Geometric shapes in construction. Geometrical forms in the architecture of Mezhdurechensk
Architecture, or architecture, surrounds a person everywhere throughout his life: it is a dwelling, and place of work, social activities, recreation, entertainment. In other words, this is a medium in which a person exists. This artificially created environment simultaneously and confronts the nature, isolating a person from her, protecting from its impacts, and connects man with nature. The architecture satisfies the practical needs of a person, it is utilitarian and therefore should be primarily a convenient, durable corresponding to its intended purpose.
The work of architecture is such an engineering, a constructive structure, which laid a certain intent - the idea of \u200b\u200bits creator. The architect puts not only scientific and technical knowledge into his creation, but also its temperament, their thoughts, feelings. This construction, in addition to utilitarian qualities, carries ideological-shaped, artistic and aesthetic beginning, affecting our emotions, causing response senses, a certain mood.
Ancient Roman theorist Art Vitruvius called three foundations on which architecture is based: "Strength, benefit, beauty."
Architecture creates a real space. This is her main distinctive feature. If the painting is defining color, for sculpture - volume, then for architecture - space. The space in architecture is limited by constructive forms made of various materials.
In the creation of space-volume architectural form, they take part, as in other art types, such artistic means and techniques, such as rhythm, symmetry and asymmetry, nuance and contrast, ratios and proportions of integer and parts.
Rhythm is the natural repetition and alternation of homogeneous elements or groups of forms - permeates the volumetric structure of the structure, informing him by harmony.
Symmetry - the same arrangement of equal parts relative to the axis of the building is a very effective means of organizing architectural forms, which contributes to a surround-spatial composition of strict orderliness, static, peace.
Asymmetry is the opposite of symmetry; It informs the composition of flexibility, dynamism, sharpness, contributing to the unity of the whole due to the integration of parts.
Specific ratios and coenms of all volumetric geometric elements, all parts of architectural structures constitute the proportions.
Contrast as opposed to the nuance - the ratio of abrupt opposite signs (shapes, elements are light and heavy, high and low, vertical and horizontal, light and dark). The contrast emphasizes, sharpens the forms and contributes to the feeling of dynamism, movement tension.
Of great importance for the perception of architectural structures has a silhouette and location, communication with the environment - natural, natural or urban; Contrasting or unity, agreement with it. 
Finally, the Commonwealth of Plastic Arts - architecture, sculptures and painting is played by an essential role in creating ideological-artistic architectural images. The leading architecture acts in this collaboration: sculpture and painting become composite elements of architecture, without losing their own originality.
Architecture, like all other arts, is a generation of your era. The architecture reflects the social system and the level of development of productive forces, life and customs of people, the dominant ideology, religious and philosophical ideas, aesthetic ideals of this time. In turn, within the framework of one style, it is brightly known to know the features of national, and in each individual work of architecture - the features of the individual handwriting of its creator.
In ancient Russia, built predominantly from the tree, the most common, affordable and relatively easily processed material. And only structures that require special strength as defense fortresses, or having particularly important in society, are temples, often built from stone and bricks. 
In Russia, very often the temples were built in memory of any significant, important event for the state. The monument built in honor of the victorious campaign of Ivan the Terrible to Kazan in 1552 was the famous Moscow Cathedral of the Intercession on the Ravy, subsequently called The temple of Vasily Blessed by the name of the yurody, funeralits walls. The Russian architect Barma and the History (for some assumptions the same person) built the temple during 1555-1561.
The idea of \u200b\u200bthe glorification of Russian warriors is very bright and figuratively expressed in an extraordinary fabulous elegant, joyful architecture of the cathedral.The cathedral consists of the central pillar-church in honor of the holiday of the Pokrov of the Virgin (the decisive assault of Kazan was started on the day of the holiday of the Intercession) and the eight pillars of the adhesions dedicated to the saints, on the days of the celebration of which had events of the Kazan campaign.The motley color, the painting of the outer moles, galleries, shooring the feathers appeared later, in the second half of the 20th century, as opposed to elegant bizarre appearance, the inner place of the temple is modest. Only the walls of the central pillar were decorated with decorative painting and inscription (chronicle) about building a temple.This is a truly monument, a monument to Russian people who gave life to the benefit of the Motherland, and he turned to the widest human masses. No wonder the cathedral was not delivered in the Kremlin, but near, on Red Square, the most crowded in Moscow.
In Russia, sincecorable was wide Monastery construction. The often created on the outskirts, the Russian state, the monasteries were not only a refuge for the monks, but at the same time important strategic defense points. In the XVI century, they, as a rule, were shared by stone or bricks (before wooden) walls with towers, which, like the Kremlin, were intended for defense.
The walls and towers were not only to protect the monastery, but also to protect him from the attack of the enemy, provide, refuge to people, to ensure their safety and create the necessary conditions for life inside the monastery in the case of its long siege. They should have been very strong to resist enemy shells, and at the same time they should have been adapted to lead the enemy shelling from them. They were folded from the huge natural boulders stones, which are replete with Solovki Islands. Boulders were not trimmed, but only customized to each other, filling the space between them with brick and lime mortar.
The towers also served as warehouses for weapons, shells, powder, were a kind of arsenals. In addition, some towers were used both both shopping facilities for grain storage and other food products. Kremlin Solovetsky - Military-defensive and at the same time a household structure. Its constructive-architectural solution is entirely responsible for these functions.
The tent is a traditional, favorite coating form in Russian wooden cult and serfdom - did the tower even higher, which was important for observing the neighborhood.
Peasant folk architecture In Russia was wooden. Wooden architecture, slowly, gradually creating its forms, retained them unchanged or with minor changes for a long time - whole eras, centuries. It was traditionally consecrated forms born in ancient times, until XVIII, Xih and even the twentieth century.Especially resistant held traditions in peasant residential construction. It has long been a type of wooden residential house-hut, well-adapted to local climatic conditions and the lifestyle of a large peasant family in the northern Russian regions.
Russian architecture of the XVIII - the first half of the XIX century developed in line with the pan-European architecture, where dominated classicism.
In the XVIII - XIX centuries, many public, buildings and residential buildings are constructed - suburban estates and urban mansions. At the same time, urban targets are solved with this architects - the organization and layout of the ensembles of space, streets, quarters.The outstanding work of the Russian architecture of the administrative and public and economic appointment was thoroughly rebuilt in 1806-1823 by Andreyan Zakharov building of the Admiralty building in St. Petersburg.Admiralty combined in itself as industrial premises - workshops, warehouses and. etc., and administrative - maritime departments and the department.
Strict admiralty forms become softer, elegant from the bright two-color color - the combinations of white and yellow, from numerous sculptural-decorative parts, naturally linked to the building design. These are sculptural reliefs on the main tower and on the front of the porticors of the side wings, and the figures of flying glory over the arch of the entrances, and wreaths on the pavilions overlooking the Neva, and the masks above the windows. On the richness of the sculptural decoration and his role in the compositional construction of the central tower and in the disclosure of the main idea of \u200b\u200bthe Admiralty has already been spoken in the chapter dedicated to the sculpture.
One of the first wonderful works Soviet architecture Mausoleum V. I. Lenin, built on the project of architect Alexei Viktorovich Shuseva (1873-1949) in 1929-1930 on Red Square. His forms are extremely concise and strict. At a low rectangular base, the discrepancy of the pyramid is calm. In the central part of the pyramid, the stands are located, to which protruding from the sides and framing the stairs. Mausoleum is lined with large, tightly fitted and carefully polished granite slabs, which in the absence of any details gives it a type of monolith. The dark red color of granite and black Labrador, which is laid out a massive block over the entrance in the mausoleum with a dedication inscription from one word "Lenin", create solemn-mourning sound. So few, but very expressive means: strict forms of calm, sustainable pyramid with clear, clear silhouette, color, surface treatment - a wise and simple solution of two interrelated tasks that were supplied to the architect are reached. The dimensions of the Mausoleum are small, but it is monumental, majestic.
Nowadays, with a huge scope of construction, with the erection of cities and new residential neighborhoods, in the first place in the architecture, there were problems of urban planning: the planning of streets, city parts, cities, the ensemble of their development, the creation among mass typical buildings leading Architectural accents - Dominant, which were a composite center, grouping and organizing around themselves all the other quarters buildings. 
The new complex of the Moscow State University, built on the project of architects, L. V. Rudneva, S. E. Chernysheva, P. V. Abrosimova, A. F. Khryakov became the same composite center of the new large South-Western district of Moscow. , Engineer V. N. Nononova in 1949-1953. It includes many separate educational and service buildings, sports facilities, botanical garden, park. And his mainly high-rise building is not only the center of the architectural complex, but also the dominant of the entire area. This building consists of many bottled volumes related to each other, grouping around the highest tower part, concluded. Side volumes gradually, as highness approaches it, it is increased, and the closest ends in turn by turrets.The new building of the University performs an important role in the panorama of the modern huge, spreading at many kilometers of Moscow, participating in its traditional "painting."
Introduction The relevance of our work is that architectural objects are an integral part of our lives. Our mood, the worldview depends on which buildings they surround us. There is a need to study that variety of objects that appeared in our world. Purpose: Investigation of the relationship between geometry and architecture. Hypothesis: All the buildings that surround us are geometric shapes. Research Object: Buildings Architecture. Subject of research: the relationship of architecture and geometry.
Tasks: 1. To explore the literature on the relationship between geometry and architecture. 2. Consider geometric forms in different architectural styles, and as a guarantor of the strength of the structures. 3. Consider the most interesting architectural structures and find out what geometric forms are found in them. Research methods: observation, photos, study and analysis of theoretical information on this issue.
"There were centuries, but the role of geometry has not changed. It still remains a grammar 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-deployed direct prism. Geometric forms in different architectural styles.
In this photo you see the clock tower, which is the mandatory attribute of any American university. It can be said that it has the form of a direct quadrangular prism, which is also called a rectangular parallelepiped. The geometric shape of the structure is so important that there are cases when the names of geometric figures are fixed in the name or title of the building. So, the US military building is called the Pentagon, which means a pentagon.
In the title of the tomb of the Egyptian pharaohs, the name of the spatial geometric shape is also used - the pyramids. Chato in the architectural structure combines various geometric shapes. For example, in the Spasskaya Tower of the Moscow Kremlin, at the base, you can see the straight parallelepiped, which turns into the middle part into the figure approaching the multifaceted prism, it is completed with the pyramid.
The architects of various eras were also their favorite parts that reflected certain combinations of geometric forms. For example, architect ancient Russia was often used for churches and bells of the so-called tent coatings. Another favorite form of ancient Russian style is the dome in the shape of a lyhead. Kiev - Nikolaev Novodevichy Monastery.
Gothic structures were directed upward, amazed by majesticity, mainly due to height. And in their forms, pyramids and cones were also widely used. Design in the style of "High Tech" is open to ferris. An example of this style a kind of student can serve as the Eiffel Tower.
Geometric shape as a guarantor of tensile strength. The strength of the construction is directly related to the geometric shape that is basic for it. Egyptian pyramids are considered the most stringent architectural structure. As you know, they have the form of the right quadrangular pyramids.
The pyramids replaced the canopy. With the advent of the arous and vaulted design in the architecture of direct lines and planes, circles, circles, spheres and circular cylinders were included. Initially, only semi-curvous arches or hemispherical dome were used in the architecture. For example, it is the hemispherical dome that has a Pantheon - the temple of all the gods - in Rome.
The geometric sediments arrive at the change of semi-Russian arches, which in terms of geometry are more complex. Arched construction served as a prototype of a frame construction, which is used today as the main under construction of modern structures from metal, glass and concrete. Telbashnya on Shabolovka This tower is built on the project of a wonderful engineer V.G. Shukhov.
Symmetry - Queen of architectural perfection. Compliance with symmetry is the first architect rule in the design of any facility. Kazan Cathedral in St. Petersburg. If you mentally hold a vertical line through the spire on the dome and the top of the front, then you can see that from two sides it is absolutely the same parts of the colonnade constructions and the building of the cathedral.
In addition to symmetry in architecture, it is possible to consider antisymmetry and dissimmetry. Antisymmetry is the opposite of symmetry, its absence. An example of antisymmetry in architecture is the Cathedral of Basil Blessed in Moscow, where symmetry is not fully in the construction in general. Dissymmetry is a partial absence of symmetry, symmetry disorder, expressed in the presence of some symmetric properties and the absence of others. An example of dissimmetry in the architectural structure can serve as the Ekaterininsky Palace in the Tsarskoye village near St. Petersburg.
Students
"Schoolchildren of the city - scienceXXI century "
Section Mathematics
Research
Geometry in architecture
Performed: , student 9b class MOU "Lyceum №31"
Leader: , teacher
mathematics
g. Oh. 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 forms in different architectural styles | |
3. Interesting architectural structures of my city | |
Conclusion | |
Bibliography |
Introduction
None of the types of arts are so closely connected with geometry as architecture. To understand the architecture should each, because it surrounds and accompanies us all his life. The great architect Le Corbusier said: "The world around us is the world of geometry is clean, true, flawless in our eyes. All around - geometry. "
Tasks and objectives of work:
Identify the relationship of the properties of architectural structures with geometric shapes
Formulate an idea of \u200b\u200bthe objectivity of mathematical relations manifested in architecture as in one of the forms of reflection of real reality
Consider geometry as a theoretical basis for creating works of architectural art
Expand the community horizon by dating with the best samples of architectural works
The structure of sections is connected with the general purpose of the work.
The main part consists of three chapters. The first considers the basic properties of architectural and spatial forms. In the second chapter, characteristic geometric forms, characteristic of various architectural styles, are illuminated. The third section presents an overview of the remarkable architectural structures of the city of Volzhsky with comments concerning their architectural styles and forms.
When working, the author used a number of literary sources. Among them are training manuals for higher and secondary educational institutions related to the history of architecture and methodology for architectural design (architectural design Barkhin. - M.: Jobsdat, 1993; Gullyansky civil and industrial buildings in five volumes. Tom I. History of architecture. - M .: Struzdat, 1984; Ilyin understanding of architecture. - M.: Struzdat, 1989; Kilip architecture. - M.: Higher School, 1989; Orlovsky: Textbook for universities. - M.: Higher School, 1984). In addition, information was used on the topic of abstract from the popular science and research literature of various authors (Zaslavsky such architecture. - Minsk: People's Asveta, 1978; Encyclopedia for children. Volume 7. Art. Part Two. Architecture, Fine and Decorative Applied Arts XVII - XX centuries. - M.: Avanta +, 1999) and Internet resources.
Of great importance in the work is attached to an illustrative material.
1. Geometric shapes in architectural structures.
"A century passed, but the role of geometry
not changed. She is still
it remains a grammar architect "
Le Corbusier
1.1. The history of geometry in architecture.
The first geometric concepts arose in prehistoric times. Different forms of material bodies observed a person in nature: form of plants, animals, mountains, convolutions of rivers, a circle and sickle of the moon, etc. However, he not only observed in nature, but also practically mastered and used her wealth. In the process of practical activity, he accumulated geometrical information. Material needs encouraged people to make workers of labor, cutting the stones and build housing, sculpt the clay dishes, pull the tent on the bow, etc.
The first architectural structures had a religious purpose. Ancient pagan tribes for rites used obelski (mengirs, dolmen or crude) (Fig. 1). The main problem in the construction of obelisk was vertical instability: the level of development of science did not allow to process the building material (most often a stone) had an uneven base. This problem was simply solved: Obelisk was put in a pre-dug hole.
Thus, the practical activity of a person served as the basis for the long-term process of developing distracted concepts, the discovery of the simplest geometric dependencies and relations.
The first information that came to us about the success of geometry are associated with the tasks of landline, calculations of volumes (ancient Egypt, Babylon, ancient Greece). Already at that time, an abstract concept of a geometric body (shape) appeared as a certain object that retains only the spatial properties of the appropriate physical body devoid of all other properties that are not related to the concept of distance, length, etc.
Thus, the geometry from the moment of the origin studied some properties of the real world. The connection of the geometry and the real world has been preserved throughout its development, while the degree of abstraction of the study object rose to an increasing level.
The geometrical information and tasks contained before us are mainly related to the calculation of areas and volumes. They have no guidance on the ways of outputting the rules used by the Egyptians to calculate them. Moreover, approximate calculations were often used. Geometry, as practical science, was used by the Egyptians to restore land plots after each spill of the Nile, with various economic work, with the construction of irrigation channels, grand churches and pyramids, when carved from the granite of famous Sphinxes. The transition from the simplest buildings to complex architectural structures was carried out slowly, as measuring instruments, materials, and mechanisms needed for construction.
1.2. The main properties of architectural and spatial forms.
Architectural structures consist of separate details, each of which is based on the basis of certain geometric shapes or on their combination. In addition, the form of any architectural structure has its own model a certain geometric shape. Mathematics would say that this construction "fits" into the geometric shape.
Of course, it is possible to talk about the compliance of architectural forms to geometric shapes only approximately, distracted by small parts. Almost all geometric shapes are used in architecture. The choice of using a particular figure in the architectural structure depends on the set of factors: the aesthetic appearance of the building, its strength, ease of operation, etc. The main requirements for architectural facilities, formulated by the ancient Roman theorist architecture Vitruviem, sound like this: "Strength, benefits, beauty". Each geometric figure has a unique, from the point of view of architecture, a set of properties.
For example, in Belarus, a hotel building has been designed near the international airport in the form of a cone. The cone converts the course of the sound wave, which has come into it. An example of using this property can be an ordinary megaphone. This feature of the cone turned out to be extremely useful for reducing noise in hotel rooms. Sometimes, trying to solve certain ideological tasks using the architecture, the authors of the projects receive a negative result. An example may be the building of the Theater of the Soviet Army, built in Moscow in Soviet times. Trying to bring the architectural image to the name of the theater as close as possible, the authors gave the form of a five-pointed star. As a result, this led to significant difficulties in layout of premises and additional costs. And the ideological five-pointed shape of the theater was able to see only birds.
Strength is one of the most important qualities of architectural structures. It depends on the properties of materials from which they are created, and from constructive 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 solid architectural construction of ancient times are the Egyptian pyramids (Fig. 2, 3).
Fig. 2 Fig. 3.
Fig. 4 Fig. five
They are known to have the form of the right quadrangular pyramids. It is this geometric form that determines the greatest stability due to the large area of \u200b\u200bthe base. On the other hand, the pyramid shape provides a decrease in the mass as the height increases above the Earth. It is these two properties that make a pyramid sustainable and especially durable. The "rationality" of the geometric shape of the pyramid allows you to choose the impressive dimensions for this structure, gives the pyramid of greatness, causes the feeling of eternity.
Currently, frame structures have maximum strength, which are used in the construction of modern structures from metal, glass and concrete. Examples of such structures can serve as well-known towers: Eiffel Tower (Fig. 4) in Paris and Telbashnya on Shabolovka (Fig. 5) in Moscow. Tenerbashnya on the Shabolovka, built by the project, consists of several parts of single-graded hyperboloids placed on each other. And each part is made of two families of rectilinear beams.
Fig. 6 Fig. 7.
https://pandia.ru/text/78/183/images/image008_15.jpg "align \u003d" left "width \u003d" 266 "height \u003d" 336 src \u003d "\u003e Hyperbolic paraboloid (Fig. 7) - this is a surface that in the section U1080 has parabolas and hyperbola. His architects are briefly called giPar. . It was Gipar who used F. Candela during the construction of the evening hall in Acapulco (Mexico) (Fig. 8).
https://pandia.ru/text/78/183/images/image010_12.jpg "Align \u003d" left "width \u003d" 354 "height \u003d" 204 src \u003d "\u003e Fig. 8 Fig. 9
Single-graded hyperboloid and hyperbolic paraboloid can be formed by moving two straight lines. The simplest non-planric surfaces are cylindrical (Fig. 10) and conical (Fig. 9) can be built by moving one straight line.
2. A variety of geometric forms in different architectural styles.
The development of architecture is largely depends on the aesthetic ideals, the artistic needs of society.
The aesthetic features of architectural structures changed during the historical process and were embodied in architectural styles. The style is made to call a set of basic features and signs of the architecture of a certain time and place. Geometrical forms peculiar to architectural structures in general and their individual elements are also signs of architectural styles. Let's try to create a system of compliance of geometric forms and basic architectural styles.
https://pandia.ru/text/78/183/images/image012_10.jpg "align \u003d" left "width \u003d" 176 "height \u003d" 280 src \u003d "\u003e Fig. 11 Fig. 12
Of course, the feudless-beam design losing the pyramid in the stability and distribution of weight, but it allowed to create internal volumes and, of course, was an outstanding achievement of human thought. The main disadvantage of such a design was the poor work of the bending stone (Fig. 14) (therefore in the temple of Amon in Karnak (Fig. 13) so much column).
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Fig. 13 Fig. fourteen
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Term "Roman style" (Fig. 17) conditioned and originated in the first half of the 12th century, when the connection of medieval architecture and ancient was discovered.
Circular "href \u003d" / text / category / tcirkulyar / "REL \u003d" BOOKMARK "\u003e Circular arches (Fig. 16). The figures are located within the vertical surfaces, and the composition does not sensate the depth. Attention is drawn to different scales of figures.
Christ is always more angels and apostles, which, in turn, more ordinary mortals. Figures are in a certain relationship with architectural forms. Images in the middle larger than those that U1085 are in the corners. The figures of squat proportions are placed on the friezes, and on the bearing parts are elongated. Such a correspondence of the image of architectural outlines is one of the characteristic features of the romance style. Romanesque art monuments are scattered throughout Western Europe. Most of them in France, which was not only the center of philosophical and theological movement, but also the wide distribution of heretical exercises. In architecture and sculpture there are the greatest variety of forms and constructive solutions.
Replaced Romanesque art came gothic. Gothic buildings are distinguished by an abundance of openwork lace parts in the form of cylinders, pyramids, cones (Fig. 18, 19). They are both outside and inside produce the impression of lightness and airiness.
Windows, portals, vaults have a characteristic fit form. Facades of buildings have axial symmetry. The stroke arc (scheme in Fig. 21) brought two constructive innovations to the Gothic architecture. Firstly, the string archers began to perform on ribs - stone edges carrying independent parts of the arch of the arch. Rights serve as if the skeleton of the arch, they take on the main burden. As a result, the design of the arch is becoming more flexible: it can withstand those deformations that will be destructive for a monolithic arch. Thus, the ribs were a prototype of a modern frame structure.
Internal supports and walls of the Gothic Cathedral remained only one vertical load - that's why they could be done more subtle and elegant. Since the vertical load of the gothic temple carried a bundle of ribs, central walls as bearing structures were unnecessary, and they were replaced with color stained glass windows.
Fig. 20 Fig. 21.
Gothic designs XII - XV echo with modern architectural structures, which have a thin reinforced concrete framework, and the walls became glass.
Gothic, which arose after the romance style became more cheerful. In all gothic architectural structures there is a desire to swell, to the sky, away from the secular bustle. The pyramid and cones used in their forms widespread in their forms corresponded to the overall idea - the desire to upward. Characteristic details for gothic structures are the fitted arches of portals, which came to replace semi-curvous arches, which are from the point of view of geometry, more complex. The stroke arch consists of two arcs
circumference of one radius. Figure 21 above the horizontal line shows a schematic image of a fitted arch.
Fig. 22. 
Fig. 23.
The architects of various eras were also their favorite parts that reflected certain combinations of geometric forms. For example, architect ancient Russia was often used for churches and bells of the so-called tent coatings. These are coatings in the form of a tetrahedral or multifaceted pyramid.
https://pandia.ru/text/78/183/images/image025_4.jpg "Align \u003d" Left "width \u003d" 288 "height \u003d" 203 src \u003d "\u003e baroque" href \u003d "/ text / category / barokko / "REL \u003d" BOOKMARK "\u003e Baroque came to replacing Renaissance. It is distinguished by the abundance of curvilinear forms. Grand architectural ensembles (group of buildings united by a common idea) of palaces and villas built in the Baroque style are striking the abundance of jewelry on the facades and inside buildings. Live lines are almost absent. Architectural forms, creating the impression of constant mobility, bended, pray for each other and intertwined with patterns, decorations, sculptures. This magnificent and lush style existed not long and already in the second half of the XVIII century. on shift it comes strict and majestic classicism.
Fig. 25 Fig. 26.
For classicism, the clarity of the forms is characterized. All buildings built in this style have clear rectilinear forms and symmetric compositions (Fig. 25). Consciously borrowed antiquity and renaissance techniques are consciously, orders with antique proportions and details are applied. Simplicity and at the same time, the monumentality that approved the power and strength of the state, the value of the human person with an amazing harmony combined in this style.
Modern appeared at the beginning of the 20th century, as an attempt to free himself from 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).
Style does not have strict symmetric structures. In fig. 26 depicted the name of the club name in Moscow. This building was built in 1929 on the project of the architect Melnikov. The base part of the building is a non-deployed direct prism due to the protrusions, which are filled with vertical rows of windows. In this case, gigantic hanging volumes are also prisms, only convex.
https://pandia.ru/text/78/183/images/image029_2.jpg "width \u003d" 217 "height \u003d" 181 "\u003e 
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Fig. 31 Fig. 32.
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Fig. 33 Fig. 34.
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Fig. 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, maintenance, markets. They are characterized by a large area of \u200b\u200ba glazed surface, openwork forms of metal structures, in the form of pyramids, cylinders, polygons. Examples are the Ministry of Finance (Fig. 31, 32), the Internet-house (Fig. 30), the greenhouse housing (Fig. 35), the Palace of Wedding (Fig. 29), Globus Store (Fig. 34), Ice Palace ( Fig.36), sports and entertainment complex (Fig. 33).
Fig. 36 Fig. 37.
Fig. 38 Fig. 39.
In addition, Classicism style buildings are present in Saransk. They are located mainly in the old part of the city. Examples of this style are the local history museum (Fig. 38), elements of the park area (Fig. 39), the National Museum (Fig. 40), the building of the Union House (Fig. 36), houses of tips (Fig. 37).
Fig. 41 Fig. 42.
Modern 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 Churches Temple Ushakov (Fig. 43), Church of Nicholas Wonderworker (Fig.44)
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Fig. 43 Fig. 44.
Conclusion
As a result of the work done, it turned out that geometry with architecture is directly connected - geometry is an indispensable part of the architecture, one of its foundations.
Geometric shapes determine the aesthetic, operational and strength properties of architectural structures of different times and styles. Moreover, for each architectural style, a certain set of geometric forms of buildings and structures in general and their individual elements are characterized. With the development of construction technologies, the possibility of using geometric shapes is expanding. On the example of the city of Saransk, various architectural styles and their geometric properties were analyzed.
Geometry was considered as a theoretical base for the creation of works of architectural art. The ideas about the objectivity of mathematical relations appear in architecture as in one of the forms of reflection of real reality were formulated.
Bibliography
1) Atanasyan: Textbook for 7-9 High School Classes. - M.: Enlightenment, 1990.
2) Bartenev and design in architecture. - L. Stroizdat, 1968
3) Barkhin architectural design. - M.: Struzdat, 1993.
4) Volzhsky 50. Chronicle. Events. Fate. - Volgograd: Publisher, 2003.
5) Big Soviet Encyclopedia (CD).
6) Voloshinov and Art - M.: Enlightenment, 2000
7) Gullyansky civil and industrial buildings in five volumes. Tom I. Architecture history. - M.: Struzdat, 1984.
8) Zaslavsky such architecture. - Minsk: Folk Asveta, 1978.
9), Zinoviev Egyptian pyramids. - Vladimir, 1999
10) Ilyin understanding architecture. - M.: Struzdat, 1989.
11) Internet resources
12) Kilip architecture. - M.: Higher School, 1989.
13) Orlovsky: Textbook for universities. - M.: Higher School, 1984.
14) Encyclopedia for children. Volume 7. Art. Part two. Architecture, visual and decorative applied arts of the XVII - XX centuries. - M.: Avanta +, 1999
Mazlova Ekaterina, Mishkevich Albina Grade 6 Mobu Sosh No. 5 Meluz RB
Scientific research work on the topic: in architecture Cities of Meleuz "
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Scientific research work on the topic: "Geometric forms and figures in the architecture of the city of Meleuz"
Performed: Studying 6 A Class MOBU SOSH No. 5G. Meleuz Mishkevich Albina Imazlova Catherine
The purpose of our work is to find out how geometry is decorated with the city of Meleuz; Explore which geometric shapes, bodies and figures are found on the streets of our city. Supplies: 1. To disrupt the variety of geometric shapes and figures. 2.Repite the options for using geometric shapes and bodies in individual architectural objects of our city. 3. To make out what geometric shapes are more common and why.
Research objects: Architectural buildings and structures, streets of Meleuz. Performance Research: Geometric shapes and figures in the architecture of the city of Meleuz. Gypothesis of research: Geometric shapes, being perfect objects, find their visual incarnation in a variety of architectural structures.
Research Methods: 1. Analyze the literature on the topic under study.2. The diversity of the architectural structures of the city of Meleuz.3. Show what form or a combination of geometric shapes have selected facilities. Questioning.5. Experiment.6. Registration of research results. The relevance of the work The architectural objects are an integral part of our life. Our mood, the worldview depends on which buildings they surround us. There is a need to study that variety of objects that appeared in our world.
1) polygons, types of polygons
Basic geometric shapes and forms
2) rounded forms
Basic geometric shapes and forms
3) Multiples
Basic geometric shapes and forms
4) Rotation Body
Do you all arrange in the architecture of our city?
What architectural structures would you like to see in our city?
What geometric shapes and forms are used in the architecture of our city?
What geometric shapes and forms make buildings clearer and expressive?
Experimentation "If I were an architect"
The work was performed - 30 students (1 B class) 28 students - used polygons (rectangle, square, rhombus) 2 student - used a circle and oval.
First direction
Second direction
Slideshow "Geometry of our city"
OUTPUT:
All architectural structures of the city of Meleuz consist of geometric shapes and their aggregates (mostly polyhedra).
Le Corbusier:
"...... the world around us is the world of geometry, clean, true, flawless in our eyes. All around - geometry. We never saw so clearly such forms like a circle, rectangle, angle, cylinder, a ball made so distinctly, with such care and so confident. "
Preview:
Municipal general education budget institution
secondary school № 5
meluzovsky district municipal district
Republic of Bashkortostan
Research work
on the topic:
"Geometric shapes and figures
in architecture
Cities of Meleuz "
Performed:
studying 6 A class
MOBU SOSH number 5
municipal Area
Meleuzovsky district
Republic of Bashkortostan
Mishkevich Albina I.
Mazlova Ekaterina
Leader: Mathematics Teacher
MOBU SOSH number 5
Melkova Angelica Nikolaevna
Meleuz 2014
Introduction ................................................................................. ... 3
- Basic geometric shapes and forms .............................. .. 5
a) polygons, types of polygons ........................................ 6.
b) rounded shapes .................................................................. .... 8
c) polyhedra ........................................................................ 8
d) the bodies of rotation .......................................................................... 10
II. Review of the architectural structures of the city .............................. .... 11
a) survey ......................................................................... 12
b) Experiment ........................................................................... 13
c) overview of architectural structures ..................................... ......... 13
Conclusion. ......................................................................... ....... 17.
Literature .. .............................................................................. 19
Applications ... ........................................................................ .. 20
Introduction
We live in the city of Meluz of the Republic of Bashkortostan. Meleuz City - District Center. It is located when the Meleuz River is shown in the White River.
Cities - like people ... sometimes they suffer from their own imperfections, mistaken, rejoice - on their streets holiday. Sometimes it seems that the city is sad or even crying.
Modern residential complexes, stylish shopping centers and beautiful shops - the architectural appearance of Meleus is changing every year, the city is good in front of her eyes.
We love our city and proudly talk to all nonresident: "I am Meleuzovets." We, we assure you, we have something to be proud - our city bloomed and became a real handsome. Clean asphalt streets, beautiful flower beds, fountains and various buildings.
Watching the architectural structures of our city, we were interested in the following: whether it is possible to determine the relationship of geometric forms with architectural structures.
We decided to consider such a question as the geometry of the city and whether it affects his image, because each city has its own structure and in every city its own aura.
The purpose of our work: Find out how geometry decorates the city of Meleuz; Explore which geometric shapes, bodies and figures are found on the streets of our city.
Tasks:
1. Examine a variety of geometric shapes and figures;
2. Consider the use of geometric shapes and bodies in separate architectural objects of our city;
3. Find out what geometric figures are more common and why.
Research objects: Architectural buildings and buildings, streets of Meleuz.
Subject of study: Geometric shapes and figures in the architecture of the city of Meleuz.
Hypothesis Research: Geometric shapes, being perfect objects, find their visual incarnation in a variety of architectural structures.
Place and timing of the study: Republic of Bashkortostan, Meleuz, September 2014 - February 2014
Research methods:
1. Analyze the literature on the topic under study.
2. Consider the manifold of architectural structures of the city of Meleuz.
3. Show what form or a set of geometric shapes have
Selected facilities.
4. Questioning.
5. Experiment.
6. Registration of research results.
The relevance of our work The fact that architectural objects are an integral part of our lives. Our mood, the worldview depends on which buildings they surround us. There is a need to study that variety of objects that appeared in our world.
The structure of sections is connected with the general purpose of the work.
The main part consists of two chapters. The first presents the main geometric shapes and forms. The second section presents an overview of the remarkable architectural structures of the city of Meleuz with comments relating to their forms.
The main estimated result of the study - Collection of material for use in the lessons of geometry in high school, the design of the Slideshow "Geometry of our city".
I. Basic geometric shapes and forms
Amazing country - geometry!
Figures and lines live in it,
Measure, draw and recognize:
Perimeter, area, length, width,
Diameter, radius and height.
Early collect your knowledge luggage!
Preparing a simple pencil!
Triangles, squares, diamonds, circles ... Each student is faced with them at school in geometry lessons.
Geometric figures occupy a central place in the school course.
The first geometric concepts arose in prehistoric times.
For primitive people, the form of them surrounding them was an important role. In shape and color, they distinguished edible mushrooms from inedible, suitable trees from trees that can be used only on firewood. Sometimes they found mineral crystals from which they made devices for hunting and at home. So, having mastered the world around them, people acquainted with the simplest geometric figures.
And when people began to build at home, I had to look more deeply in what form to give the walls and roof. It became clear that the logs are better to dangle, and the roof is to do the way to the water flowed from it. And, without knowing it, people all the time engaged in geometry. Women engaged in geometry, making clothes, hunters, making spears and boomerangs of complex shape. Only the very word "geometry" was not then, and the form of bodies were not considered separately from their other properties.
When they began to build houses from the stone, I had to drag heavy stone blocks. For this, sincerely used rollers. So people got acquainted with one of the most important figures - the cylinder. Carrying loads on rinks was difficult due to the big weight of the logs themselves. To make it easier for work, people began to cut out thin flat round plates from the trunks. So the first wheel appeared. Unknown inventor of the first wheel made the greatest discovery! Just for a moment, imagine that all the wheels on the ground disappeared. It will be a real catastrophe. Because in every car, dozens and hundreds of various wheels work from pocket hours to spacecraft.
But not only during the work people with geometric shapes were acquainted. They have long been loved to decorate themselves, their home and their clothes. Ancient masters have learned to give the beautiful shape of bronze and gold, silver and precious stones. And the artists, painting palaces, found all new geometric forms. Gonchar needed to know which form to make a vessel so that this or that amount of liquid consisted in it, and the ancient Egyptians have learned to find the volume of rather complex figures. Astronomers who observed the sky and giving their observations on the basis of their observations when starting field work should learn to determine the position of the stars in the sky. To do this, you need to measure the angles.
Various and the form of peasant fields. The fields were separated from each other by mezhami, and the spill of the Nile every spring washed away with these modes. Therefore, there were special officials who were engaged in the survey of lands, the Russians say - land. So from the practical task of the survey, the science of landereria arose. According to - Greek, the land was called "Geos", measuring - "metrico", and therefore the science of measuring the fields was called "Geometry". Just do not try to name the modern geometer to the land. For many thousands of years with its occurrence, it is only a small degree engaged in the landline.
Geometric figures were interested in our ancestors not only because they helped solve practical tasks. Some of the figures had a magic value for people. So, the triangle was considered a symbol of life, death and revival; Square - symbol of stability. Universe, infinity was denoted by the right pentagon - the Pentagon, the correct hexagon - hexagon, was a symbol of beauty and harmony. The circle is a sign of perfection.
Diverse geometric shapes created by nature and human hands; In geometry, they are considered as forms flat (figures) and forms of volume (body).
Geometry is divided into two sections: planimetry and stereometry.
It is from the planimetry that the study of geometry in schools begins.
Planimetry it comes from the Latin "Planum" - the plane, and the Greek "Metreo" - measuring.
This section of geometry studies shapes that are located on the plane: point, direct, Square, rectangle, triangle, rhombus, pentagon and other polygons, circle, oval. Geometric shapes on the plane have two dimensions: length and width.
Stereometry - This is a section of geometry, which studies the shapes in space. They, except for length and width, is height.
The volume includes: cube, parallelepiped, prism, pyramid, cylinder, cone, ball.
So, what geometric shapes and forms we studied.
1) polygons, types of polygons
Polygon - This is a geometric shape, limited from 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 calledtriangle , of four sections -quadrangle, of five segments -pentagon and so on.
a) Triangles
Triangle - This is a flat geometric figure consisting of three points that are not lying on one straight line, and three segments connecting these points.
The triangle is the simplest closed straightforward figure, one of the first, whose properties of a person learned still in ancient times, since this figure has always been widely used in practical life.
b) quadrangles
Quadrangle - this is a flat geometric shape consisting of four points (quadrangle vertices) and four sequentially connecting their segments (sides of the quadrangle). They have four corners and four sides. The quadrangle never has three vertices on one straight.
Pitrangles are divided into:
- If the opposite sides are parallel parallel
Parallelogram - This is a quadricon who has opposite parties pairly parallel, that is, lie on parallel straight lines.
Since childhood, familiar to us, the square and the rectangle turned out to be a private case of a parallelogram.
Square - The right quadriller or rhombus, in which all corners are direct, or a parallelogram, in which all sides and corners are equal.
The square by definition has equal side and angles, and, as it turned out, has all the properties of the parallelogram, rectangle and rhombus.
Rectangle - This is a parallelogram that has all the corners direct.
Rhombus - This is a parallelogram that all parties are equal.
The rhombus also has all the properties of the parallelogram, but its diagonal is mutually perpendicular and are bisector of the corners. Roma heights are equal.
2) if only two sides are parallel
Trapeze - Quadril, in which exactly one pair of opposite sides is parallel.
The trapezium is calledequalized (or equilibrium), If its side sides are equal.
A trapezium, one of the corners of which is straight, calledrectangular.
Rectangular trapezium Equality trapezium
2) rounded forms
Circle - The geometric location of the plane points equidalized from a given point, called the center, to a given non-zero distance, called its radius.
A circle - This is part of a plane limited by a circle.
The circle is only part of the circle, its border, at that time -
I like a circle is a more extensive and full-fledged figure.
Oval - this is a flat geometric shape.
It is a slightly elongated horizontally or vertical circle. Unlike the circle, the oval does not have a smooth form. At some points, the form of oval is most twisted.
- Multointers
a) Prism
Prism is called a polyhedron, which consists of two flat polygons lying in different planes and combined with parallel transfer, and all segments connecting the corresponding points of these polygons.
Based on: Triangular prism, quadrangular prism, pentagonal prism, etc.
By the location of the side ribs:
Inclined prism - The lateral edge is tilted to the base at an angle different from 90º.
Direct prism - The side edge is perpendicular to the base.
Pentagonal, inclined triangular, inclined pentagonal, straight
b) parallelepiped
The parallelepiped is a prism, at the base of which is a parallelogram.
Parallelepipeds, like all sorts of prisms, can be straight and inclined.
Inclined parallelepiped - This is an inclined prism, at the base of which parallelogram (Fig. And).
Direct parallelepiped - This is a direct prism, at the base of which parallelogram (Fig. B) or a parallelepiped, in which the lateral edge perpendicular to the base plane.
Rectangular - this is a straight parallelepiped, at the base of which a rectangle (or Direct prism, at the base of which lies a rectangle).
Cubic - It is a straight parallelepiped, all the face of which squares.
c) Pyramid
The pyramid is called a polyhedron, which consists of a flat polygon - the base of the pyramid, the points that are not lying in the base plane - the vertices of the pyramids and all segments connecting the vertex of the pyramid with the points points.
Segments connecting the vertex of the pyramid with the tops of the base are called side ribs.
- Body of rotation
A new group of geometric bodies - the bodies of rotation, because obtained by rotation of flat figures.
A) cylinder.
The cylinder is called the body, which consists of two circles combined by parallel transfer, and all segments connecting the corresponding points of these circles. Circles are called the base of the cylinder, and the segments of the cylinder forming. The base of the cylinder is equal and lie in parallel planes forming parallel and equal. The cylinder is obtained by the rotation of the rectangle around one of the sides.
b) cone
The cone is called the body, which consists of a circle - the base of the cone, the point that is not lying in the plane of this circle, are the vertices of the cone and all segments connecting the vertex of the cone with the base points.
Cone is formed by a rectangular triangle rotating around one of the cathets.
C) sphere and ball.
The sphere is a set of all points of space that are at a positive distance R from this point of O, called the center of the sphere.
Calzo sphere is the Latin form of the Greek word (sfyra) - the ball.
The ball is the set of all points of space, the distance of which from this point does not exceed the specified positive number R. The ball is obtained when the semicircular rotates relative to the diameter.
The beauty of geometry has repeatedly fascinated by the human eye. It would seem that you would build the most ordinary and fairly ordinary buildings, and then, if you look at them from another point of view, and try to a few change a picture, it turns out something else, unusual, very beautiful. Thus, from geometric shapes, you can get the constructions of unusual and fascinating.
II. Overview of the architectural structures of the city
Some may believe that various intricate lines, figures, surfaces can only be found in the books of mathematician scientists. However, it is worth seeing, and we will see that many items have a form similar to the geometric figures already familiar to us. It turns out there are a lot of them. We just don't always notice them.
Architectural structures consist of separate details, each of which is based on the basis of certain geometric shapes or on their combination. In addition, the form of any architectural structure has its own model a certain geometric shape. Mathematics would say that this construction "fits" into the geometric shape.
So, when building, both modern buildings and buildings of past centuries need knowledge of geometry. Architectural formation using geometric constructions is preserved in all cases. This problem stood before the architects of the past centuries, she did not disappear today.
Of course, it is possible to talk about the compliance of architectural forms to geometric shapes only approximately, distracted by small parts. Each geometric figure has a unique, from the point of view of architecture, a set of properties.
In modern architecture, a variety of geometric shapes are boldly. The house approximately has a view of a rectangular parallelepiped. At the same time, many residential buildings, public buildings are decorated with columns.
District as a geometric figure has always attracted the attention of Hu-devils, architects. Solemnity and aspiration is swept - such an effect in the architecture of buildings is achieved by using the arches representing the arc of circles. The architecture of the Orthodox churches includes both the mandatory elements of the dome, arches, rounded vaults, which visually increases the space, creates the effect of flight, ease.
And how many geometric figures can be found in the structures of the bridges. On the parapet of the bridge, rescue circles often strengthen. They are very close to the Torah.
In our work, we have investigated which geometric shapes and bodies surround us, and made sure how many of the most diverse geometric lines and surfaces use a person in its activities - in the construction of various buildings, bridges, fences and fences. They are not used from simple love for interesting geometric figures, but because the properties of these geometric lines and surfaces allow you to solve a variety of tasks with the greatest ease.
A) survey results
Before starting to work on the topic, we conducted a sociological survey among the students of our school. 54 student of the 6th grades participated in the survey.
When a learning survey was suggested to answer the following questions:
Profile
1. Do you all arrange in the architecture of our city?
and all -
b) partially -
c) I would like to change -
2. What architectural structures would you like to see in our city?
a) arrange these -
b) more modern -
c) radically change the architecture of the city -
3. What geometric shapes and forms are used in the architecture of our city?
b) pyramid -
c) triangle -
d) circle -
e) polygons -
4. What geometric shapes and shapes make buildings clearer and expressive?
a) rectangular parallelepiped -
b) pyramid -
c) triangle-
d) circle -
e) polygons -
5. The most beautiful building of our city?
The results of the survey are given inAppendix 1.
Many of the surveyed guys would like to see the city as a modern metropolis, and many would like to change his architecture in the root.
The guys believe that the use of a variety of geometric shapes will make the city attractive not only for residents, but also for guests.
To the question What kind of building in the city they consider the most beautiful, 38 students answered that they consider the city palace of culture as the most beautiful building of our city.
City, urban space can be reduced to some combination of elements. In fact, everything that surrounds us in the city is a set of geometric shapes. This "geometrism" practically do not perceive at the daily level from the point of view of the city, passing, tourist.
Almost all geometric shapes are used in architecture. The choice of using a particular figure in the architectural structure depends on the set of factors: the aesthetic appearance of the building, its strength, ease of operation, etc. The main requirements for architectural facilities, formulated by the ancient Roman theorist architecture Vitruviem, sound like this: "Strength, benefits, beauty".
b) Experiment.
Each of us played in childhood into the game "Cubes", invented the projects of buildings and built them, considering themselves the builder or architect. Most often we used in construction cube, parallelepiped, cone and cylinder. In the form of the first two, bricks were made and concrete blocks, of which buildings, cones - roofs, cylinders - columns.
One of the questionnaire issues was the question: what geometric shapes and forms are used in the architecture of our city? Most guys answered that this is a rectangular parallelepiped and various types of polygons.
To verify the assumption that the cube, parallelepiped, the cone and the cylinder are most often used in construction, an experiment was conducted.
1b class students were asked to make appliques from paper on the topic: "If I were an architect" (Appendix 2).
The guys, a set of geometric shapes (rectangle, square, pyramid, cone, circle, cylinder) was proposed. It turned out that the majority (28 students of 30) used only a triangle, rectangles and squares. Only 2 guys additionally used a circle and oval.
This experiment confirmed the hypothesis that geometric shapes, being perfect objects, find their visual embodiment in a variety of architectural structures.
c) review of architectural structures of the city
In the modern world, we are surrounded by many buildings consisting of complex geometric figures, most of which are polyhedra. There are a lot of examples of that very much, just look around and we will note that the buildings in which we live, shops in which we go, schools and kindergartens, etc. Presented in the form of polyhedra.
Let us turn to the modern urban landscape. There are two directions here.
1) Public, cultural buildings
These buildings are designed to attract people's attention to creating positive emotions. When they design, architects used combinations of various geometric shapes and tel. And our view most often stops on buildings combining various geometric shapes.
For example, in Meleuza is the buildings of the city Palace of Culture, the Orthodox Church and the Mosque(Appendix 3 photos 1, photo 2, photo 3).
The word Temple has Russian origin (from the word choirs - a festive structure). The temple is the house of God on Earth. Each detail of the temple has a deep meaning and meaning.
The construction of the new Orthodox church for the city of Meluza was launched in the era of perestroika - in 1990, on the spot of a large Troitskaya-Nikolsk Church, demolished before that (the building existed from ~ 1898, and before that the old Trinity Church was standing here).
In 1994, the construction of a new brick church, named in memory of the last acting church of Meleuza, Kazan-Bogorodsky, was completed.
The temple is 7-challenging with a three-tier bell tower.
Architectural style - modern eclectication with remote East Romanesque motifs.
The "bulbous" form of the dome is chosen notunder. It resembles a sharply flame, a burning candle, which is lit during prayer. Such a form of the dome symbolizes spiritual ascent and striving for perfection.
Bulb is a part of the sphere that smoothly turns into and the end cone.
The dome is a hemisphere or just part of the sphere limited to the plane. The figure underlying the dome is the right six, octagonal prism.
Spiers - either pyramids or cones.
The architecture of the church includes both the mandatory elements of the arch, rounded vaults, which visually increases the space, creates the effect of flight, ease. Round auditory window in the end of the wall in the form of a circle.
The mosque is quite unusual in appearance.
It is decorated with an eight-marched minaret (the correct octagonal direct prism), which is completed with a high pyramidal (correct octagonal pyramid) by the tent. A minaret spire is usually crowned with a crescent.
2) residential buildings
High-altitude houses are constructions from rectangular parallelepipeds. Prevailing geometric shapes - squares and rectangles (cubes and parallelepipeds). And with a detailed consideration, you can see such geometrical forms as cylinders, cones, with which the facades of houses are decorated. In modern architecture, a variety of geometric shapes are boldly. Many residential buildings, public buildings are decorated with columns.(Appendix 3 photos 4, photo 5, photo 6).
One of the most "durable", "stable" and "confident" geometric shapes is a well-known square, in other words, an absolutely correct rectangle. The shape of the rectangle has a brick, board, stove, glass - that is, everything we need to build the building has a rectangular shape.
For example, a rectangle is a basic part of the building, and cylinders and cones are the components of the porch, railings.
Without geometry there would be nothing, because all the buildings that surround us are geometric shapes. First are simpler, such as square, rectangle, ball. Then - more complex: prisms, tetrahedra, pyramids, etc. But we do not always pay attention to the buildings around us.
3) fences, parisades
Geometric shapes of various shapes can be found in other wonderful facilities erected by builders and architects(Appendix 4).
Circle as a geometric figure has always attracted the attention of artists, architects. Delight and surprise causes "cast-iron lace" - garden fences, bridge railing, balcony grilles and lights. Clearly visible against the background of the facade of buildings in summer, in the frost in the winter, it gives a special charm to the city.
As independent buildings cones in construction are not used. Always always they make up some part of the building, such as roofs and architectural decorating parts. Construction piles are also used in construction.
The expressive contrast of the triangle and rectangle on the facade attracts attention. Round, rectangular, square - all these forms are perfectly rummaged in the building.
Unfortunately, Meleuz is a young city, there are practically no historical buildings in it that would have their own individual face. But it should be noted that the construction in our city is currently actively developing. In recent years, architects in building attract more modern designs. The unusual form buildings attract much more attention than buildings with standard forms.
The most "young" buildings are TC "Arkim", TC "Sweet Sleep", the "Sunny" market. These facilities have modern, non-standard forms, are radically different from the already familiar "buildings - parallelepiped. These new objects will be a kind of "visiting card not only the Meleus and the Republic of Bashkortostan, but also the time we live in.
More and more objects are the right geometric shapes, and glass (stained glass, panoramic, frameless, solid and structural glazing) prevails in the facade solutions)
Widespread use of steel and glass, metal and plastic, set of floors, limit functionality and laconism - these are the features of the city of Meleuz in the 21st century.
It should be noted that by applying different geometric forms in the architecture, you can create a variety of architectural structures, unlike each other. Analyzing some architectural buildings of cities, and comparing the geometric forms included in their designs, it can be noted that, despite the similarity of buildings, in the architecture of each there are such geometric forms that make them different.
Conclusion
Geometry decorates the city, gives him a rigor, individuality and beauty.
Studying the used literature to prepare this work, many interesting knowledge were acquired from the history of architecture and geometry, which once again convinces the use of this science (geometry) and the need for studying it.
Thus, the following conclusions can be drawn:
The use of various geometric forms in architectural structures makes it possible to change the traditional architecture of the city.
Building a city abstract, modern designs makes it more attractive.
So, we plunged into the world of architecture, studied some of her forms, designs, compositions. Having considered the many objects, we were convinced that geometry plays an important, if not the main role in architecture.
Output: All architectural structures of the city of Meleuz consist of geometric shapes and their aggregates (mostly polyhedra).
We believe that our work corresponds to the goals and objectives declared earlier.
The results of our work Can be used as a textbook on geometry lessons or optional classes for the study of this subject.
how the main result of our study It was the creation of a slideshow "Geometry of our city".
What did we manage to work?
First, we got acquainted with the training material on geometry.
Secondly, they did painstaking work and collected a working material to study the relationship between architecture and geometry.
Thirdly, we collected a lot of interesting material about the architectural structures of our city, which allowed us to come to certain conclusions regarding its architecture:
1) the architects of the city recently, creating projects of new buildings, include in their designs a variety of geometric shapes;
2) the beauty of buildings in our city is their symmetry and dissimmetry;
3) the use of various geometric forms in architectural structures makes it possible to change the traditional architecture of the city;
4) The construction of the city is abstract, modern designs makes it more attractive for residents and guests.
The purpose of this work was the allocation of basic geometric figures (on the example of modern architecture).
To achieve the goal:
The main geometric shapes were allocated.
An experiment was carried out on the study of the most frequently used geometric figures in the application.
Analyzed the main features of using various geometric shapes in architecture.
The features of the modern architecture of the Meleuza are characterized.
The person gradually reduces the number of geometric forms used, in particular in architecture, in favor of straightforward (cubes and parallelepiped), thereby dinner around him.
Thus, there are several questions that can become topics for future research. How will the reduction in the geometric forms of the surrounding person in favor of straightforward, for example, on the health of people, in particular on their eyesight. Who came up with polygons and polyhedra, where they apply?
And we would finish our work, we would like the words of the great French architect, the creator of the architecture of international style, artist and designer of the XX century Le Corbusier (1887-1965): "I think that you have never lived in such a geometric period to the present. It is worth thinking about the past, remember what was previously, and we will be stunned, seeing that the world around us is the world of geometry, clean, true, flawless in our eyes. All around - geometry. We never saw so clearly such forms like a circle, rectangle, angle, cylinder, a ball made so distinctly, with such care and so confident. "
With the thought of Le Corbusier remains only to agree. Years, centuries pass, but the role of geometry does not change.
LITERATURE
1. A.V. Voloshin. "Mathematics and art."
M.: Enlightenment. 2000.
2. Magazine "Mathematics in School". - 2005. - № 4.
3. A.V. Icons. "Art language of architecture."
M: Stroyzdat. 1992.
4. A.V. Pogorelov. " Geometry 10-11 class. "
M.: Enlightenment. 2009.
5. L.S. Atanasyan. "Geometry 7-9 class"
M.: Enlightenment. 2011.
6. Internet - Resources: http://ru.wikipedia.org
REPORT
about laboratory workshop
By discipline Information technology in construction
Mark about the standings ..
Head of Workshop
Yu.N. Belisov.
(position) (signature) (initials, surname)
Arkhangelsk 2014.
The sheet for comments ______________________________________________________________________________________________________________________________________________________
1 Development of information technologies in construction .. 4
2 Work in Microsoft Excel .. 5
3 Information systems ... 5
4 settlement software complexes in construction .. 6
List of sources used .. 9
Development of information technologies in construction
The smart home technology is becoming a popular day of day by a number of reasons, but along with the benefits of this technology there are disadvantages (Table 1.1).
Table 1.1 - Advantages and disadvantages of the technology of "Smart Home"
Information pollution of the Internet does not most effect on the development of information technologies in construction. Pollution on the Internet has the following manifestations:
- Informational suggestion of the user. People actively using the network consume a large number of different kinds of information every day;
- artificial initiation of needs. This problem causes many negative consequences, from managing a self-built lifestyle to a critical level of mass consumption, which carries other, deeper problems that will affect humanity in a longer-term perspective;
- The problem of the truthfulness of information. The network hosts a large number of obviously false information. The reasons for this may be different, starting with simple ignorance and ignorance on any question and ending with a certain goal that a user pursues or a group of users by placing such information on the network.
With such a number of negative consequences of information pollution, the network does not provide sufficiently high-quality tools for filtering information flows. All filtering is usually reduced to the screening of banner advertising and pop-up windows. These problems need a speedy solution, as the network has already firmly entered into the lives of almost every modern person, will only strengthen its position.
Digital architecture
2.1 Basic provisions
Today, studies aimed at studying and developing technologies in architecture are becoming increasingly popular among professionals-architects. What is the role of digital technology in architecture? Is it possible to say that the architecture created by digital technologies automatically becomes digital? The boundaries of these concepts are blurred, everyone understands them in its own way. Therefore, it is advisable to define digital architecture and suggest the classification of its possible directions.
For the basis of four categories, meaningful to defining digital architecture: ISSUE (architect belonging to the flow of digital-virtual architecture), Concept (idea), Form (form), Technology (technology), considered in Evgenia Hilkevich article "Virtual architecture: an attempt Systematization. " This approach allows us to approach the definition of digital architecture quite accurately, but for a more detailed analysis of the concept of "digital architecture" it is worth identifying the criteria hierarchy and clarify their characteristics.
First of all, the ISSUE category is not significant to assign a project to a certain flow, since, first, not every author positions itself as a representative of one or another direction, and secondly, at this stage of the development of architecture it is impossible to spend clear frames between the directions . Therefore, to determine only in the category "Idea", "Technology", "Form". Thus, under the idea it is understood as a leading plan, the constructive principle of various activities, under technology - technological methods of design, means of implementing and functioning an object, under the form - geometric forms of space and their spatial characteristics.
In the Triade "Idea - Technology - Form", you can identify the dependence of categories, the ratio and characteristics of which determine the architectural direction. So, depending on the formed idea, the architect chooses the technology of its incarnation. The idea is fundamental, however, the choice of technology of its implementation can lead to the adjustment of the concept. Further, the technology affects the form of the selected form of formation, and in the future - and on how the object will function. Technology becomes defining in understanding digital architecture. Active introduction of technologies does not imply transform the creation of architecture into a mechanized process without human participation: the technology is an intermediary between the architect and the implementation of his idea. Manages the architect to the entire process, receiving the architectural space of a certain quality at the exit.
Based on the characteristics and hierarchies of these categories, present the structure of the meaning of the term digital architecture graphically (Fig. 1).
Figure 1 - Digital Architecture
The developed structure allows us to conclude that the digital architecture (Digital Architecture) is a direction in architecture, which is based on digital technologies involved both at the level of design and construction levels and in its operation.
The illustration of the "full cycle" digital architecture (using modern technologies at all stages of design) can be the work of the Gramazio & Kohler architectural bureau. Architecture based on accurate computer calculations of complex grids, forms and relationships of internal spaces, taking into account insolation, heat loss is embodied with the help of industrial construction robots. While these buildings have relatively small sizes, as a rule, these are pavilions already embodied in Zurich, London, Barcelona, \u200b\u200bNew York and other cities (Table 1).
Table 1
In many digital architecture projects, the idea of \u200b\u200bvirtuality is traced. It is expressed, first of all, in creating an interactive medium, that is, the environment that combines real and virtual validity, as well as in the departure from the traditional metric of space; This creates another, unusual, environment. The main goal is to create the most calculated architecture that most incoming in contact with the person and the environment.
2.2 Technologies
Digital technologies are included at all design stages: from pre-project to the project implementation stage. In the pre-project stage, computer simulation is used to analyze, to explore complex systems (computer experiment forecasting or imitation of processes). At the project stage, computer programs are used to simulate form that produce assessment and calculation of loads, insolation, heat loss, as well as programs for optimizing structures (minimization of stress, minimizing the deformation, ensuring maximum stability, etc.). In addition, connected computer support allows you to synchronize the process of creating work documentation. At the implementation stage, 3D printers, laser milling mills and other methods of high-precision making complex structures are used. The technology is also used in the functioning of the building (sensory and photo sensors, "intelligent" systems, etc.).
2.3 Forms of Representation
The appeal of architects to non-child geometry, topological geometry, the refusal to the usual metric of space led to the emergence of new complex architectural forms that became possible thanks to new technologies based on complex computing systems. However, despite the tendency to design curvilinear spaces and forms, curvilinearity is not a fundamental characteristic of digital architecture. The form can be classically rectangular, the main thing is a method that it was created, as erected and functions.
The form obtained by computer simulation can be classified in two ways: based on geometric properties (topological, isomorphic, fractal, rectangular shapes) or based on the characteristics of the system as dynamic or static: static, dynamic, virtual-dynamic form.
As part of the direction of digital architecture, a number of currents can be distinguished. The brightest of them: parametric architecture, responsive architecture and media architecture. Each of the directions has its own specifics, philosophy and approaches to design, however, they are based on digital technologies, and we can say that they relate to one phenomenon (Table 2).
table 2
Geometric forms in modern architecture
Now it is modern architecture that forms the appearance of the city. A man thinks about the beauty of his city, walking down the street, he looks not under his feet, but on the sides. But how it is not pleasant to see simple rectangles of houses, because in nature there are many other intricate forms: triangles, trapezoids, parallelograms, spirals ...
At the moment, architecture develops, many talented architects appear, they create new buildings using all the variety of geometric shapes.
Modern architects: Norman Foster, Cedric Price, Richard Rogers, Nicolas Grimschow - connect the image of science fiction with the possibilities of new technologies. Therefore, the style they created became known as High Tech. Another tradition of modern architecture is the so-called environmental architecture.
Architecture is called frozen music. Yes, it carries harmony forms, which reflects not only the spiritual life of generations, but also the eternal secrets of the human soul. Harmony, which delivers us aesthetic pleasure and continues to worry.
The architecture paradoxically combines the result of construction activities, geometric shapes and the top of artistic creativity. On the one hand, geometry, complex technologies, on the other - art. Engineering calculation, scientific knowledge and - artist inspiration.
3.1 Norman Foster
Famous British architect, imperial and prize laureate. I was produced by the queen first in the knights, and then in the barons.
Born on June 1, 1935 in Manchester, in the family family. In 1953-1955 served as a pilot in the Royal Air Force. Then he entered the architectural department of the University of Manchester; Replacing several universities, as a result, received a diploma of the Architectural School of the Yale University in the United States (1962), where he received a learned degree of a master and met Richard Rogers, together with whom he created the "four" bureau. From the subsoil of this institution, the high-widespread style of High-Tech was published.
Returning to England, was a partner at the team "Team 4", and in 1967 founded his own Foster Assosiates firm.
Figure 2 - Norman Foster. Central Office of Hurst Corporation in New York
The building consists of glass blocks, which are correct triangles. And the right triangles constitute the right hexagons.
Figure 3 - Norman Foster. Central office "Swiss Re" in London, also known as "cucumber"
It consists of diamond-shaped glass panels of different shades, in turn, consist of smaller rhombuses. All diamonds form a spiral.
Figure 4 - Norman Foster. Central Tower in Tokyo
Central Tower in Tokyo. A twenty-storey building, well-fitted in the architectural environment of the city, but at the same time having its own character.
The structure of the house is clearly viewed, some geometric shapes: trapezoids, triangles and rectangles.
This building consists of two towers. Due to the fact that the building is built of glass, the minimum number of concrete and iron floors, the light falls into the heart. Thus, the contrast of the deaf surface of the walls and the soft rays of light is created, which is very loved by the Japanese.
Figure 5 - Norman Foster. Bank in Hong Kong
In this building there is symmetry and an equifiable triangles.
Figure 6 - Norman Foster. Center microelectronics
The building has a cylindrical shape. Also the building is symmetrically.
3.2 Zha Hadid
Zha Hadid was born in Baghdad in 1950. At 11, during a trip to England, she decided that he would like to become an architect. In 1972, after graduating from American University in Beirut, Hadid arrived in London and entered the architectural school of the Architectural Association.
Soviet constructivists were strong on her as an architect, but her creative language remains brightly original.
One of the first to implemented buildings was the fire fighter of the manufacturer of designer furniture Vitra.
2006 - Puerta America Hotel, Madrid, Spain
2005 - Central Building of the factory BMW, Leipzig, Germany
2005 - Scientific Center "Feno", Wolfsburg, Germany
2005 - Cable Car Station, Innsbruck, Austria
2005 - Ordrukard Art Museum: New Wing, Copenhagen, Denmark
2002 - Spruklin Bergisel, Innsbruck, Austria
2001 - Hoenheim-North Station and Parking, Strasbourg, France
1998 - Center for Contemporary Art Rosentyl in Cincinnati, Ohio, USA
1994 - Fireplace of the manufacturer of designer furniture "Viter", Weil Am Rhein, Germany
Figure 7 - Zha Hadid. Fire Department.
This building consists of rectangular trapezium.
Figure 8 - Zha Hadid. Draft Museum in Perm
The project is an oval building, with a glass on the roof made in the form of an ellipse.
3.3 Freidersrey Hundertwasser
Austrian artist Fredenshraich Hundertwasser (1928-2000). He became the most famous Master of Fine Arts in Austria, connecting the stylistry of modern, a floral ornament with the principles of abstract art. In recent years, he also was fond of "ecological architecture", giving the natural forms of his painting and graphics the monumentality of real buildings.
Its perfect house is a safe cozy Nora, which covers her grass from above, but Nora with a multitude of windows-eye. In New Zealand, he built such a house where the roof passes on the sides in the hill. It grows on her grass, which is sometimes come to pinch the rams.
