and their capitals.

Other types of symmetry in architecturerarely used, but they can bothsinter practical and artistic purposeconformity of form.

To rarely used speciessymmetry also applies to helical. She ishas long been used for building elementsniya - spiral staircases and ramps, twisted column stems.

Dissymmetry.

Absolute symmetry in large and complex structures, strictly speaking, is impossible. The complexity of functional systems causespartial deviations from the main one, I determinethe general nature of the composition of the symmetrical schemewe. Broken, partially upset simwe call metricsdissymmetry .

Dissymmetry is a phenomenon that is widespreadstrange in nature. She is characteristicand for a person. The person is dissymmetricaldespite the fact that the outlines of his body haveplane of symmetry. Narrative dissymmetryis in the best possession of one of the hands, in the bearingmetric arrangement of the heart and many othershy organs, in the structure of these organs.

free locationparts within a symmetrical schemebut for Russian folk architecture and givesspecial attraction and individualitythe value of his works.

Partially broken symmetrythe complexity of life processes and at the same timeat the same time serving as an artistic mediumthe first expression of this complexity, often encounteredoften found 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 compoposition is not at all covered by this negativedefinition. In architecture, symmetry and asymmetry are two opposite methods.regular organization of spatialforms. Subjugated by my own innerlaws, asymmetry by no means exhaustsby breaking the symmetry. Unity is the goal of building an asymmetric system sothe same as symmetrical, but it is achievedit is in a different way. Identity of parts and their locationposition is replaced by visual balance.Asymmetric compositions in progressdevelopment of architecture arose as the embodimentcomplex combinations of life processesand environmental conditions. Specificthe forms of such compositions grow as rethe result of a unique combination of factors. Asymmetry is therefore individual, while in the very principle of symmetry liescommonality, a sign that connects all structuresions having this type of symmetry.

Subordination of parts - the main environmentthe property of combining an asymmetric composition.Subordination is manifested not only in correlationsizing, arranging silhouette and pla static accents, but in the direction of systhemes of spaces and volumes to the main partsbuilding or ensemble, the location of which does not coincide with the geometric center.

Asymmetric composition can warehousesbe made up of symmetrical parts, connections betweenthat don't follow the rulessymmetry. Many natural forms also have this character - symmetries are subject toparts, the whole is asymmetrical (example - leavesand the tree as a whole).

Architecture - amazing area of ​​human activity. Science, technology and art are closely intertwined and strictly balanced in it. Only a proportionate, harmonious combination of these principles makes a building erected by man an architectural monument.

3. Symmetry in the architecture of buildings in Kaduy village.

An example of an amazing combination of symmetry and dissymmetry is the Church of Philip of Irap.Considering the Church of Philip of Irap, I mentally drew the axes of symmetry and measurement. The church has well-balanced proportions, strict symmetry of the facades; looking at it creates a feeling of clarity and balance.

Conclusion: According to the architectural canons of the construction of Russian churches, the laws of symmetry were used in the appearance of the church of Philip of Irapsky.

In architecture, axes of symmetry are used as a means of expressing architectural intent. An example of the use of axial symmetry in architecture is the building of the kindergarten "Kid".

Dissymmetry is broken, partially detuned symmetry. An example of dissymmetry is the building of the station, the building of the Victoria swimming pool, the building of the medical center.

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 show different types of symmetry.

Studies have shown that all types of symmetry are used in the design and construction of architectural structures and the design of building facades.

Symmetry resists chaos, disorder. It is present in our

life is literally in everything, but we are so used to it that we do not notice

this. But no matter how we treat her, she is in our lives, adding to

her peace, tranquility and the state of something not alien to the eye.

I believe that no matter how art develops in the future, the elements

symmetries in it will still prevail and be improved.

Literature.

I know the world. Moscow monasteries and temples: an encyclopedia. OOO

Astrel Publishing House 2006

The 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.