Urban space is a world of geometric bodies. Look around. Stately prisms rise everywhere. Sometimes powerful pyramids appear in front of your eyes. Here and there, catchy Platonic and Archimedean solids that amaze the imagination flicker. Architectural buildings are mostly polyhedra, as well as their simple and complex combinations. And this is not a modern trend. So it was. Geometry and human needs for comfort, beauty and self-expression dictate their own rules.

Geometry in architecture

Science and art have gone hand in hand since ancient times. Geometry and architecture were born, developed and improved together: from the simplest residential structures and unspoken rules to carefully designed masterpieces and clear laws. The strength, beauty and harmony of buildings at all times was provided by geometry. In the architecture of cities, its rules were combined with the needs and imagination of man.

Rectangular buildings are stable and multifunctional, so there are more of them on the streets than others. Pyramids are inferior to them in practicality, but they look more impressive. They are built in exceptional cases. With Platonic and Archimedean bodies, people dilute the architectural forms that have become familiar. Designing buildings that take the form of these polyhedra is, in most cases, a difficult task. But art is more important. Therefore, architects make a lot of efforts to cope with it. And as a result, they create world masterpieces. So, let's analyze each case on a separate example.

straight prism

Straight prisms are the most common polyhedra in the architecture of any city. These are small "Khrushchev", multi-storey buildings, as well as massive skyscrapers.

A typical example of a direct prism is the world-famous hexagonal Pirelli Tower, built in Milan in 1960. The skyscraper was distinguished by an unprecedented height for those times - 127 meters. And contained 32 floors. The reinforced concrete giant surpassed even the Milan Cathedral, which was crowned with a statue of the Madonna, which caused great public outrage. After all, the building turned out to be higher than the shrine. To smooth out dissatisfaction, P. L. Nerva and J. Ponti, who designed the skyscraper, had to place a copy of it on the roof of their creation.

The tower was built by order of the famous Pirelli tire company, on the very spot where its first factory was located. The graceful building with a facade of aluminum and glass became a symbol of the revival of the Italian economy after the war and received the title of the most elegant skyscraper in the world.

tilted prism

Another not less remarkable architectural object is located in Madrid. Towers "Gate to Europe", having the form of inclined prisms, gather around them no less tourists than the Pirelli building. Skyscrapers 114 meters high lean towards each other at an angle of 15 °.

It is to this architectural feature that they owe their name. American engineers and architects F. Johnson and J. Burgey broke the stereotype of the usual appearance of high-rise buildings, and the Gateway to Europe towers became the first inclined reinforced concrete giants in the world and one of the most popular attractions in Madrid.

Correct pyramid

Prism buildings compete with architectural objects in the form of truth, not in quantity, but in popularity.

If an architect plans to create a structure of this form, then it will certainly become a real masterpiece. Maybe it's all about the magic of the ancient Egyptian pyramids, built more than 4 thousand years ago for the burial of the pharaohs? Who knows, however, the "Palace of Peace and Accord" in Astana, the capital of the Republic of Kazakhstan, is an outstanding example of this.

An architectural creation made of aluminum, glass and steel was created according to the principles of the Fibonacci Golden Ratio. It reaches a height of 61.8 meters and has the same base width. The pyramid is known for its elevators, which do not move vertically, but diagonally to the top of the structure. The palace serves as a meeting place for leaders of world religions and is considered a symbol of friendship between different faiths and nations. Anyone can visit it: get acquainted with the culture of Kazakhstan and the world as a whole.

Truncated pyramid

Architectural buildings can take the form of not only regular pyramids, but also truncated ones. The buildings look more massive due to their seemingly cut tops. Truncated is the Mayan Indian built in the ancient city of Chichen Itza in Mexico. It reaches a height of 30 meters and a width of 55. It consists of 9 square blocks, and there is a temple on its top. 4 stairs lead to it: one from each side of the world. In the days of spring, a mysterious visual effect appears on the pyramid: a deity woven from the sun's rays, a feathered Serpent, in whose honor the pyramid was erected, glides along its steps. In the spring it creeps up, and in the fall - down.

Such polyhedra are considered rare in modern architecture. An example is the building of the Slovak radio. It is an inverted truncated pyramid. The building looks spectacular and, despite the outward gloom, attracts tourists.

regular polyhedron

Platonic solids or in architecture in their pure form are also extremely rare. And these are mostly hexahedra. So, in China, an original Cube Tube complex was built, the main element of which is an office building in the shape of a cube.

Sako Architects filled its façade with an incredible array of square windows punctuated by terraces. Due to this, the structure looks spectacular and seems weightless.

The original project of the cubic-shaped mountain hotel Cuboidal Mountain Hut was proposed by a team of Czech architects Atelier. A huge hexahedron, according to him, will be built of wood, and sheathed with aluminum panels on top. and walls, a system of accumulation and purification of rainwater, as well as electric generators will make it possible to live in it regardless of the outside world. The cube looks like a giant ice floe that has fallen from high mountains. One of its peaks is directed to the sky, the other seems to have gone under the snow. If the project is, it will become a real sensation.

Semi-regular polyhedron

To create non-standard objects, Archimedean solids (or, in other words, semi-regular polyhedra) are used. In the architecture of various cities, such buildings become real magnets for tourists. Pay attention to the National Library of Belarus. It has rightfully earned the status of one of the most original buildings in the world because of its rhombicuboctahedron shape. This Archimedean solid consists of 18 squares and 8 triangles.

Because of this shape, the library is often compared to a diamond or diamond. The building becomes especially similar to these gems when it lights up at night. The "Belarusian diamond" project appeared in the 1980s and even became the winner of the all-Union competition. But it was only at the beginning of the 21st century that it was possible to bring it to life. The library has 23 floors and reaches a height of 75 meters. In addition to a huge book fund and reading rooms, the building houses an observation deck with a magnificent view of Minsk, a room for children, and a restaurant.

Non-convex polyhedron

The urban landscape requires constant changes, so the use of polyhedrons in architecture has recently acquired a slightly different character.

Truly human imagination has no limits. Innovative architects are breaking the stereotype of the beauty of buildings by using now non-convex geometric bodies in their projects. All of their points lie on opposite sides of each face, which allows you to achieve a stunning effect.

A typical example would be the Seattle Public Library. The architect R. Koolhaas tried to make the building as futuristic as possible. The broken, asymmetric architectural forms of the eleven-story building made of glass and steel mesh did not appeal to all residents of the city, and for many they simply caused indignation. The library even got the nickname: "a huge ventilation shaft." But she also has a lot of fans. The architectural features of the building attract an unprecedented number of visitors, and many come to see it from other cities and countries.

Polyhedra and architectural styles

Each architectural style has its own striking features. And polyhedrons emphasize them favorably. Massive pyramids highlighted the power of Ancient Egypt. Now the buildings made in the form of this polyhedron are known all over the world, the attractiveness of the style is so strong. The shape of the prism that skyscrapers have is characteristic of modernism. They embody the ideas of internationality and functionality. Compare the Pirelli Tower in Italy and the Metlife Building in America. Regular and semi-regular polyhedrons in architecture are typical of postmodernism, as they oppose the everyday life of urban buildings.

Non-convex polyhedra are used in deconstructivism to create kinks and destructive shapes that bring a pleasant dissonance to the ordinariness of rectangular buildings. Architects and engineers turn the familiar on its head, changing styles. But our space still remains filled with immutable and eternal geometric bodies, be it pyramids or prisms.

students

"Schoolchildren of the city - scienceXXIcentury"

Section Mathematics

Research work

Geometry in architecture

Performed:, a student of class 9B of the MOU "Lyceum No. 31"

Supervisor:, teacher

mathematics

g. o. Saransk 2009

Introduction
1. Geometric shapes in architectural structures
1.1. History of Geometry in Architecture
1.2. The main properties of architectural and spatial forms
2. A variety of geometric shapes in different architectural styles
3. Interesting architectural structures of my city
Conclusion
Bibliography

Introduction

None of the arts is so closely related to geometry as architecture. Everyone should understand architecture, because it surrounds and accompanies us all our lives. The great architect Le Corbusier said: “The world around us is a world of pure, true, flawless geometry in our eyes. Everything around is geometry.

Tasks and goals of the work:

Reveal the relationship between the properties of architectural structures and geometric shapes

Formulate an idea of ​​the objectivity of mathematical relations that manifest themselves in architecture as one of the forms of reflection of reality

Consider geometry as a theoretical basis for creating works of architectural art

Expand your general cultural horizons by getting to know the best examples of works of architectural art

The structure of sections is connected with the general idea of ​​the work.

The main part consists of three chapters. The first deals with the main properties of architectural and spatial forms. The second chapter highlights the characteristic geometric forms inherent in various architectural styles. The third section presents an overview of the notable architectural structures of the city of Volzhsky with comments on their architectural styles and forms.

During the work the author used a number of literary sources. Among them are textbooks for higher and secondary educational institutions related to the history of architecture and the methodology of architectural design (Barkhin architectural design. - M .: Stroizdat, 1993; Gulyanitsky civil and industrial buildings in five volumes. Volume I. History of architecture. - M .: Stroizdat, 1984; Ilyin understanding of architecture. - M .: Stroizdat, 1989; Kilpe of architecture. - M .: Higher school, 1989; Orlovsky: textbook for universities. - M .: Higher school, 1984). In addition, information was used on the topic of the abstract from popular science and research literature by various authors (Zaslavsky is architecture. - Minsk: Narodnaya asveta, 1978; Encyclopedia for children. Volume 7. Art. Part two. Architecture, fine and decorative arts XVII - XX centuries - M.: Avanta +, 1999) and Internet resources.

Great importance in the work is given to illustrative material.

1. Geometric figures in architectural structures.

“Centuries have passed, but the role of geometry

hasn't changed. She still

remains the grammar of the architect"

Le Corbusier

1.1. History of geometry in architecture.

The first geometric concepts arose in prehistoric times. Man observed various forms of material bodies in nature: the forms of plants, animals, mountains, meanders of rivers, the circle and crescent of the moon, etc. However, he not only passively observed nature, but also practically mastered and used its riches. In the process of practical activity, he accumulated geometric information. Material needs prompted people to make tools, hew stones and build dwellings, sculpt earthenware, string a bow, etc.

The first architectural structures had a religious purpose. The ancient pagan tribes used obelisks (menhirs, dolmens or cromlechs) for rituals (Fig. 1). The main problem in the construction of the obelisk was vertical instability: the level of development of science did not allow processing building material (most often stone) that had an uneven base. This problem was solved simply: the obelisk was placed in a pre-dug hole.

Thus, the practical activity of a person served as the basis for a long process of developing abstract concepts, discovering the simplest geometric dependencies and relationships.

The first information about the successes of geometry that has come down to us is connected with the problems of land surveying, calculations of volumes (Ancient Egypt, Babylon, Ancient Greece). Already at that time, the abstract concept of a geometric body (figure) arose as an object that retains only the spatial properties of the corresponding physical body, devoid of all other properties not related to the concept of distance, length, etc.

Thus, since its inception, geometry has studied some properties of the real world. The connection between geometry and the real world has been preserved throughout its development, while the degree of abstraction of the object of study has risen to an ever higher level.

The geometric information and problems contained in the papyri that have come down to us are mainly related to the calculation of areas and volumes. They do not contain any indication of the methods of derivation of the rules that the Egyptians used to calculate them. Moreover, approximate calculations were often used. Geometry, as a practical science, was used by the Egyptians to restore land after each flood of the Nile, during various household works, in the construction of irrigation canals, grandiose temples and pyramids, and in carving the famous sphinxes from granite. The transition from the simplest buildings to complex architectural structures was carried out slowly, with the development of measuring instruments, materials, and mechanisms necessary for construction.

1.2. Basic properties of architectural and spatial forms.

Architectural structures consist of individual parts, each of which is built on the basis of certain geometric shapes or on their combination. In addition, the form of any architectural structure has a certain geometric figure as its model. A mathematician would say that this structure "fits" into a geometric figure.

Of course, one can speak about the correspondence of architectural forms to geometric figures only approximately, digressing from small details. Almost all geometric shapes are used in architecture. The choice of using one or another figure in an architectural structure depends on many factors: the aesthetic appearance of the building, its strength, ease of use, etc. The main requirements for architectural structures, formulated by the ancient Roman architectural theorist Vitruvius, are: the beauty". Each geometric figure has a unique, in terms of architecture, set of properties.

For example, in Belarus, a cone-shaped hotel building near the international airport was designed. The cone transforms the course of the sound wave entering it. An example of using this property would be a regular megaphone. This feature of the cone has proven to be extremely useful in reducing noise in hotel rooms. Sometimes, when trying to solve certain ideological problems with the help of architecture, project authors get a negative result. An example is the building of the theater of the Soviet Army, built in Moscow during the Soviet era. Trying to bring the architectural image as close as possible to the name of the theater, the authors gave the building the shape of a five-pointed star. As a result, this led to significant difficulties in the layout of the premises and additional costs. And only the birds could see the ideological five-pointed form of the theater.

Strength is one of the most important qualities of architectural structures. It depends on the properties of the materials from which they are created, and on the design features. And the strength of the structure of the structure as a whole is directly related to the basic geometric shape of this structure. The most durable architectural structures of ancient times are the Egyptian pyramids (Fig. 2, 3).

Rice. 2 Fig. 3

Rice. 4 Fig. 5

They are known to have the shape of regular quadrangular pyramids. It is this geometric shape that determines the greatest stability due to the large base area. On the other hand, the shape of the pyramid ensures that the mass decreases as the height above the ground increases. It is these two properties that make the pyramid stable and especially durable. The "rationality" of the geometric shape of the pyramid allows you to choose an impressive size for this structure, gives the pyramid greatness, evokes a feeling of eternity.

Currently, frame structures, which are used in the construction of modern structures made of metal, glass and concrete, have maximum strength. Famous towers can serve as examples of such structures: the Eiffel Tower (Fig. 4) in Paris and the television tower on Shabolovka (Fig. 5) in Moscow. The TV tower on Shabolovka, built according to the project, consists of several parts of one-sheeted hyperboloids stacked on top of each other. Moreover, each part is made of two families of straight beams.

Rice. 6 Fig. 7

https://pandia.ru/text/78/183/images/image008_15.jpg" align="left" width="266" height="336 src="> Hyperbolic paraboloid (Fig. 7) - this is a surface which in section u1080 has parabolas and a hyperbola. Its architects briefly call it gipar . It was gipar that F. Candela used in the construction of the Evening Hall in Acapulco (Mexico) (Fig. 8).

https://pandia.ru/text/78/183/images/image010_12.jpg" align="left" width="354" height="204 src="> Fig. 8 Fig. 9

A one-sheeted hyperboloid and a hyperbolic paraboloid can be formed by moving two straight lines. The simplest non-planar surfaces - cylindrical (Fig. 10) and conical (Fig. 9) can be built by moving one straight line.

2. A variety of geometric shapes in different architectural styles.

The development of architecture to a large extent depends on the aesthetic ideals and artistic needs of society.

The aesthetic features of architectural structures changed during the historical process and were embodied in architectural styles. It is customary to call a style a set of basic features and signs of architecture of a certain time and place. The geometric forms characteristic of architectural structures in general and their individual elements are also signs of architectural styles. Let's try to create a system of matching geometric shapes and basic architectural styles.

https://pandia.ru/text/78/183/images/image012_10.jpg" align="left" width="176" height="280 src="> Fig. 11 Fig. 12

Of course, the post-and-beam structure was inferior to the pyramid in terms of stability and weight distribution, but it made it possible to create internal volumes and, of course, was an outstanding achievement of human thought. The main drawback of this design was the poor work of the stone in bending (Fig. 14) (that is why there are so many columns in the temple of Amun at Karnak (Fig. 13).

https://pandia.ru/text/78/183/images/image014_8.jpg" align="left" width="331" height="360 src=">

Rice. 13 Fig. fourteen

https://pandia.ru/text/78/183/images/image016_6.jpg" width="325" height="255">

Term "Roman style" (Fig. 17) is conditional and arose in the first half of the 12th century, when a connection between medieval and ancient architecture was discovered.

Circular" href="/text/category/tcirkulyar/" rel="bookmark">circular arches (Fig. 16). The figures are located within vertical surfaces, and the composition does not give a sense of depth. Different scales of the figures attract attention.

Christ is always greater than the angels and apostles, who in turn are greater than mere mortals. The figures are in a certain relationship with architectural forms. The images in the middle are larger than those in the u1085's corners. Figures of squat proportions are placed on the friezes, and elongated ones on the bearing parts. Such a correspondence of the image of architectural outlines is one of the characteristic features of the Romanesque style. Monuments of Romanesque art are scattered throughout Western Europe. Most of them are in France, which for centuries was not only the center of the philosophical and theological movement, but also the wide spread of heretical teachings. In architecture and sculpture, there is the greatest variety of forms and constructive solutions.

Romanesque art was replaced Gothic. Gothic buildings are distinguished by an abundance of openwork lace details in the form of cylinders, pyramids, cones (Fig. 18, 19). Both outside and inside they give the impression of lightness and airiness.

Windows, portals, vaults have a characteristic lancet shape. The building facades are axially symmetrical. The lancet arch (diagram in Fig. 21) introduced two design innovations into Gothic architecture. Firstly, lancet vaults began to be made on ribs - stone ribs carrying independent parts of the vault - stripping. The ribs serve as a skeleton of the vault, they take on the main load. As a result, the design of the vault becomes more flexible: it can withstand those deformations that would be fatal for a monolithic vault. Thus, the ribs were the prototype of the modern frame structure.

The internal supports and walls of the Gothic cathedral had only one vertical load - that's why they could be made thinner and more elegant. Since the vertical load of the Gothic temple was carried by a bundle of ribs, the central walls as load-bearing structures turned out to be unnecessary, and they were replaced with colored stained-glass windows.

Rice. 20 Fig. 21

Gothic structures of XII-XV echo modern architectural structures, in which a thin reinforced concrete frame took over the load, and the walls became glass.

Gothic, which arose after the Romanesque style, became more cheerful. In all Gothic architectural structures, there is a desire to rise up, to the sky, away from the hustle and bustle of the world. Pyramids and cones, widely used in their forms, corresponded to the general idea - aspiration upwards. Characteristic details for Gothic structures are the lancet arches of the portals, which replaced the semicircular arches, which, from the point of view of geometry, are more complex. The lancet arch consists of two arcs

circles of the same radius. In Figure 21, a schematic representation of a lancet arch is visible above the horizontal line.

Rice. 22 Rice. 23

Architects of different eras had their favorite details, which reflected certain combinations of geometric shapes. For example, the architects of Ancient Russia often used the so-called tent coverings for the domes of churches and bell towers. These are coverings in the form of a tetrahedral or polyhedral pyramid.

https://pandia.ru/text/78/183/images/image025_4.jpg" align="left" width="288" height="203 src=">Baroque" href="/text/category/barokko/ " rel="bookmark">Baroque replaced the Renaissance. It is distinguished by an abundance of curvilinear forms. The grandiose architectural ensembles (a group of buildings united by a common design) of palaces and villas built in the Baroque style amaze with an abundance of decorations on the facades and inside the buildings. Straight lines are almost non-existent. Architectural forms, creating the impression of constant mobility, are bent, piled on top of each other and intertwined with patterns, decorations, sculptures. This magnificent and magnificent style did not last long and already in the second half of the 18th century. it is replaced by a strict and majestic classicism.

Rice. 25 Fig. 26

Classicism is characterized by clarity of form. All buildings built in this style have clear rectilinear forms and symmetrical compositions (Fig. 25). The techniques of antiquity and renaissance are deliberately borrowed, orders with antique proportions and details are applied. Simplicity and at the same time monumentality, which affirmed the power and strength of the state, the value of the human person, are combined with amazing harmony in this style.

Modern appeared at the beginning of the 20th century as an attempt to get rid of the long imitation of antiquity, as a desire to create new forms from new materials - metal, glass, concrete, ceramics. The search for new forms and the development of new materials led to new types of compositions (Fig. 27).

The style does not have strict symmetrical designs. On fig. 26 shows the building of the name club in Moscow. This building was built in 1929 according to the design of the architect Melnikov. The base part of the building is a non-convex straight prism thanks to the ledges that are filled with vertical rows of windows. At the same time, giant overhanging volumes are also prisms, only convex.

https://pandia.ru/text/78/183/images/image029_2.jpg" width="217" height="181">

https://pandia.ru/text/78/183/images/image032_3.jpg" width="229" height="170">

Rice. 31 Fig. 32

https://pandia.ru/text/78/183/images/image034_3.jpg" width="174" height="290 src=">

Rice. 33 Fig. 34

https://pandia.ru/text/78/183/images/image036_1.jpg" align="left" width="232" height="191 src=">

Rice. 35 Fig. 36

So, for example, the most modern buildings of the city are made in the style of " high tech". These are mainly trade, technical service, and markets enterprises. They are characterized by a large area of ​​glazed surface, openwork forms of metal structures, in the form of pyramids, cylinders, polygons. Examples are the Ministry of Finance (Fig. 31, 32), Internet House (Fig. 30), greenhouse buildings (Fig. 35), Wedding Palace (Fig. 29), Globus store (Fig. 34), Ice Palace ( fig.36), sports and entertainment complex (fig.33).

Rice. 36 Fig. 37

Rice. 38 Fig. 39

In addition, buildings of the classicism style are present in Saransk. They are located mainly in the old part of the city. Examples of this style are the museum of local lore (Fig. 38), elements of the park area (Fig. 39), the national museum (Fig. 40), the building of the House of Unions (Fig. 36), the House of Soviets (Fig. 37).

Rice. 41 Fig. 42

The Art Nouveau style is represented by the buildings of the national theater (Fig. 42), the railway station (Fig. 41).

Representatives of the Russian-Byzantine style are the buildings of the churches of the Ushakov Temple (Fig. 43), the Church of St. Nicholas the Wonderworker (Fig. 44)

https://pandia.ru/text/78/183/images/image045_1.jpg" align="left" width="252" height="189 src=">

Rice. 43 fig. 44

Conclusion

As a result of the work done, it turned out that geometry is directly related to architecture - geometry is an indispensable part of architecture, one of its foundations.

Geometric forms determine the aesthetic, operational and strength properties of architectural structures of different times and styles. Moreover, each architectural style is characterized by a certain set of geometric shapes of buildings and structures in general and their individual elements. With the development of building technologies, the possibilities of using geometric shapes are expanding. On the example of the city of Saransk, various architectural styles and their geometric properties were analyzed.

Geometry was considered as a theoretical basis for creating works of architectural art. Ideas were formulated about the objectivity of mathematical relations that manifest themselves in architecture as one of the forms of reflection of reality.

Bibliography

1) Atanasyan: textbook for 7-9 grades of secondary school. – M.: Enlightenment, 1990.

2) Bartenev and construction in architecture. - L. Stroizdat, 1968

3) Barkhin architectural design. – M.: Stroizdat, 1993.

4) Bashlykova T. Volzhsky 50. Chronicle. Developments. Fate. - Volgograd: Publisher, 2003.

5) Great Soviet Encyclopedia (CD).

6) Voloshinov and art - M .: Education, 2000

7) Gulyanitsky civil and industrial buildings in five volumes. Volume I. History of architecture. – M.: Stroizdat, 1984.

8) Zaslavsky is architecture. - Minsk: People's Asveta, 1978.

9), Zinoviev's Egyptian pyramids. – Vladimir, 1999

10) Ilyin understanding of architecture. – M.: Stroizdat, 1989.

11) Internet resources

12) Kilpe architecture. - M .: Higher School, 1989.

13) Orlovsky: a textbook for universities. - M .: Higher School, 1984.

14) Encyclopedia for children. Volume 7. Art. Part two. Architecture, fine and decorative applied arts of the 17th - 20th centuries. – M.: Avanta+, 1999

Fifth Lyceum Scientific and Practical Conference "Knowledge and Creativity"

Physics mathematics

Topic: "Architecture in geometric shapes"

research project

Student 9 "A" class MAOU

"Lyceum №21"

Supervisor:

Krotova Irina Leonidovna,

mathematic teacher

Table of contents

Relevance

In our time, cities and countries are increasingly built up. New buildings are coming up. New architects appear, new directions in architecture appear. As Louis Henry Sullivan said: "Architecture is the art that affects a person most slowly, but most firmly." Our outlook and mood depends on what is happening in the city and how it looks. And it seems to me that any building or structure is built on the basis of geometric shapes and combinations of geometric bodies. And none of the arts is not so closely connected with geometry as architecture. Everyone should understand architecture, because it surrounds and accompanies us all our lives.

Hypothesis

All the buildings that surround us are geometric figures; on the one hand, they are abstractions from real objects, and, on the other hand, they are prototypes, models of the shape of those objects that the architect creates.

Targets and goals:

Target:

Consider what buildings are, and what geometric shapes they consist of

Tasks:

Explore the history of geometry and architecture

Find geometric shapes in buildings:

In Russia;
In own city

Find contemporary Russian architects

Create your building in geometric shapes

Theoretical part

“The world around us is a world of pure, true, flawless geometry in our eyes. Everything around is geometry. Le Corbusier

Geometry is a branch of mathematics that studies spatial relations and forms, as well as other relations and forms similar to spatial ones in their structure.

Architecture is the art of modeling the human environment and designing people's behavior in this environment, through a special functional and artistic organization of space and form, artistic work with plastic elements, colors.

Story

It is traditionally believed that the founders of geometry as a systematic science are the ancient Greeks, who adopted the craft of land surveying and measuring the volumes of bodies from the Egyptians, and turned it into a rigorous scientific discipline. Greek scientists, based on the discovery of many geometric properties, were able to create a coherent system of knowledge in geometry. Geometric science was based on the simplest geometric properties taken from experience. The remaining provisions of science were derived from the simplest geometric properties with the help of reasoning. This entire system was published in its final form in Euclid's Elements around 300 BC. The very first proofs of geometric statements appeared in the works of Thales and, apparently, used the principle of superposition, when the figures, the equality of which must be proved, were superimposed on each other.

Thanks to the great Archimedes, who was able to calculate the number Pi, and was also able to determine how to calculate the surface of a ball, a problem that no one before him could solve. Archimedes asked to knock out a ball inscribed in a cylinder on his grave. Archimedes was able to establish that the volumes of a cone and a ball inscribed in a cylinder, and the cylinder itself, are related as 1:2:3. The system developed by Euclid was considered immutable for more than two thousand years. However, in the future, the history of the development of geometry received an unexpected turn, when in 1826 the brilliant Russian mathematician N.I. Lobachevsky was able to create a completely new geometric system named after him. Lobachevsky's axiom states that through a point that does not lie on a line, more than one line parallel to the given one can be drawn. In fact, the main provisions of his system differ from those of Euclid's geometry in only one point, but it is from this point that the main features of Lobachevsky's system follow. This is the position that the sum of the angles of a triangle in Lobachevsky's geometry is always less than 180 degrees. At first glance, it may seem that this statement is not true, however, with small sizes of triangles, modern measuring instruments do not correctly measure the sum of its angles. The subsequent history of the development of geometry proved the correctness of Lobachevsky's brilliant ideas and showed that the Euclidian system is simply unable to solve many problems.

Thus, since its inception, geometry has studied some properties of the real world.

The first architectural structures had a religious purpose. Ancient pagan tribes used obelisks for rituals. The main problem was vertical instability, at that time science was not yet highly developed. Then it is believed that they began to build the Egyptian pyramids.

The Greeks made the theme of architecture as an art the architecture itself, or rather, the story of the work of its structures. From this point on, the supports of the post-and-beam system not only decorate the building, but also show that they support something and that it is hard for them. They ask for the sympathy of the audience and, for persuasiveness, imitate the structure and proportions of the human figure - male, female or girlish.

The Romans begin to widely use arches and arched structures (vaults and domes). The horizontal beam may crack if it is too long; the wedge-shaped parts in the arched arc do not break under load, but are compressed, and it is not easy to destroy the stone with pressure. Therefore, arched structures can cover much larger spaces and load them much more boldly.

A technological breakthrough in Byzantine architecture is the staging of the dome, invented in ancient Rome, not on round walls that enclose the interior space, but on four arches - respectively, with only four points of support. Between the arches and the dome ring formed biconcave triangles - sails.

By the beginning of the second millennium of our era, powerful empires began to take shape in Europe, and each considered itself the heir of Rome. The traditions of Roman architecture were also revived. The majestic Romanesque cathedrals were again covered with arched structures similar to antique ones - stone and brick vaults.

The Renaissance gave the world the greatest domes, but from that moment on, great styles arose not so much due to building innovations, but as a result of a change in the very picture of the world. The Renaissance, Mannerism, Baroque, Rococo, Classicism and Empire were born more due to philosophers, theologians, mathematicians and historians (and to some extent those who introduced gallant manners into fashion) than to the inventors of new ceiling designs. Until the era of the industrial revolution, innovations in building technology cease to be a determining factor in the change of styles.

In 1850, the factory production of large window glass made it possible to work out the construction technologies, first of large greenhouses, and then of grandiose buildings for other purposes, in which either all walls or roofs were made of glass. Fairy-tale "crystal palaces" began to come true.

The history of architecture is both a historical and a theoretical science. This feature is due to the specifics of the subject - the history of the emergence and development of architecture, theoretical knowledge about architecture, architectural language, architectural composition, as well as the observation of such common features and signs of architecture of a certain time and place that allow us to distinguish architectural styles.

Architecture as a method of artistic creation arises from the fact that the human mind has an innate need from God, knowing the world, expressing oneself, one's feelings, thoughts, ideas about Infinity, which are composed of finite forms. Therefore, a building structure is a functional type of structure, and an architectural composition is an artistic and figurative integrity.

Architecture in geometric shapes

There are many fountains in Russia, which consist of different geometric shapes. Consider the fountain in Moscow "Stone Flower". If you look at it, you can see circles from above. There are also details that consist of a sphere and cubes. Along the perimeter there are figures that also consist of geometric shapes.

Consider another fountain "Doves" in Kazan. Here we can also see circles, we can see cylinders and truncated cones.

Also, new shopping and entertainment centers began to appear. There are such centers in Yekaterinburg, for example, Alatyr. We can see the cube, but it is in a slice. In this section, we can see part of the cylinder.

There is also such a center "Fan-Fan", in the same place in Yekaterinburg. It is in the shape of a cube, but its faces are cylindrical and therefore its edges are not sharp, but rounded.

We can also find architecture in geometric shapes. These are innovative and cultural centers: in Skolkovo, in Pervouralsk - "Puck" (such as in Pervouralsk are planned in Vladivostok and Kaluga)

In 2015, a building, a business center, was built in Moscow, it was created by a wonderful woman, Zaha Hadid. It was her last building. On March 31, 2016, she died, but left behind a lot of interesting, diverse buildings.

For example, this building is located in Baku and was built in 2012.

Hadid has created a lot: she made the Expocentre project in Moscow; created the design of furniture, shoes, etc. for different companies, including Russian ones. But the most unusual is the business center in Moscow. Outside, this building is made up of several cubes of different thicknesses and sizes. They are all located differently. But inside this building looks even more unusual and an illusion is created. It looks different from different sides and angles.

Of course, Hadid has more buildings, but they all also consist of various geometric shapes.

Modern Russian architects

Architectural studio "MEL"

Fedor Dubinnikov and Pavel Chaunin. Founded in 2009. The affordable housing project Checkers in 2009 brought the award of the International Architecture Biennale in Rotterdam (IABR), the Avangard award and the title of the Best Young Architect of Russia as part of the curatorial program ARCH Moscow NEXT!

“We are creating a new architecture typology with simple and functional solutions. The stylistic basis of our projects is minimalism and contrast. We are looking for unusual uses for ordinary materials and try to emphasize the architectural originality of the context,” say the founders of Mel.

Architectural workshop ZA BOR

Arseniy Borisenko and Petr Zaitsev. Founded in 2003. Their clients are large companies and businessmen, interesting and extraordinary people. To date, ZA BOR has a successful international practice. The portfolio of the bureau is diverse and includes both private houses and interiors, as well as offices, office complexes, territory development projects, urban planning concepts. The original projects and concepts of the workshop have received dozens of awards, are included in the trend books of international advertising agencies and are presented in the furniture catalogs of leading office furniture manufacturers.

Architectural bureau FORM

Olga Treivas and Vera Odyn. Founded in 2011. Among the objects are the exhibition space in the new pavilion of the CSK Garage, the Russian pavilion at the International Book Fair in Turin, the conference hall Onexim Hall, converted from the old Stalinist cinema. FORM knows how to work with space, making it where necessary, moderately inconspicuous and, on the contrary, forcing it to delicately emphasize itself when the situation requires it. It is as if architecture suddenly "takes the form" of the art that is intended to demonstrate, and does not simply contain it in itself, like a foreign body.

Of course, these are not all companies, but when viewing projects, I liked these guys the most. Their projects have a zest that is hidden somewhere, but you admire it. Looking through some projects, I wondered why they were so simple, but looking at them, I liked them more and more.

Practical part

I decided to try to draw a building from geometric shapes myself. I drew a building consisting of cubes, pyramids, cylinders and spheres. Buildings can be divided into parts. The first part is the entrance in the form of a cube and the cube itself with rectangular and oval windows. The second part is also a cube, but it is very thin and a cut is made in it. It has large rectangular panoramic windows. Between these parts there is another cube with rectangular windows, but various figures are already coming out of it. There is a pyramid with a triangular window and trapezoidal windows. A sphere with square windows joins the pyramid. In addition to the pyramids, there is another figure emerging from the cube - this is a hexagonal cylinder with windows in the shape of a circle.

I think this building can be both a shopping and entertainment center and a business center, and maybe even an innovative cultural, scientific, etc. center.

When constructing such a building, you need to carefully consider the choice of material, correctly calculate so that it does not fall from gusts of wind. You also need to choose a suitable area for construction.

The conclusion from the practical part: it is very difficult to create buildings and structures, because you need to calculate the practicality, choose the right material and color.

Conclusion

We examined where geometric figures meet in the buildings of Yekaterinburg and Pervouralsk. Considered several projects of architectural workshops. We got acquainted with their goals and plans for the future. They also proved our hypothesis that all structures and buildings begin with the construction and alignment of geometric bodies, and then calculations begin. Seeing these buildings today, we realized that the importance in choosing the use of geometric shapes and their setting, as well as the correct choice of material and color, greatly affects the mood and thoughts of a person. December 14, 2016 21.17 http://zabor.net/ 14.12.2016 22.09

Pervouralsk

2017

Old or new, with complex or simple structures, these buildings are undoubtedly the most incredible in the world. There are attractive, there are unusual, and there are just crazy buildings that do not look like anything. Sometimes it is even difficult to immediately understand what is in front of you - a house or something else?

Lotus Temple

(Delhi, India)

The main Bahai temple in India and neighboring countries, built in 1986. Located in New Delhi, the capital of India. A huge building made of snow-white Pentelian marble in the shape of a blossoming lotus flower is one of the most popular tourist attractions in Delhi. Known as the main temple of the Indian subcontinent and the main attraction of the city.

The Lotus Temple has won several architectural awards and has been featured in numerous newspaper and magazine articles. In 1921, the young Bombay Baha'i community asked 'Abdu'l-Bahá for permission to build a Baha'i temple in Bombay, to which the answer was allegedly given: "By the will of God, in the future, a majestic temple of worship will be erected in one of the central cities of India," that is, in Delhi. .

"Khan Shatyr"

(Astana, Kazakhstan)

A large shopping and entertainment center in the capital of Kazakhstan, Astana (architect - Norman Foster). Opened on July 6, 2010, it is considered the largest tent in the world. The total area of ​​"Khan Shatyr" is 127,000 m2. It houses retail and entertainment complexes, including a supermarket, a family park, cafes and restaurants, cinemas, gyms, a water park with an artificial beach and wave effect pools, service and office premises, parking for 700 cars and much more.

The highlight of "Khan Shatyr" is a beach resort with a tropical climate, plants and a temperature of + 35 ° C all year round. The sandy beaches of the resort are equipped with a heating system that creates the feeling of a real beach, and the sand was brought from the Maldives. The building is a giant tent 150 m high (spire), constructed from a network of steel cables, on which a transparent ETFE polymer coating is fixed. Thanks to its special chemical composition, it protects the interior of the complex from sudden temperature changes and creates a comfortable microclimate inside the complex. "Khan Shatyr" entered the top ten world eco-buildings according to Forbes Style magazine, becoming the only building from all over the CIS that the publication decided to include in its hit parade.

The opening of the Khan Shatyr shopping and entertainment center took place as part of the celebration of Astana Day with the participation of the President of Kazakhstan, Nursultan Nazarbayev. During the opening ceremony, a concert was held by the world performer, the Italian tenor of classical music Andrea Bocelli. The most interesting thing is that any Tyumen citizen can visit this amazing place: it is only a nine-hour drive to Astana.

Guggenheim Museum

(Bilbao, Spain)

Designed by American architect Frank Gehry, the Guggenheim Museum is a magnificent example of the most innovative architecture of the 20th century. Constructed from titanium, it is adorned with wavy lines that change color under the sun's rays. The total area is 24,000 m2, 11,000 of which are devoted to exhibitions.

The Guggenheim Museum is a true architectural landmark, a piece of daring configuration and innovative design that provides a seductive backdrop for the artwork it houses. This building has changed the world's view of modern architecture and museums and has become a symbol of the rebirth of the industrial city of Bilbao.

National Library

(Minsk, Belarus)

The history of the National Library of Belarus begins on September 15, 1922. On this day, the Belarusian State and University Library was founded by the Decree of the Council of People's Commissars of the BSSR. The number of readers has been constantly increasing. During its history, the library has changed several buildings, and soon it became necessary to build a new large and functional library building.

Back in 1989, a competition was held at the level of the republic for designing a new library building. The "glass diamond" by architects Mikhail Vinogradov and Viktor Kramarenko was recognized as the best. On May 19, 1992, by the Decree of the Council of Ministers, the Belarusian State Library received the status of a national library. On March 7, 2002, the president of the republic signed a decree on the construction of the building of the state institution "National Library of Belarus". But its construction began only in November 2002.

The opening ceremony of the "Belarusian diamond" took place on June 16, 2006. President of Belarus Alexander Grigoryevich Lukashenko (who, by the way, received a library card No. 1) noted at the opening ceremony that “this unique building combines the austere beauty of modern architecture and the latest scientific and technical solutions.” Indeed, the National Library of Belarus is a unique architectural, construction, software and hardware complex, built in accordance with the latest scientific and technical developments and aimed at meeting the information and socio-cultural needs of society.

The new building of the library has 20 reading rooms, which are designed for 2000 users. All halls are equipped with electronic departments for issuing documents, modern equipment that allows scanning and copying documents, printing from electronic copies. The halls have computerized workplaces, workplaces for visually impaired and blind users, equipped with special equipment.

crooked house

(Sopot, Poland)

In the Polish city of Sopot, on Heroes Monte Cassino Street, there is one of the most unusual houses on the planet - the Crooked House (in Polish - Krzywy Domek). It seems that it either melted in the sun, or it is an optical illusion, and this is not the house itself, but only its reflection in a huge crooked mirror.

A crooked house is really crooked and does not contain a single even place and corner. It was built in 2004 according to the project of two Polish architects - Shotinsky and Zalevsky - impressed by the drawings of the artists Jan Marcin Schanzer and Per Oskar Dahlberg. The main task of the authors in front of the customer, which was the Resident shopping center, was to create such an appearance of the building that would attract as many visitors as possible. A variety of materials were used in the design of the facade: from glass to stone, and the roof made of enameled plates resembles the back of a dragon. Doors and windows are equally asymmetrical and bizarrely curved, giving the house the appearance of some kind of fabulous hut.

The crooked house works around the clock. During the day, a shopping center, cafes and other establishments are open here, and in the evening - pubs and clubs. In the dark, the house becomes even more beautiful. In 2009, the building was recognized as one of the seven wonders of the Tricity, which includes the cities of Gdynia, Gdansk and Sopot. According to a recent poll by The Village of Joy, the Crooked House topped the list of the fifty most unusual buildings in the world.

teapot building

(Jiangsu, China)

In China, the construction of the cultural and exhibition center Wuxi Wanda Exhibition Center, made in the form of a clay teapot, is nearing completion. This building has already officially entered the Guinness Book of Records as the tallest teapot in the world. The choice of this form is not accidental: clay teapots have been considered symbols of the Celestial Empire since the 15th century. They are still produced in Jiangsu Province, where the Wuxi Wanda Exhibition Center is located. In addition to the manufacture of clay teapots, China is also famous for its elite varieties of tea.

Real estate developer The Wanda Group announced that it has spent 40 billion yuan ($6.4 billion) to build the cultural and exhibition center. The result is a structure with an area of ​​3.4 million m2, a height of 38.8 m and a diameter of 50 m. Outside, the building is sheathed with aluminum sheets, which provide the necessary curvature of the frame. In addition to them, stained-glass windows of various sizes play an important role.

Exhibition halls, a water park, a roller coaster, and a Ferris wheel will be located in the Wuxi Wanda center. In addition, each of the three floors of the building will be able to rotate on its own axis. The cultural and exhibition center is part of the Tourism City shopping and entertainment complex, the construction of which is planned to be completed by 2017.

"Habitat 67"

(Montreal, Canada)

An unusual residential complex in Montreal was designed by architect Moshe Safdie in 1966-1967. The complex was built for the start of the Expo 67 exhibition, one of the largest world exhibitions of that time, the theme of which was houses and residential construction.

The basis of the structure is 354 cubes built on top of each other. It was they who made it possible to create this gray building with 146 apartments, where families live who have exchanged a quiet house in a residential area for such a non-standard house. Most apartments on the roof of the neighbor downstairs have a private garden.

Brutalism is considered the building style. Habitat 67 was built over 45 years ago, but it still impresses with its scale. This is, without a doubt, one of the few modern utopias that not only came true, but also became very popular and was even recognized as elite.

dancing building

(Prague, Czech Republic)

Office building in Prague in the style of deconstructivism consists of two cylindrical towers: conventional and destructive. Jokingly called "Ginger and Fred", the Dancing House is an architectural metaphor for the dancing couple Ginger Rogers and Fred Astaire. One of the two cylindrical parts, which expands upward, symbolizes a male figure (Fred), and the second visually resembles a female figure with a thin waist and a skirt fluttering in dance (Ginger).

Like many deconstructivist buildings, the building contrasts sharply with its neighbor - an integral architectural complex of the turn of the 19th-20th centuries. The office center, which houses several international companies, is located in Prague 2, on the corner of Resslova Street and the embankment. On the roof there is a French restaurant with a view of Prague La Perle de Prague.

forest spiral building

(Darmstadt, Germany)

The Austrian genius Friedensreich Hundertwasser presented the unique building to the German city of Darmstadt in 2000. Painted in different colors, a magical house from a children's fairy tale with floating lines of a curved facade, it looks into the world with 1048 windows of non-repetitive shapes, sizes and decor. Real trees grow from some of the windows.

This original building in the form of a horseshoe, spiraling upwards, is called "an unusual house among the usual monotony." It was built in a "biomorphic" style, although, in fact, it is a real residential 12-storey complex, or rather, a kind of fabulous green village. It includes not only a house with 105 comfortable apartments, but also a quiet courtyard with artificial lakes, figured bridges and paths trodden right in the grass; artistically designed playgrounds; closed parking lots; shops; pharmacy and other elements of developed infrastructure.

upside down house

(Szymbark, Poland)

The unique house, which stands on the roof, is decorated in the socialist style of the 1970s. An upside-down house evokes strange sensations: the entrance is on the roof, everyone enters through the window, and the guests walk along the ceiling. The interior is decorated in the style of socialist realism: there is a lounge with a TV and chest of drawers. There is also a table made of the longest solid board in the world - 36.83 m. Of course, the Guinness Book of Records did not ignore him.

The construction of the building took more time and money than for the erection of a conventional house of the same size. The foundation required 200 m³ of concrete. The author of the project was asked many times if his project is related to commercial purposes. The answer was always a stubborn "no". However, the house-shifter turned out to be a commercial success.

Not only Poles, but also foreign tourists come to test their strength and look at an interesting building. Through the attic window, you can enter the house and, carefully maneuvering between the chandeliers, walk around the rooms. Some sources claim that the developer was going to use the new building as his own home. Whether this is so is not known, but the upside-down house in Shimbark did not become residential.

However, there is nothing to complain about: the line of tourists who want to walk inside does not dry out, so there would be no question of any quiet life. A few years ago, in the vicinity of the house, there was even a kind of gathering of local Santa Clauses, who not only discussed their problems, but also practiced getting inside the house through a pipe, since, fortunately, it rests on the ground.

Wat Rong Khun

(Chiang Rai, Thailand)

Wat Rong Khun, better known as the "White Temple", is considered one of the most recognizable temples in Thailand and undoubtedly one of the most beautiful buildings in the world. The temple is located outside the city of Chiang Rai and attracts a large number of visitors, Thai and foreign. This is one of the most visited attractions in Chiang Rai and the most unusual Buddhist temple.

Wat Rong Khun looks like an ice house. Because of its color, the building is noticeable from afar, and it also sparkles in the sun thanks to the interspersed pieces of glass in the plaster. The white represents the purity of the Buddha, while the glass symbolizes the wisdom of the Buddha and the Dharma, the Buddhist teachings. They say the best time to visit the White Temple is at sunrise or sunset, when it is beautifully reflected in the sun.

The construction of the temple began in 1997 and continues to this day. It is being built by Thai artist Chalermchai Kositpipat using his own funds from the sale of paintings. The artist refused sponsors: he wants to make the temple the way only he wants.

basket building

(Ohio, USA)

The basket building was built in 1997. The weight of the structure is approximately 8500 tons, the weight of the supporting supports is 150 tons. Nearly 8,000 m3 of reinforced concrete was used in the construction. The usable area of ​​the building is 180,000 square feet. The basket is located on the territory of about 20,000 square feet (approximately 2200 m2) and completely copies one of the trademarks of its owner.

When the architect of the project, Nikolina Georgievsha, found out about what was ahead of her, she exclaimed: “Wow! I have never done this before!" Indeed, this building cannot be called standard in any way. Unlike other buildings, it expands upwards. This made it possible to significantly increase the working space of the offices: the building is designed for a staff of 500 employees. Not bad, considering that the building also has a seven-story atrium with an area of ​​3300 m2, around which the offices are located. In addition, the first floor is occupied by a theater-like auditorium with 142 seats. The building claims to be a bit pompous: the design includes two slabs attached to the building with the owner's trademark, covered with 23 carat gold.

(Sanji, Taiwan)

The strange and wonderful town of Sanji in Taiwan is an abandoned resort complex. The houses in it were shaped like a flying saucer, so they were called UFO houses. The city was purchased as a resort for US military personnel serving in East Asia.

The original idea of ​​building such houses belonged to the owner of the Sanjhih Township plastics company, Mr. Yu-Ko Chow. The first building license was issued in 1978. The design was developed by Finnish architect Matti Suuronen. But in 1980, construction was halted when Yu-Chow declared himself bankrupt. All efforts to resume work came to nothing. In addition, several serious accidents occurred during construction due to the supposedly disturbed spirit of the mythical Chinese dragon (as superstitious people claimed). Many believed that the place was haunted. As a result, the village was abandoned and soon became known as a ghost town.

Stone house

(Fafe, Portugal)

House Casa do Penedo in the mountains of Portugal, erected between four boulders, resembles a Stone Age dwelling. Standing on the outskirts of the hut was built in 1974 by Vitor Rodriguez and was intended for relaxation away from the hustle and bustle of the city.

The desire for simplicity did not make the members of the Rodriguez family hermits, but brought them closer to a natural lifestyle without frills. Electricity was never brought into the house; candles are still used for lighting. The room is heated with a fireplace carved into one of the boulders. The stone walls serve as a continuation of the interior decoration: even the steps leading to the second floor are carved right into the stones.

The stone hut, reminiscent of the dwelling of the characters from the American animated series The Flintstones, blended so seamlessly into the surrounding landscape that it aroused great interest among architects and tourists. The curiosity of local residents and passing travelers forced the Rodriguez family to leave the house. Now no one lives in the hut, but the owners sometimes visit their unusual house. Only in this case there is a chance to see unusual interiors, at other times it is impossible to get inside Casa do Penedo.

central Library

(Kansas City, Missouri, USA)

Located in the heart of Kansas City, this is one of the first projects to regenerate the city and its historical and tourist value. Residents were asked to remember the most famous books that are somehow connected with the name of Kansas City, and they selected twenty fiction books over the course of two years. The appearance of these titles was incorporated into the innovative design of the Central City Library to encourage visits.

The library building looks like a bookshelf, on which giant books are laid out. Each of them reaches a height of seven meters, and a width of about two. Now the library has at its disposal not only the most modern technologies and excellent quality of service, but also conference rooms, a cafe, an observation room and much more. The Kansas City Public Library has a unique architecture that boggles the imagination. Today it is the pride of the people of the city of Kansas. Its construction was one of the most significant events on the way to turning a provincial town into a prosperous metropolis. The library has ten branches, the main of which is the largest and has special funds. The library's arsenal is 2.5 million books, attendance is more than 2.4 million customers a year.

The history of the library begins in 1873, when it opened its doors to readers and immediately became not only a source of educational resources, but also an excellent alternative to other entertainment establishments of that time. The public library has moved many times, and in 1999 it was moved to the former building of the First National Bank. The century-old building was a real masterpiece of craftsmanship: marble columns, bronze doors and walls richly decorated with stucco. But still it required reconstruction. With the help of public-private partnerships, raised funds from the state and municipal budget, as well as sponsorship, the doors of the Kansas Public Library were opened in 2004 in the form in which it is now.

solar oven

(Odelio, France)

A stunning structure that looks like a furnace and, in fact, is one, the Solar Furnace in France is designed to generate and concentrate the high temperatures required for various processes. This happens by capturing the sun's rays and concentrating their energy in one place.

The structure is covered with curved mirrors, their radiance is so great that it is impossible to look at them. The structure was erected in 1970, the Eastern Pyrenees were chosen as the most suitable place. To this day, the Furnace remains the largest in the world. The mirror array functions as a parabolic reflector, and the high temperature regime at the focus itself can reach up to 3500°C. You can adjust the temperature by changing the angles of the mirrors.

Using a natural resource such as sunlight, the Solar Furnace is considered indispensable for obtaining high temperatures. And they, in turn, are used for various processes. Thus, the production of hydrogen requires a temperature of 1400°C. Test modes of spacecraft and nuclear reactors provide for a temperature of 2500°C, and without a temperature of 3500°C it is impossible to create nanomaterials. In a word, the Solar Furnace is not just an amazing building, but also a vital and efficient one. At the same time, it is considered an environmentally friendly and relatively cheap way to get high temperatures.

"Robert Ripley's House"

(Niagara Falls, Canada)

Ripley's House in Orlando is an illustration not of a technical revolution, but of a natural disaster. This house was built to commemorate the magnitude 8 earthquake that hit here in 1812.

Today, the supposedly cracked building is recognized as one of the most photographed in the world. "Believe it or not!" (Ripley's Believe It or Not!) is a patented network of so-called Ripley's Auditoriums (museums of strange and incredible things), of which there are more than 30 in the world.

The idea belongs to Robert Ripley (1890–1949), an American cartoonist, entrepreneur and anthropologist. The first traveling collection, Ripley's Auditorium, was presented in Chicago in 1933 during the World's Fair. On a permanent basis, the first museum "If you want - believe it, if you want - no!" was opened after the death of Ripley, in 1950 in Florida, in the city of St. Augustine. The Canadian museum of the same name was founded in 1963 in the city of Niagara Falls (Niagara Falls, Ontario) and still has a reputation as the best museum in the city. The Auditorium building was built in the form of a falling Empire State Building (New York) with King Kong standing on the roof.

shoe house

(Pennsylvania, USA)

The shoe house in Pennsylvania (York County) was conceived by a very successful businessman, Colonel Mahlon N. Heinz. At that time, he owned a thriving shoe company, which included about 40 shoe stores. At that time, Heinz was already 73 years old, but he loved his business so much that he commissioned an architect to create an unusual structure in the shape of a boot. This was in 1948. Already in 1949, the dream of a shoe businessman was realized, and the restless Mahlon N. Heinz was able not only to admire the extraordinary building, but also to settle there.

The length of this house is 12 m, height - 8. Its facade was made as follows: first a wooden frame was created, which was then poured with cement. Surprisingly, even the mailbox of this house is made in the shape of a shoe. There are shoes and bars on the windows and doors. Near the house there is a dog kennel, which was also made in the form of a boot. And even on the sign, located on the road, there are shoes. But in fact, the shoe house has such an orientation only from the outside. Inside, this is quite a comfortable dwelling, quite cozy and spacious. On the side of the house, there is an external staircase (most likely a fire escape) that allows access to all five tiers of the unusual building.

dome house

(Florida, USA)

After a series of devastating hurricanes and tropical storms in Florida (USA), which left Mark and Valeria Sigler homeless every time, they decided to build a house that could withstand the pressure of the elements and at the same time be beautiful and comfortable. The result of their work was a house with an unusually strong construction and unique design.

For people living in the coastal zone, it is very important that they have somewhere to return after a storm. Ordinary houses are very often destroyed to the ground, while the "Dome House" can stand as if nothing had happened even under a wind rushing at a speed of 450 km / h. At the same time, the Siglers' house fits perfectly into the surrounding landscape: the dome is the best suited to the surroundings of dunes, ponds and vegetation. The construction of the building is made of modern environmentally friendly materials that can last for several centuries.

cube buildings

(Rotterdam, the Netherlands)

A number of unusual houses were built in Rotterdam and Helmond according to the innovative design of the architect Piet Blom in 1984. Blom's radical decision was that he turned the box of the house by 45 degrees and placed it at an angle on a hexagonal pylon. There are 38 such houses in Rotterdam and two more super-cubes, and all the houses are articulated with each other. From a bird's eye view, the complex has an intricate appearance, resembling an impossible triangle.

The houses consist of three floors:
● Ground floor - entrance.
● First - living room with kitchen.
● Second - two bedrooms with a bathroom.
● Upper - sometimes a small garden is laid out here.

The walls and windows are inclined at an angle of 54.7 degrees with respect to the floor. The total area of ​​the apartment is about 100 m2, however, about a quarter of the space is unusable due to the walls, which are at an angle.

Burj Al Arab Hotel

(Dubai, United Arab Emirates)

A luxury hotel in Dubai, the largest city in the United Arab Emirates. The building stands in the sea at a distance of 280 m from the shore on an artificial island connected to the land by a bridge. With a height of 321 m, the hotel was considered the tallest hotel in the world, until another Dubai hotel appeared - the Rose Tower - 333 m high, which opened in April 2008.

The construction of the hotel began in 1994; it opened to visitors on December 1, 1999. The hotel was built in the form of a dhow sail, an Arab ship. Closer to the top is a helipad, and on the other side is the El Muntaha restaurant (from Arabic - “highest”). Both are supported by cantilever beams.

Towers "Absolute"

Like any other rapidly developing suburb in North America, Mississauga is looking for a new architectural look. The Absolute Towers have become a new opportunity to respond to the needs of an ever-expanding city, to create a residential landmark that will claim to be more than just efficient housing. They can create a permanent emotional connection for residents with their hometown. Such a structure can be safely included in the list of the most beautiful skyscrapers in the world.

Instead of the simple, functional logic of modernism, the design of the towers expresses the complex multiple needs of contemporary society. These buildings are much more than just a multifunctional machine. It is something beautiful, human and alive. The towers serve as an important gate to the city, located at the intersection of two main city streets.

Despite the special status of these towers as significant landmarks, the emphasis in the project was by no means on their height, as is the case with most of the tallest buildings in the world. Due to the design features, continuous balconies surround the entire building, eliminating the vertical barriers traditionally used in high-rise architecture. Towers "Absolute" rotate in different projections at different levels, combined with the surrounding landscapes. The aim of the designers was to provide a good 360-degree view from any point of the building, as well as to ensure the contact of residents with natural elements, awakening in them a reverent attitude towards nature. The height of tower A with 56 floors is 170 m, and tower B with a height of 50 floors is 150 m.

Pabellon de Aragon

(Zaragoza, Spain)

A building that looks like a wicker basket appeared in Zaragoza in 2008. The construction was timed to the full-scale exhibition "Expo-2008", dedicated to the problems of water shortage on the planet. The pavilion of Aragon, literally woven of glass and steel, is crowned with strange-looking structures placed on the roof.

As conceived by its creators, the building reflects the deep trace that five ancient civilizations left on the territory of Zaragoza. In addition, inside the building you can learn about the history of water and how man learned to manage water resources on the planet.

(Graz, Austria)

This museum-gallery of contemporary art was opened as part of the European Capital of Culture program in 2003. The concept of the building was developed by London-based architects Peter Cook and Colin Fournier. The facade of the museum was designed by realities:united using BIX technology as a 900 m2 media installation consisting of luminous elements that can be programmed with a computer. It allows the museum to communicate with the surrounding urban space.

The installation has won a number of awards. The BIX façade was conceived when the rest of the building was already being developed. In addition to the late deadlines, it was difficult to integrate into the concept of other authors. In addition, the facade, without a doubt, became the dominant element of the architectural image. The design architects accepted the façade design because it was based on their original ideas for a large luminous surface.

Concert hall

(Canary Islands, Spain)

One of the most famous and recognizable buildings in Spain, the symbol of the city of Santa Cruz de Tenerife, one of the most significant works of modern architecture and one of the main attractions of the Canary Islands. The opera was designed by Santiago Calatrava in 2003.

The Auditorio de Tenerife building is located in the city center, close to the César Manrique Marine Park, the city's port and the twin towers of Torres de Santa Cruz. There is a tram station nearby. You can enter the opera hall from two sides of the building at once. The Auditorio de Tenerife has two terraces overlooking the sea.

coin building

(Guangzhou, China)

In the Chinese city of Guangzhou, there is a unique building in the form of a huge disk with a hole inside. It will house the Guangdong Plastics Exchange. Now the final cosmetic work is going on here.

At 33 floors and 138 meters high, the coin-shaped building has an opening with a diameter of almost 50 meters, which has a functional, and not only design, value. The main shopping area will be located around it. The fact that the building has already become one of the main attractions of Guangdong is obvious. However, opinions are divided about its symbolic meaning.

The Italian company that developed the project claims that the form was based on jade discs owned by ancient Chinese rulers and nobility. They symbolized the high moral qualities of a person. In addition, together with its reflection in the Pearl River, on which the building stands, it forms the number 8. According to the Chinese, it brings good luck. However, many citizens of Guangzhou saw in this building a Chinese coin, symbolizing the desire for material wealth, and among the people this building has already been nicknamed the "disc of the prodigal rich." No word yet on when the building will be open to the public.

"Stone Cave"

(Barcelona, ​​Spain)

Construction began in 1906, and in 1910 the five-story building had already become one of the most famous buildings in Barcelona. The locals dubbed it "La Pedrera" - a stone cave. Indeed, the house resembled a real cave. When it was created, Gaudí basically abandoned straight lines. The five-story residential building was erected without a single corner. The architect did not make walls as load-bearing structures, but columns and vaults, which gave him unlimited scope in the layout of rooms, the ceiling heights of which are different.

In order to get enough light into each room with such a complex layout, Gaudí had to make several courtyards with light ovals. Thanks to these numerous ovals, windows and undulating balconies, the house looks like a block of solidified lava. Or on a rock with caves.

Music building

(Huainan, China)

Piano House consists of two parts depicting two instruments: a transparent violin rests on a translucent piano. The unique building was built for music lovers, but it has nothing to do with music. An escalator is located in the violin, and an exhibition complex is located in the piano, in which the plans of streets and districts of the city are presented to the attention of visitors. The object was created at the suggestion of local authorities.

The unusual building seeks to attract the attention of Chinese people and numerous tourists to the new developing area, which has become the most iconic object. Thanks to the continuous glazing of the facades with transparent and tinted glass, the premises of the complex receive the maximum possible natural light. And in the dark, the body of the object is hidden in the dark, leaving visible only the neon contours of the silhouettes of giant "tools". Despite its popularity, the building is often criticized as a kind of postmodern kitsch and a typical student project, in which there is much more shocking than art and functionality.

CCTV Headquarters

(Beijing, China)

The headquarters of CCTV is a skyscraper in Beijing. The building will house the headquarters of China Central Television. Construction work began on September 22, 2004 and was completed in 2009. The architects of the building are Rem Koolhaas and Ole Scheeren (OMA).

The skyscraper with a height of 234 m consists of 44 floors. The main building is built in an unusual style and is a ring-shaped structure of five horizontal and vertical sections, forming an irregular lattice on the facade of the building with an empty center. The total floor area is 473,000 m².

The construction of the building was considered a daunting task, especially given its location in an earthquake-prone area. Because of its unusual shape, it has already acquired the nickname "pants". The second building, the Television Cultural Center, will house the Mandarin Oriental Hotel Group, a visitor center, a large community theater and exhibition space.

Ferrari World Amusement Park

(Yas Island, Abu Dhabi)

The Ferrari Theme Park is housed under a 200,000 m² roof and is the largest indoor theme park in the world. Ferrari World officially opened on November 4, 2010. It is also home to the world's fastest pneumatic roller coaster, the Formula Rossa.

The emblematic roof of Ferrari World was designed by Benoy architects. It was designed based on the profile of the Ferrari GT. Ramboll provided the structure design, integrated planning and urban design, geotechnical engineering, and building facade design. The total roof area is 200,000 m² with a perimeter of 2200 m, and the area of ​​the park is 86,000 m², making it the largest theme park in the world.

The roof of the building is decorated with the Ferrari logo measuring 65 by 48.5 m. This is the largest company logo ever created. 12,370 tons of steel were used to support the roof. In its center is a hundred-meter glazed funnel.

Innovative residential complex Reversible-Destiny Lofts

(Tokyo, Japan)

As conceived by the architect, the apartments in the complex he created are designed in such a way that their inhabitants are always on the alert. Uneven multi-level floors, concave and convex walls, doors that can only be entered by bending over, sockets on the ceiling - in a word, not life, but a continuous adventure. Relax in such conditions will not succeed.

A person is constantly struggling with the environment, so there is simply no time left to mope or think about sores. What is it - shock therapy or a joyful game, is not yet clear. But restrained and subservient to traditions and taste, the Japanese are ready to pay twice as much for uncomfortable apartments than for comfortable and familiar ones located in the same area. It is interesting that all the "apartments" are rented, they are not for sale. Moreover, the 83-year-old Buddhist nun and popular writer Jakute Setouti, who was the first to live in a new house, claims that since the move she began to feel younger and much better.

"Slim House"

(London, Great Britain)

An unusual residential building, also known as "Slim House", is located near the Natural History Museum in South Kensington (London). This house became famous throughout the world due to its wedge-shaped shape, or rather, the width of one of the sides of the building - a little more than a meter.

At first glance, the incredibly narrow structure of the building is just an optical illusion. Despite this, The Thin House has become very popular with Londoners and tourists. The reason for such an architectural idea is not accidental. South Kensington tube station train line runs right behind the house.

Due to the unusual design of the house, the apartments do not have a standard rectangular shape, but a trapezoid shape. For narrow rooms it is necessary to select non-standard furniture. In any case, despite a number of shortcomings, apartments in a “thin” structure are very popular among those who want to acquire new housing.

Air Force Academy Chapel

(Colorado, USA)

The striking appearance of the Air Force Academy Cadet Chapel in Colorado Springs caused some controversy when it was completed in 1963, but it is now considered one of the finest examples of modern American architecture.

The Cadet Chapel, made of steel, aluminum and glass, has 17 pointed spiers, reminiscent of jet fighters taking off into the sky. Inside there are two main levels and one basement. There is a Protestant chapel with 1200 seats, a 500-seat Catholic chapel and a 100-seat Jewish chapel. Each chapel has a separate entrance, so sermons can be held simultaneously without interfering with each other.

The Protestant chapel, which occupies the upper level, has stained-glass windows between the tetrahedral walls. The colors of the windows vary from dark to light, representing God coming from darkness into light. The altar is made of a smooth marble slab 15 feet long, shaped like a ship, symbolizing the church. The pews are designed in such a way that the end of each pew resembles the propeller of a World War I aircraft. Their backs are topped with a strip of aluminum, similar to the leading edge of a wing of a fighter plane. The walls of the chapel are decorated with paintings that are divided into three groups: brotherhood, flight (in honor of the Air Force) and justice.

On the lower level are multiver rooms, defined as places of worship for cadets of other religious groups. They are left without religious symbols so that they can be used by many people.

Dzhambaeva M.B. one

1 Municipal state educational institution "Secondary school aul Upper Uchkulan"

Dzhambaeva F.N. one

1 Municipal state educational institution "Secondary school aul Upper Uchkulan".

The text of the work is placed without images and formulas.
The full version of the work is available in the "Job Files" tab in PDF format

Introduction

Idea of our study appeared in geometry lessons.

Relevance our research is that architectural objects are an integral part of our lives. Our mood, attitude depends on what buildings surround us. There is a need to study the variety of objects that have appeared in our world. If earlier architectural structures were monotonous structures, now geometric shapes have made it possible to diversify the architectural appearance of cities.

Target of our work - the study of the relationship of geometry and architecture.

Hypothesis: all the buildings that surround us are geometric shapes.

Object of study: architecture of buildings and pyramids.

Subject of study: relationship between architecture and geometry.

The objectives of our study:

To study the literature on the relationship between geometry and architecture.

Consider geometric forms in architectural styles, and as a guarantor of the strength of structures.

Consider the most interesting architectural structures, and find out what geometric shapes are found in them.

Research methods: observation, photographs, study and analysis of theoretical information on this issue.

Geometric shapes in different architectural styles.

Architectural works live in space, are part of it, fitting into certain geometric shapes. In addition, they consist of separate parts, each of which is also built on the basis of a specific geometric body.

Often geometric shapes are combinations of different geometric bodies.

Look at the photo, which shows the building of the club named after I.V. Rusakov in Moscow (see appendix fig. 1). this building was built in 1929 according to the project of the architect K. Melnikov. the base part of the building is a non-convex straight prism. At the same time, giant overhanging volumes are also prisms, only convex.

Some architectural structures have a rather simple form. For example, in the photograph (see Appendix Fig. 2), you see a clock tower, which is a mandatory attribute of any American university. Abstracting from some details, we can say that it has the shape of a right quadrangular prism, which is also called a rectangular parallelepiped.

The geometric shape of a building is so important that there are cases when the names of geometric shapes are fixed in the name or name of the building. So, the building of the US military department is called the Pentagon, which means pentagon. This is due to the fact that if you look at this building from a great height, it will really look like a pentagon. In fact, only the contours of this building represent a pentagon. It itself has the shape of a polyhedron (see Appendix Fig. 3).

Often in an architectural structure various geometric shapes are combined. For example, in the Spasskaya Tower of the Moscow Kremlin, at the base you can see a straight parallelepiped, turning in the middle part into a figure approaching a polyhedral prism, but it ends with a pyramid (see Appendix Fig. 4). With a detailed examination and study of the details, we can see: circles - dials of chimes; ball - the basis for attaching a ruby ​​star; semicircles - arches of one of the rows of loopholes on the facade of the tower, etc.

It must be said that architects have favorite details that are the main components of many structures. They usually have a certain geometric shape. For example, columns are cylinders; domes - a hemisphere or simply a part of a sphere bounded by a plane; spiers - either pyramids or cones (see appendix fig. 5).

Architects of different eras had their favorite details, which reflected certain combinations of geometric shapes. For example, the architects of Ancient Russia often used the so-called tent coverings for the domes of churches and bell towers. These are coverings in the form of a tetrahedral or polyhedral pyramid. Another favorite form of the Old Russian style are onion-shaped domes. The onion is a part of the sphere, smoothly transitioning and ending with a cone. In Figure 6 (see Appendix) you see the Church of Elijah the Prophet in Yaroslavl. It was built in Yaroslavl in the middle of the 17th century. When it was created, the architects used both hipped roofs and domes in the form of onions.

Consider another striking architectural style - medieval Gothic (see Appendix Fig. 7). gothic buildings were directed upwards, struck by their majesty, mainly due to their height. And pyramids and cones were also widely used in their forms.

Finally, let's turn to geometric forms in modern architecture. In the architectural style of "High Tech", the entire structure is open for viewing. Here we can see the geometry of lines that run parallel or intersect, forming an openwork space of the structure. An example, a kind of progenitor of this style is the Eiffel Tower.

Modern architectural style, thanks to the possibilities of modern materials, uses bizarre forms that are perceived by us through their complex, curved (convex and concave) surfaces. Their mathematical description is difficult, so we do not present it here. Architecture, or architecture, is the art and science of building, designing buildings and structures, as well as the very set of buildings and structures that create a spatial environment for human life and activity. Architecture certainly creates a materially organized environment that people need for their life and activities, in accordance with their aspirations, as well as modern technical capabilities and aesthetic views. In architecture, functional, technical and aesthetic properties of objects are interconnected.

Architectural works are often perceived as cultural or political symbols, as works of art. Historical civilizations are characterized by their architectural achievements. Architecture allows the vital functions of society to be carried out, while at the same time directing life processes. However, architecture is created in accordance with the capabilities and needs of people.

The subject of work with space is the organization of the populated place as a whole. This has separated into a separate area - urban planning, which covers a complex of socio-economic, construction, technical, architectural, artistic, sanitary and hygienic problems. For the same reason, it is difficult to give a correct assessment of an architectural structure without knowing urban planning.

One of the highest international awards in the field of architecture is the Pritzker Prize, awarded annually for the most outstanding achievements in the field of architecture.

By decision of the Twentieth General Assembly of the International Union of Architects (UIA), held in Barcelona in 1996, every year on the first Monday of October, the international professional holiday of architects and connoisseurs of architectural masterpieces is celebrated - World Architecture Day.

Architecture surrounds a person everywhere throughout his life: it is both a home and a place of work, social activities, recreation, entertainment. In other words, it is the environment in which a person exists. This artificially created environment simultaneously opposes nature, isolating man from it, protecting him from its influences, and connects man with nature. Architecture satisfies the practical needs of a person, it is utilitarian and therefore must first of all be convenient, durable, corresponding to its purpose.

A work of architecture is such an engineering, constructive structure, in which a certain plan is laid - the idea of ​​its creator. The architect invests in his creation not only scientific and technical knowledge, but also his temperament, his thoughts, feelings. This building, in addition to utilitarian qualities, carries an ideological and figurative, artistic and aesthetic beginning, influencing our emotions, causing reciprocal feelings, a certain mood.

The ancient Roman art theorist Vitruvius named three foundations on which architecture is based: "Strength, Benefit, Beauty."

Architecture creates real space. This is its main distinguishing feature. If for painting color is decisive, for sculpture - volume, then for architecture - space. Space in architecture is limited by constructive forms made of various materials.

In the creation of a spatial-volumetric architectural form, as in other types of art, such artistic means and techniques as rhythm, symmetry and asymmetry, nuance and contrast, ratios and proportions of the whole and parts take part.

Rhythm- regular repetition and alternation of homogeneous elements or groups of forms - permeates the volumetric and spatial structure of the structure, imparting harmony to it.

Symmetry- the same arrangement of equal parts in relation to the axis of the building is a very effective means of organizing architectural forms, introducing strict orderliness, static, peace into the volumetric and spatial composition.

Asymmetry is the opposite of symmetry; she gives the composition flexibility, dynamism, sharpness, contributing to the unity of the whole due to the subordination of parts.

Certain ratios and subordination of all three-dimensional geometric elements, all parts of an architectural structure constitute proportions.

Contrast versus nuance- the ratio of sharply opposite features (shapes, elements light and heavy, high and low, vertical and horizontal, light and dark). Contrast emphasizes, sharpens forms and contributes to a sense of dynamism, tension of movement.

Of great importance for the perception of an architectural structure are the silhouette and location, connection with the environment - natural, natural or urban; opposition or unity, agreement with it.

Finally, a significant role in the creation of an ideological and artistic architectural image is played by the community of plastic arts - architecture, sculpture and painting. Architecture is the leader in this community: sculpture and painting become compositional elements of architecture without losing their originality.

Architecture, like all other arts, is a product of its era. Architecture reflects the social system and the level of development of productive forces, the life and customs of people, the dominant ideology, religious and philosophical ideas, and the aesthetic ideals of the time. In turn, within the framework of one style, national traits clearly make themselves felt, and in each individual work of architecture, traits of the individual handwriting of its creator.

Geometric shape as a guarantor of the strength of structures.

The strength of the structure is directly related to the geometric shape that is basic for it. A mathematician would say that the geometric shape (body) into which the structure fits is very important here. It turns out that the geometric shape also determines the strength of the architectural structure. The Egyptian pyramids have long been considered the most durable architectural structure. As you know, they have the shape of regular quadrangular pyramids. It is this geometric shape that provides the greatest stability due to the large base area.

The pyramids were replaced by a rack-and-beam system. Which is one rectangular parallelepiped based on two rectangular parallelepipeds. With the advent of the arched-vaulted structure, circles, circles, spheres and circular cylinders entered the architecture of straight lines and planes. Initially, hemispherical domes were used in architecture. This means that the border of the arch was a semicircle, and the dome was half a sphere. For example, it is the hemispherical dome that has the Pantheon - the temple of all the gods - in Rome.

The arched structure served as a prototype of the frame structure, which today is used as the main one in the construction of modern structures made of metal, glass and concrete. The TV tower on Shabolovka (see Appendix Fig. 11) consists of several parts of hyperboloids stacked on top of each other. Moreover, each part is made of two straight beams. This tower was built according to the project of the remarkable engineer V.G. Shukhov.

When people began to build houses, they had to go deeper into what shape to give the walls and roof. It became clear that it is better to cut the logs and make the roof sloping so that water flows from it. And, without knowing it, people have been doing geometry all the time. Women were engaged in geometry, making clothes, hunters, making spears and boomerangs of complex shape. Only the word "geometry" itself did not exist then, and the shape of bodies was not considered separately from their other properties.

When they began to build houses of stone, they had to drag heavy blocks of stone. Rollers have been used for this since ancient times. So people got acquainted with one of the most important figures - the cylinder. It was difficult to transport goods on rollers due to the large weight of the logs themselves. To facilitate the work, people began to cut thin flat round plates from the trunks. This is how the first wheel appeared. The unknown inventor of the first wheel made the greatest discovery! Just imagine for a moment that all the wheels on the earth have disappeared. It will be a real disaster. Because in every car, from pocket watches to spaceships, there are dozens and hundreds of different wheels.

But not only in the process of work people got acquainted with geometric shapes. Since ancient times, they loved to decorate themselves, their homes and their clothes. Ancient craftsmen learned how to give a beautiful shape to bronze and gold, silver and precious stones. And the artists, painting the palaces, found more and more new geometric forms. The potter needed to know what form to make a vessel so that one or another amount of liquid would enter it, and the ancient Egyptians learned to find the volumes of rather complex figures. Astronomers who observed the sky and gave instructions based on their observations when to start field work, had to learn to determine the position of the stars in the sky. For this, it was necessary to measure the angles.

The shape of the peasant fields was also different. The fields were separated from each other by boundaries, and the flood of the Nile washed away these boundaries every spring. Therefore, there were special officials who were engaged in land surveying, in Russian say - land surveyors. Thus, the science of land surveying arose from the practical problem of land surveying. In Greek, the earth was called "geos", I measure - "metrio", and therefore the science of measuring fields was called "geometry". Just don't think of calling a modern geometer a land surveyor. For many thousands of years since its inception, it has only to a small extent been engaged in land surveying.

Geometric figures were of interest to our ancestors not only because they helped to solve practical problems. Some of the figures had a magical meaning for people. So, the triangle was considered a symbol of life, death and rebirth; the square is a symbol of stability. The universe, infinity was designated by a regular pentagon - a pentagon, a regular hexagon - a hexagon, was a symbol of beauty and harmony. The circle is a sign of perfection.

Various geometric forms created by nature and human hands; in geometry they are considered as flat forms (figures) and three-dimensional forms (bodies).

Geometry is divided into two sections: planimetry and solid geometry.

It is with planimetry that the study of geometry in schools begins.

Planimetry comes from the Latin "planum" - plane, and the Greek "metreo" - measure.

This section of geometry studies figures that are located on a plane: a point, a straight line, a square, a rectangle, a triangle, a rhombus, a pentagon and other polygons, a circle, an oval. Geometric figures on the plane have two dimensions: length and width.

Stereometry is a branch of geometry that studies shapes in space. They, in addition to length and width, have a height.

Volumetric ones include: a cube, a parallelepiped, a prism, a pyramid, a cylinder, a cone, a ball.

So, what geometric shapes and forms have we studied.

1) Polygons, types of polygons

A polygon is a geometric figure bounded on all sides by a closed broken line, consisting of three or more segments (links).

If a closed broken line consists of three segments, then such a polygon is called a triangle, of four segments - a quadrangle, of five segments - a pentagon, etc.

a) triangles

Triangle- This is a flat geometric figure consisting of three points that do not lie on one straight line, and three segments connecting these points.

Triangle- the simplest closed rectilinear figure, one of the first, the properties of which a person learned in ancient times, since this figure has always been widely used in practical life.

b) Quadrangles

quadrilateral- This is a flat geometric figure, consisting of four points (the vertices of the quadrangle) and four segments connecting them in series (the sides of the quadrangle). They have four corners and four sides. A quadrilateral never has three vertices on the same line.

A parallelogram is a quadrilateral whose opposite sides are pairwise parallel, that is, they lie on parallel lines.

Square- a regular quadrilateral or rhombus, in which all angles are right, or a parallelogram, in which all sides and angles are equal.

A square, by definition, has equal sides and angles, and, as it turned out, has all the properties of a parallelogram, a rectangle, and a rhombus.

Rectangle is a parallelogram with all right angles.

Rhombus is a parallelogram with all sides equal.

A rhombus also has all the properties of a parallelogram, but its diagonals are mutually perpendicular and are angle bisectors. The heights of the rhombus are equal.

Trapeze is a quadrilateral with exactly one pair of opposite sides parallel.

A trapezoid is called isosceles (or isosceles) if its sides are equal.

A trapezoid with one right angle is called a right angled trapezoid.

2) Round shapes

Circle- the locus of points of the plane, equidistant from a given point, called the center, at a given non-zero distance, called its radius.

A circle is the part of a plane bounded by a circle.

The circle is only a part of the circle, its border, while the circle is a more extensive and complete figure.

Oval is a flat geometric figure.

It is a circle slightly elongated horizontally or vertically. Unlike a circle, an oval does not have an even shape. At some points, the shape of the oval is most curved.

Polyhedra

a) Prism

A prism is a polyhedron, which consists of two flat polygons lying in different planes and combined by parallel translation, and all segments connecting the corresponding points of these polygons.

By base: triangular prism, quadrangular prism, pentagonal prism, etc.

According to the location of the lateral ribs:

Inclined prism - the lateral edge is inclined to the base at an angle other than 90º.

Straight prism - the lateral edge is located perpendicular to the base.

b) Parallelepiped

Parallelepiped A prism with a parallelogram at its base.

Parallelepipeds, like any prisms, can be straight and inclined.

Inclined box is an oblique prism with a parallelogram at its base Right parallelepiped- this is a straight prism, at the base of which is a parallelogram or parallelepiped, in which the lateral edge is perpendicular to the plane of the base.

Rectangular is a right parallelepiped, at the base of which is a rectangle (or a right prism, at the base of which lies a rectangle).

A cube is a right parallelepiped, all of whose faces are squares.

c) Pyramid

A pyramid is a polyhedron, which consists of a flat polygon - the base of the pyramid, a point that does not lie in the plane of the base - the top of the pyramid and all segments connecting the top of the pyramid with the points of the base.

The segments connecting the top of the pyramid with the tops of the base are called lateral edges.

Solids of revolution

A new group of geometric bodies - bodies of revolution, because are obtained by rotating plane figures.

a) cylinder

A cylinder is a body, which consists of two circles, combined by parallel translation, and all segments connecting the corresponding points of these circles. The circles are called the base of the cylinder, and the segments are called the generators of the cylinder. The bases of the cylinder are equal and lie in parallel planes, forming parallel and equal. The cylinder is obtained by rotating a rectangle around one of its sides.

b) Cone

A cone is a body that consists of a circle - the base of the cone, a point that does not lie in the plane of this circle - the top of the cone and all segments connecting the top of the cone with the points of the base.

Cone - formed by a right triangle rotating around one of the legs.

c) Sphere and ball

Sphere is the set of all points in space that are at a positive distance R from a given point O, called the center of the sphere.

The word sphere- the Latin form of the Greek word (sfire) - ball.

Ball is the set of all points in space whose distance from a given point does not exceed a given positive number R. A ball is obtained by rotating a semicircle about the diameter.

The beauty of geometry has repeatedly fascinated the human eye. It would seem that you build the most ordinary and rather ordinary constructions, and then, if you look at them from a different point of view, and try to change the picture a little, you get something different, unusual, very beautiful. Thus, from geometric shapes, you can get unusual and bewitching constructions.

3. Symmetry - the queen of architectural perfection.

You are familiar with the word symmetry. Probably, when you pronounce it, you remember a butterfly or a maple leaf, in which you can mentally draw a straight axis and parts that will be located on opposite sides of this straight line and will be almost the same. This view is correct. But this is only one of the types of symmetry that mathematics studies, the so-called axial symmetry. In addition, there is a more general concept of symmetry.

Considering symmetry in architecture, we will be interested in geometric symmetry - the symmetry of form, as the proportionality of the parts of the whole. it has been noticed that when certain transformations are performed on geometric figures, their parts, having moved to a new position, will again form the original figure.

Architectural structures created by man are mostly symmetrical. They are pleasing to the eye, people consider them beautiful. Symmetry is the first rule of an architect when designing any structure.

One has only to look at the magnificent work of A.N. Voronikhin Kazan Cathedral in St. Petersburg (see Appendix Fig. 12) to be convinced of this. If we mentally draw a vertical line through the spire on the dome and the top of the pediment, we will see that on both sides of it there are absolutely identical parts of the colonnade structure and the cathedral building.

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 (see appendix fig. 13), where symmetry is completely absent in the structure as a whole.

Dissymmetry is a partial lack of symmetry, a symmetry disorder 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.

In modern architecture, the techniques of both antisymmetry and dissymmetry are increasingly used. These searches often lead to very interesting results. A new urban aesthetic is emerging.

Unusual architecture

Skyscraper DC Tower One

In Vienna, Dominique Perrault built Austria's tallest building, the 250-meter DC Tower One. Thanks to its graceful form, the skyscraper on the banks of the Danube, immediately after its completion in February, took second place in the annual Emporis competition, losing only to Renzo Piano's "Shard". Inside the building there are offices of medical companies, and on the first fifteen floors there is a four-star hotel. Next year, a second skyscraper 150 meters high will appear next to DC Tower One - Perrault conceived the entire complex as two parts of a divided monolith, between which a new public space will be located.

"Innovation Tower"

Zaha Hadid is the most famous and massive architect of our time, an industry superstar in an era when stars, in general, are no longer needed. Hundreds of architects from her bureau open five large-scale buildings every year in different parts of the world, and projects are repeatedly nominated for the Sterling Prize. The most interesting new project of Hadid is worth looking for in Hong Kong: the building of the local Polytechnic University, made of glass, aluminum and reinforced concrete, has opened there.

The Innovation Tower is an advanced technological product, a large gadget that looks like a fragment of a perfectly computerized future, suddenly found itself on an imperfect planet. The fifteen-story building, which will host one and a half thousand students, was squeezed between a wide highway and an existing football field, but the architectural bureau found a way out and created a flying volume that resembles either a rock protruding from the sea, or a spaceship that would fit jockeys from "Prometheus" by Ridley Scott.

The study building is Hadid's personal attempt to settle accounts with Hong Kong: in the early 1980s, the first architect's building was to appear here, which could launch her career. However, the project was canceled due to negotiations on the annexation of the city to China, and until the very beginning of the 21st century, the British had to remain a “paper” architect with almost no orders.

Aspen Art Museum

Shigeru Ban is known for his "paper architecture" projects of prefabricated housing and public buildings for refugees and those affected by natural disasters. For their construction, the Japanese uses cardboard treated with a special impregnation, this is an ideal material for unsightly temporary buildings. It’s inexpensive, easy to manufacture, can be quickly built into large structures, and can be easily recycled after a home’s lifespan (yes, you heard that right: in 2014, architecture finally ceased to be perceived as something unshakable). It was for his social work that Ban won the Pritzker Prize in 2014.

Ban's permanent buildings are much less frequently mentioned. In them, he shows himself as a consistent Japanese minimalist who loves white, glass, metal and wood. His first project after receiving Pritzker was the building of an art museum in the American ski resort of Aspen. The facade of the museum resembles a large basket, and the roof is supported by a beautiful wooden frame. A staircase to the roof of the building is sandwiched between the interior spaces and the light facade made of intertwined and specially processed plywood sheets. There is a public area and the lobby of the museum: visitors must inspect the collections, gradually descending to the lower floors.

Louis Vuitton Foundation

The patriarch of American architecture and the author of the Guggenheim Museum in Bilbao, Frank Gehry, is the complete opposite of Shigeru Bana. He is a wasteful deconstructivist who, for the sake of a spectacular visual image, is ready to come up with dozens of innovative technical solutions. At the same time, the effectiveness of the use of the building may be questionable. This is exactly what happened with his opus magnum and this year's flagship building, the Fondation Louis Vuitton, which opened in the autumn in the Bois de Boulogne in Paris.

The creation of a private museum of contemporary art cost the billionaire and richest man in France Bernard Arnault $ 150 million and stretched over eight years. The result is a huge glass whale with references to Tatlin and traditional park architecture. When designing the curved forms of the museum, Gehry had to use special software used in the aviation and aerospace industries.

Inside the building, covered with a dozen glass plates, there are 11 rooms, which showcase the works of contemporary artists from the Arno collection. Only a third of the total space is reserved for exhibitions, the rest is a transforming hall with 350 seats and public areas, including a cafe and a bookstore.

Pathé Foundation

Renzo Piano himself, the author of the Pompidou Center and the London Shard, this year completed the construction of the headquarters of the Pathé Foundation, which is engaged in preserving the heritage of the film studio of the same name. The building is located in the 13th arrondissement of Paris, significantly rebuilt during the modernist experiments of the 1960s, but despite its radical form, it does not break the preserved historical buildings. The architect placed the spherical volume of the office, reminiscent of the armadillo shell due to its decoration, in a small courtyard hidden behind the historic facade. The contrast of old and new only emphasizes the sophistication of the solution.

4.Conclusion.

The principles of symmetry are fundamental to any architect, but each architect decides the relationship between symmetry and asymmetry in different ways. An asymmetrical building as a whole can be a harmonic composition of symmetrical elements.

A successful solution is determined by the talent of the architect, his artistic taste and his understanding of beauty. Take a walk around our city and see that there can be a lot of successful solutions, but one thing remains unchanged - the architect's desire for harmony, and this is to some extent connected with symmetry.

“I think that we have never lived in such a geometrical period until now. It is worth reflecting on the past, remembering what was before, and we will be stunned to see that the world around us is a world of geometry, pure, true, flawless in our eyes. Everything around is geometry. We have never seen so clearly such forms as a circle, a rectangle, an angle, a cylinder, a sphere, made so clearly, with such care and so confidently. "Le Corbusier"

Conclusion.

So, we plunged into the world of architecture, studied some of its forms, designs, compositions. Having considered many of its objects, we were convinced that geometry plays an important, if not the main role in architecture.

Geometry adorns architecture, gives it severity, individuality and beauty.

Studying the literature used for the preparation of this work, a lot of interesting knowledge was acquired from the history of architecture and geometry, which once again convinces of the versatility of the application of this science (geometry) and the need to study it.

Bibliography

1. Academy of Pedagogical Sciences of the USSR “What is it? Who it?" M.; Publishing house "Enlightenment" 1968; 479 pages

2. "Big illustrated encyclopedia of the student" M.; Makhaon Publishing House 2003; 490 pages

3.http://5klass.net/mkhk-11-klass/Geometrija-v-arkhitekture/004-Istorija-geometrii.html.

4. http://www.myshared.ru/slide/40354/.