Geometric volumetric figures in architecture. Geometric shapes in architectural structures, variety, purpose

08.05.2020

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Scientific research on the topic: "Geometry in Architecture" Author: Vyakhireva Victoria Valerievna Student of class 10 "B" of the MOU gymnasium No. 39 "Classic" Supervisor: Zhivaeva Nadezhda Nikolaevna Mathematics teacher of the highest category MOU gymnasium No. 39 "Classical" Togliatti 2010 Municipal educational institution Gymnasium No. 39 "Classic"

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Introduction The relevance of my work is that architectural objects are an integral part of our life. 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. Purpose: study of the relationship between geometry and architecture. Hypothesis: All the buildings that surround us are geometric figures Object of study: architecture of buildings Subject of study: the relationship between architecture and geometry. Tasks: 1. To study the literature on the relationship between geometry and architecture. 2. Consider geometric shapes in different architectural styles, and as a guarantee of structural strength. 3. Consider the most interesting architectural structures and find out what geometric shapes are found in them. Research methods: observation, photography, study and analysis of theoretical information on this issue.

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“Centuries have passed, but the role of geometry has not changed. It still remains the grammar of the architect.” Le Corbusier Architectural works consist of separate details, each of which is also built on the basis of a certain geometric body. the building of the club named after I.V. Rusakov in Moscow. The base part of the building is a non-convex straight prism. Geometric shapes in different architectural styles

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In this photo you see the 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.

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The name of the tombs of the Egyptian pharaohs also uses the name of a spatial geometric figure - pyramids. Often, various geometric figures are combined in an architectural structure. 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 cylinder, but it ends with a pyramid.

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Architects of different eras had their favorite details, which reflected certain combinations of geometric shapes. For example, architects Ancient Russia often used for the domes of churches and bell towers so-called tent coverings. Another favorite form of the Old Russian style are onion-shaped domes. Church of Elijah the Prophet in Yaroslavl.

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Gothic buildings were directed skyward, striking majesty, mainly due to the height. And in their forms, pyramids and cones were also widely used. The design in the style of "High Tech" is open for viewing. An example, a kind of progenitor of this style is the Eiffel Tower.

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Geometric shape as a guarantor of the strength of structures The strength of a structure is directly related to the geometric shape that is basic for it. The most durable architectural structure has long been considered Pyramids of Egypt. As you know, they have the shape of regular quadrangular pyramids.

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The pyramids were replaced by a rack-and-beam system. With the advent of the arched-vaulted structure, circles, circles, spheres and circular cylinders entered the architecture of straight lines and planes. Initially, only semicircular arches or hemispherical domes were used in architecture. For example, it is the hemispherical dome that has the Pantheon - the temple of all the gods - in Rome.

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Semicircular arches are being replaced by lancet arches, which are more complex in terms of geometry. 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. TV tower on Shabolovka This tower was built according to the project of the remarkable engineer VG Shukhov.

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Symmetry is the Queen of Architectural Excellence Symmetry is the architect's first rule when designing any structure. Kazan Cathedral in St. Petersburg If you mentally draw a vertical line through the spire on the dome and the top of the pediment, you can see that on both sides of it there are absolutely identical parts of the colonnade structure and the cathedral building.

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In addition to symmetry in architecture, one can consider antisymmetry and dissymmetry. Antisymmetry is the opposite of symmetry, its absence. An example of antisymmetry in architecture is St. Basil's Cathedral in Moscow, where symmetry is completely absent in the building as a whole. Dissymmetry is a partial lack of symmetry, 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.

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Conclusion So, I plunged into the world of architecture, studied some of its forms, designs, compositions. Having considered many of its objects, I was convinced that geometry plays an important, if not leading role in architecture. Indeed, the figures that I study in geometry are those mathematical models on the basis of which architectural forms are built. I believe that my work is consistent with the goals and objectives stated earlier. The results of the work can be used as study guide in geometry lessons, as well as in elective and optional classes in the MHC. And I would like to finish with the statement of the American engineer Weidlinger: “The beauty of forms is achieved not by means of“ cosmetics ”, but follows from the essence of the design. The form itself is almost a law of the effort it must take.

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Introduction The relevance of our work is that architectural objects are an integral part of our life. 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. Purpose: study of the relationship between geometry and architecture. Hypothesis: all the buildings that surround us are geometric shapes. Object of study: architecture of buildings. Subject of study: the relationship between architecture and geometry.

Tasks: 1. To study the literature on the relationship between geometry and architecture. 2. Consider geometric shapes in different architectural styles, and as a guarantee of structural strength. 3. 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.

“Centuries have passed, but the role of geometry has not changed. It still remains the grammar of the architect.” Le Corbusier Architectural works consist of separate details, each of which is also built on the basis of a certain geometric body. The building of the club named after I.V. Rusakov in Moscow. The base part of the building is a non-convex straight prism. Geometric shapes in different architectural styles.

In this photo you see the clock tower, which is a mandatory attribute of any American university. 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.

The name of the tombs of the Egyptian pharaohs also uses the name of a spatial geometric figure - the pyramid. Often, various geometric shapes are combined in an architectural structure. 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.

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. Another favorite form of the Old Russian style are onion-shaped domes. Kiev-Nikolaevsky Novodevichy Convent.

Gothic buildings were directed skyward, striking majesty, mainly due to the height. And pyramids and cones were also widely used in their forms. The design in the style of "High Tech" is open for viewing. An example, a kind of progenitor of this style is the Eiffel Tower.

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. The Egyptian pyramids have long been considered the most durable architectural structure. As you know, they have the shape of regular quadrangular pyramids.

Symmetry is the queen of architectural perfection. Symmetry is the first rule of an architect when designing any structure. Kazan Cathedral in St. Petersburg. If you mentally draw a vertical line through the spire on the dome and the top of the pediment, you can see that on both sides of it there are absolutely identical parts of the colonnade structure and the cathedral building.

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

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. 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 my 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 the behavior of people 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 the set 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 took 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. Further history The development of geometry proved the correctness of Lobachevsky's brilliant ideas and showed that Euclid's 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, then science was not yet strongly 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 that moment 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 difficult 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 AD, 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. Today, ZA BOR successfully leads 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 won 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 building 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

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Cylinder A cylinder is a body obtained by rotating a rectangle around a straight line containing its side.

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built in the II century. BC. in Rome at the Bull Forum. It is the earliest surviving marble building in Rome. Twenty columns of Pentelian marble, resting on a tuff pedestal, were installed under the direction of a Hellenic architect, possibly Hermodorus of Salamis. `Temple of Hercules

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"temple of all gods" in Rome, a monument of centric-domed architecture ancient rome built in the 2nd century AD. e. under Emperor Hadrian on the site of the previous Pantheon, built two centuries before by Mark Vipsanius Agrippa. Pantheon

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free-standing chapel-rotunda, erected by Donato Bramante by order of the Spanish monarchs Ferdinand and Isabella on the Roman Janiculum hill in 1502 Tempietto

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in the city of Kasimov, Ryazan region, was built in 16 in the first ruler of the Kasimov Khanate, Tsarevich Kasim. A two-story building with a dome in the style of classicism with a two-tiered minaret in the form of a low cylinder under a pointed dome placed on a massive base. Khan's mosque

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located in Belgorod region, was built in 1790. Built of brick, the structure consists of two cylinders - a large one, with a diameter of 26 m, and a small one inside it, with a diameter of approx. 10 m. The inner cylinder rises 4 m above the outer one in the form of a drum and ends with a dome. round building

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Chaev's mansion is located in St. Petersburg. Built in 1906-1907. for the railway engineer S. N. Chaev. Architects: Apyshkov V.P., Lidval F.I., Roslavlev M.I. The plan has a diagonal axis, on which three cylindrical volumes are placed: a vestibule, a hall and a winter garden.

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built in 1927-1929. in Moscow, designed by Konstantin Melnikov. The volumetric composition of the house consists of two vertical cylinders of the same diameter, cut into each other by a third of the radius, thereby forming unusual shape plan in the form of the number "8". House-workshop of architect K.S. Melnikova

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built in 1927-1929. in Moscow, designed by Ilya Golosov. The compositional center of the building is a vertical glass cylinder, on which the entire body with unusually large window surfaces is “put on”. In such a spectacular way the staircase was solved. House of Culture named after Zuev

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built in 1930-1935. Architects: Fomin I.I., Daugul V.G., Serebrovsky B.M. A round tower adjoins the horizontal body. The building is markedly asymmetrical. The south wing is round. Inside it is a huge hall covered with a dome. Moscow District Council

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is located in Munich. Its construction was completed for the 1972 Olympics. In 2004, it was closed for reconstruction (part of the exposition was exhibited near the museum). On June 21, 2008, the museum was reopened - a new pavilion was added to the museum premises, which expanded the total museum area to 5000 m². BMW Museum

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the administrative complex Porta Fira Towers was built in Barcelona (Spain) in 2004-2008. Architect: Toyo Ito. The design of the hotel building is made in the form of a distorted cylinder, expanded to the top. The second tower - an office building - is a rectangle. Porta Fira Towers

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Parallelepiped A parallelepiped is a prism with a parallelogram as its base. All faces of a parallelepiped are parallelograms. Opposite faces of a parallelepiped are equal and parallel.

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Muslim shrine in the form of a cubic building in the courtyard of the Sacred Mosque (Mecca, Saudi Arabia). The Kaaba serves as a qibla - a landmark to which Muslims around the world turn their faces during prayer. Kaaba

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church in Palermo (Italy), located on Piazza Bellini, next to the temple of Martorana. The church in the name of St. Catalda was founded by Mayo of Bari in 1161. The building of San Cataldo is an almost regular parallelepiped, on which a smaller parallelepiped is hoisted, decorated with three hemispherical domes. San Cataldo

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Museum of Modern Art in New York. Built in 1977. Japanese designers Kazuo Sejima and Ryue Nishizawa were invited to build the building of the New Museum of Modern Art. So this unusual building in a minimalist style appeared, similar to six shoe boxes stacked on top of each other. Modern Art Museum

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built in Rotterdam and Helmond by architect Piet Blom in 1984. In Rotterdam, houses stand on Overblaak Street, not far from the metro station of the same name. Blom's radical decision was that he turned the box of the house 45 degrees and placed it at an angle on a hexagonal pylon. Cube Houses or Cube Houses

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a complex of three skyscrapers in the center of Tel Aviv (Israel). Construction1996-2007 The square tower has 42 floors and 154m, it is the lowest of the three towers of the Azrieli complex. Aeriel's Tower

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built for the 2008 Olympics in Beijing. The structure was built by the Australian company PTW. The total area of the complex is about 70 thousand square meters. m. The design used elements that outwardly resemble crystal lattice from water bubbles. water cube

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located in Lumino (Switzerland). This house with a total area of 220 square meters was designed by the architectural bureau Davide Macullo Architects in 2007-2009. The plan of the villa looks like two offset parallelepipeds, the deformation of which is due to the natural topography of the area. House in Lumino

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Cube Tube is a massive building in the shape of a cube, it seems very light. The house was designed by architecture and design studio Sako Architects and built in the Jinhua Economic Development Zone in China. Built in 2010 Cube Tube

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Municipal Autonomous Educational Institution

gymnasium №16

Geometry in architecture

Gubanova Evgenia Maksimovna

MAOU gymnasium №16 7 "B" class

Introduction

Architecture

Geometry

Geometry in architecture

Practical part of the work

Conclusion

Bibliography

Applications

Introduction

Goals and objectives of the work: To reveal the relationship between the properties of architectural structures and geometric shapes, as well as the dependence of geometry and architecture on each other. Show the possibilities of geometry in architecture. Find out what role geometry plays in architecture. Using various sources to collect information on this topic, to reveal the concepts of geometry and architecture, to characterize their meanings, role and applicability.

Recommendations: this work will be useful for many who want to delve into the world of architecture and its constituent geometry, the diversity of the geometric world that surrounds us everywhere, where geometry is the theoretical basis for creating works of architectural art, thanks to which a lot of opportunities have appeared in architecture.

Geometry in architecture

“Centuries have passed, but the role of geometry

hasn't changed. She still

remains the grammar of the architect"

Le Corbusier

None of the arts is as closely related to geometry as architecture. Everyone should understand architecture, because it surrounds and accompanies us all our lives.

Geometry and architecture are sciences of different fields, but closely related to each other. Therefore, in order to identify their relationship, you need to get to know them better.

Architecture

Architecture is an art form, which is a system of buildings and structures that form a spatial environment for human life. This is the art of designing buildings and other structures that must be not only reliable and functional, but also pleasing to the eye.

The choice of architectural style depends on the materials available, on the architect's intent, and on how practical purposes should serve as the planned building. The architecture is very interesting for its diversity. In every era, in every nation, their unusual and individual styles buildings, certain materials.

Geometry

Geometry is the science of the properties of geometric shapes.

Ggeometry means from the ancient Greek "land surveying". Such a concept is associated with geometry for measurements on the ground. One of the first scientists to study geometry in detail was Euclid, who lived as early as the 3rd century BC.

Thousands of years have passed. And now the significance of geometry in the life and work of people has expanded immeasurably. Science itself has also grown; scientists of many generations have supplemented it with a lot of important information. And it is difficult to find a profession today that would not need geometry, because without it it is impossible to cope with many things.

Architectural proportions and geometry

The theory of architectural proportions developed not only as a professional and aesthetic reflection of practice, but also as a process of adaptation to architectural problems of ideas about geometry and the laws of space obtained in other fields of knowledge (physics, philosophy, biology, psychology). Within the framework of professional practice, empirical knowledge of the laws of harmony was carried out through a dialectical reflection of the unity and opposition of modular and geometric systems of proportions.

A serious step in this direction was made by Zeising (mid-19th century), who established the relationship between the proportions of the human body and the “golden section” ratios (Fibonacci numbers) and revived the anthropocentric idea in architectural metrology. Nearly a century later, Le Corbusier realized Zeising's idea in "Modulor" - a modular building system that corresponded to the static and dynamic proportions of a person (Fig. No. 1). The list of applied mathematical tools of architectural proportion has been expanded: vector analysis applied to natural forms, models of geometric coding of visual information, the so-called codes of dimensional-spatial structures, the use of systems of equations (the Pythagorean theorem and the mean proportional ratio), as a mechanism for highlighting priority relations and constructing special ones, architectural, modular-geometric spatial formations.

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 a particular figure in an architectural structure depends on many factors: aesthetic appearance building, its strength, ease of use, etc. The main requirements for architectural structures, formulated by the ancient Roman theorist of architecture Vitruvius, sound like this: "strength, usefulness, 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 a theater building. Soviet army built in Moscow in Soviet time. 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.

Geometry in architecture

Man has always sought to idealize natural forms, creating his creations on the basis of simple geometric figures, but their overabundance in the architecture of the 20th century turned into a new quality - the impoverishment of the visual emotional environment, which was always overcome by the diversity and complexity of forms. Accordingly, if we evaluate the architecture of the beginning of the 21st century, we can see that it goes beyond the framework of elementary geometrism and develops in the direction of complicating the constituent structures. In projects recent years there is an excessive enthusiasm for the almost complete freedom of form creation, which building technologies provide the architect with, a freedom that reduces creativity to competition in unusualness and novelty. It should be appreciated that the modern architecture in terms of the essence of creating objects is more complicated than, for example, the classical one. When designing new buildings for almost every object, an architect needs more and more new solutions, unique expressive forms. In this situation lies the enormous complexity of modern architecture, its troubles and rare successes.

The notion of an artist, an architect, which was established in the middle of the 12th century, as, first of all, a person with knowledge in the field of geometry, clearly reflects the state of artistic practice in the era of the emergence and growth of the trend towards the development of Gothic structures and a new architectural style. In the era of the mature Middle Ages, architecture is understood, in essence, as applied geometry. In some documents of the XIII and XIV centuries, the art of geometry is treated as a synonym for architecture. In a number of documents of the 12th-13th centuries related to building practice, the term "geometrici" - "geometers" appears to designate architects and, above all, builders of fortresses and military fortifications.

Practical part of the work

architecture geometric space figure

Architectural details consist of separate details, each of which is also built on the basis of a certain geometric body.

Often in an architectural structure various geometric shapes are combined. This building is the city church. The base of the front tower is a straight regular parallelepiped, turning in the middle part into a smaller regular quadrangular prism, which is decorated with arches on all sides. It ends with an onion-shaped dome, which consists of a cylinder and part of a sphere smoothly turning into a cone. The central tower consists of a large hemisphere on which the dome is located. At the base of the church are polyhedrons symmetrical with respect to the front tower (Fig. No. 2).

High-rise buildings on the avenue are structures made of cuboid. And upon closer examination, one can notice such geometric shapes as cylinders, cones, with which the facades of houses are decorated. In this case, cylinders are just decoration, but in general, in architecture, cylinders are a model for creating columns. Such cylindrical columns can be seen in the architectural design of the Tyumen Drama Theater (Fig. No. 3).

Fig. No. 4 shows a clock tower, which is a mandatory attribute of any American university. 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 Pentagon which means pentagon. Also, the name of the tombs of the Egyptian pharaohs also uses the name of a spatial geometric figure - the pyramid.

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 (Fig. No. 5).

In addition to symmetry in architecture, one can consider antisymmetry and dissymmetry. Antisymmetry is the opposite of symmetry, its absence. An example of antisymmetry in architecture is St. Basil's Cathedral in Moscow, where symmetry is completely absent in the building as a whole (Fig. No. 6). 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 (Fig. No. 7).

Conclusion

Thus, I proved that without such a science as geometry, there will be no other - architecture. Architectural structures 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.

So, I plunged into the world of architecture, studied some of its forms, designs, compositions. Having examined many of its objects, I was convinced that geometry plays an important, if not the main role in architecture. Indeed, the figures that I study in geometry are those mathematical models on the basis of which architectural forms are built. In the course of my work, I considered the dependence of architecture on geometry, in practice I was convinced of this and presented photos and drawings of individual geometric bodies. The purpose of my work was to study geometry outside school curriculum. I tried to reveal the application of geometry in the practical activity of man, in the construction of famous buildings.

And I would like to finish with the statement of the American engineer Weidlinger: “The beauty of forms is achieved not by means of“ cosmetics ”, but follows from the essence of the design. The form itself is almost a law of the effort it must take.

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/.

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Geometric volumetric figures in architecture. Geometric shapes in architectural structures, variety, purpose

Table of contents

Relevance

Hypothesis

Targets and goals:

Theoretical part

Story

Architecture in geometric shapes

Modern Russian architects

Architectural studio "MEL"

Practical part

Conclusion

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