Dzhambaeva M.B. one

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

Dzhambaeva F.N. one

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

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Introduction

Idea of our study appeared in geometry lessons.

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

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

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

Object of study: architecture of buildings and pyramids.

Subject of study: relationship between architecture and geometry.

The objectives of our study:

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

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

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

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

Geometric shapes in different architectural styles.

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

Often geometric shapes are combinations of different geometric bodies.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Geometric shape as a guarantor of the strength of structures.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

So, what geometric shapes and forms have we studied.

1) Polygons, types of polygons

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

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

a) triangles

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

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

b) Quadrangles

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

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

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

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

Rectangle is a parallelogram with all right angles.

Rhombus is a parallelogram with all sides equal.

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

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

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

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

2) Round shapes

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

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

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

Oval is a flat geometric figure.

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

Polyhedra

a) Prism

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

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

According to the location of the lateral ribs:

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

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

b) Parallelepiped

Parallelepiped A prism with a parallelogram at its base.

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

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

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

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

c) Pyramid

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

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

Solids of revolution

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

a) cylinder

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

b) Cone

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

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

c) Sphere and ball

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

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

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

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

3. Symmetry - the queen of architectural perfection.

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

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

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

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

In addition to symmetry in architecture, one can consider antisymmetry and dissymmetry. Antisymmetry is the opposite of symmetry, its absence. An example of antisymmetry in architecture is St. Basil's Cathedral in Moscow (see appendix fig. 13), where symmetry is completely absent in the building as a whole.

Dissymmetry is a partial lack of symmetry, a symmetry disorder expressed in the presence of some symmetrical properties and the absence of others. An example of dissymmetry in an architectural structure is the Catherine Palace in Tsarskoye Selo near St. Petersburg.

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

Unusual architecture

Skyscraper DC Tower One

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

"Innovation Tower"

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

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

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

Aspen Art Museum

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

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

Louis Vuitton Foundation

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

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

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

Pathé Foundation

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

4.Conclusion.

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

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

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

Conclusion.

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

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

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

Bibliography

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

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

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

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

students

"Schoolchildren of the city - scienceXXIcentury"

Section Mathematics

Research

Geometry in architecture

Performed:, student of class 9B of the municipal educational institution "Lyceum No. 31"

Supervisor:, teacher

mathematics

g. o. Saransk 2009

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

Introduction

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

Tasks and goals of the work:

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

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

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

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

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

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

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

Great importance in the work is given to illustrative material.

1. Geometric figures in architectural structures.

“Centuries have passed, but the role of geometry

hasn't changed. She still

remains the grammar of the architect"

Le Corbusier

1.1. History of geometry in architecture.

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

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

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

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

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

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

1.2. Basic properties of architectural and spatial forms.

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

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

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

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

Rice. 2 Fig. 3

Rice. 4 Fig. 5

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

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

Rice. 6 Fig. 7

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

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

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

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

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

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

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

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

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

Rice. 13 Fig. fourteen

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

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

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

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

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

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

Rice. 20 Fig. 21

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

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

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

Rice. 22 Rice. 23

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

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

Rice. 25 Fig. 26

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

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

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

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

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

Rice. 31 Fig. 32

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

Rice. 33 Fig. 34

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

Rice. 35 Fig. 36

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

Rice. 36 Fig. 37

Rice. 38 Fig. 39

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

Rice. 41 Fig. 42

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

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

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

Rice. 43 fig. 44

Conclusion

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

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

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

Bibliography

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

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

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

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

5) Great Soviet Encyclopedia (CD).

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

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

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

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

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

11) Internet resources

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

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

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

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.

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.

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.

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.

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.

The well-known saying of F. Engels about the subject of mathematics contains the statement that mathematics, along with quantitative relations, studies spatial forms. Geometry is the study of spatial forms. We know quite a lot of flat and spatial figures, which are called geometric bodies. On the one hand, they are abstractions from the real objects that surround us, and, on the other hand, they are prototypes, models of the shape of those objects that a person creates with his own hands.

Of course, this seems strange, but if you think about it, you can imagine that the first man began to look for a home. At first it was caves, then huts, and later man began to build and apply geometry in construction.

During the time of primitive people, paganism appeared. People began to build the first obelisks. They were carved from stone and were unstable, then people realized that in order for this obelisk to be stable, its base must be even.

In general, without geometry, there would be nothing. All the buildings that surround us are geometric shapes. For example, a log can form the basis for the formation of a geometric cylinder, and the cylinder is a model for creating columns, which are widely used in architectural structures.

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.

Being on excursions, competitions, visiting cities of the region and Russia, I noted that there are no similar cities, each of them has such architectural structures that distinguish them from each other. For example, let's take Krasnoyarsk and Novokuznetsk. These are old Siberian cities, in which the former buildings are similar to each other, and yet they have differences. But if we consider the modern architectural structures of these cities, we can see their fundamental difference. In the modern architecture of cities, a variety of geometric shapes are used, which are assembled into unusual architectural structures.

Observing the architectural structures of our city, I was interested in the following: what geometric forms are used in the architecture of the city and how they affect architectural structures.

Before starting to work on the topic, I conducted a sociological survey among the residents of the city. The survey asked residents to answer the following questions:

1. Are you satisfied with the architecture of our city?
a) all - 12%
b) partially - 35%
c) I would like changes - 53%
2. What architectural structures would you like to see in our city?
a) satisfied with these - 21%
b) more modern - 52%
c) fundamentally change the architecture of the city - 27%

Many of the respondents would like to see the city as a modern metropolis. I assume that the use of various geometric shapes will make the city more attractive not only for residents, but also for visitors.

It should be noted that, using different geometric shapes in architecture, it is possible to create a variety of architectural structures that are unlike each other. Analyzing some of the architectural structures of the city, and comparing the geometric forms included in their designs, one can notice that, despite the similarity of the buildings, in the architecture of each there are such geometric forms that make them different.

In the architecture of G. Mezhdurechensk, one can see various geometric shapes. Their diversity depends on the age of the city and the degree of its development. In the 1940s and 1950s, when the village of Tomusa was located on the site of the modern city, people lived in barracks. But even in this "barrack" architecture one could discern geometric shapes. For example, a rectangular parallelepiped, which is the base part of the building, and cylinders and cones are the constituent parts of the porch, railing.

Over time, the city developed and built. Communist Avenue, the Kuzbass cinema, the Railwayman club appeared.

High-rise buildings on the avenue are structures made of rectangular parallelepipeds. 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.

We see such cylindrical columns in the architectural design of the "Railwayman" club.

The entrance to the cinema "Kuzbass" is decorated with columns built in the form of a quadrangular prism smoothly turning into a circular arch, which has the shape of a semicircle. And the cinema itself is built in the form of a convex polyhedron.

The construction of the Kuzbass cinema and the memorial to the dead miners are separated by almost 50 years, but their architectural ensemble has one thing in common - columns.

At the time of mass buildings, the architecture of the city was monotonous. The parallelepiped houses, with which the entire city is practically built up, do not differ from each other in any way and, therefore, are not of particular interest for studying their geometric shapes.

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

Despite the fact that the city is young, its city park is decorated with a children's town, built in the form of an old fortress, in the architectural structures of which you can see spiers, which are pyramids, truncated pyramids, cones. They are presented in various combinations. The entrance to the town is decorated with a circular arch.

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

Looking at this small temple, we will notice that its dome is made in another favorite form of the Old Russian style - an onion-shaped dome. The onion is a part of the sphere, smoothly transitioning and ending with a cone. The figure lying at the base of the dome is a regular hexagonal prism.

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.

The architecture of our city is developing at the present time. Relatively recently, a fountain appeared on Communist Avenue, in the architecture of which we see traditional geometric shapes. Fountains of a similar shape can be seen in other cities of the region, Russia. Having considered the fountain as an architectural structure, I identified the main geometric shapes that are included in the design of the fountain. The base part (base) of the fountain is a concentric hollow cylinder. Also, smaller cylinders are parts located inside the fountain itself. Figures connecting the central cylinder with other smaller cylinders have an interesting shape. They have the shape of a part of a rectangular parallelepiped, from which, as it were, a circular sector was cut out.

In recent years, architects in the development of the city are attracted by more modern designs. So the buildings of the Metelitsa shopping complex, the Kristall ice palace, and the Avrora shopping and entertainment complex appeared in the city. These constructions have an unusual, abstract form and are a set of polyhedrons connected to each other in a non-standard way.

I want to note that buildings with such an unusual shape attract much more attention than buildings with standard shapes. And of course, if more such structures are built in our city, the city will be attractive not only for residents, but also for guests. I think that the attraction of abstract architectural forms in the further development of the city is necessary not only for the construction of shopping and entertainment facilities, but also in the construction of residential buildings. For example, such houses began to appear during the construction of Shakhtyorov Avenue. 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 the city with abstract, modern designs makes it more attractive to guests.

Using the materials of the Architectural and Urban Planning Council published in the media, it can be noted that the projects presented at the meetings of the council for the further development of the city have modern, non-standard forms, radically different from the already familiar "parallelepiped buildings".

I believe that my work is currently relevant.

Bibliography.

1. Vilchik N. P. "Architecture of buildings" - Publisher: Infra-M, 2005 Textbook.
2. Reshto A.D. "Mezhdurechensk". - M.: Nedra, 1990. Production practical edition.
3. LLC Publishing House "Contact" Mezhdurechensk "Mezhdurechensk 45". Biographical guide.
4. LLC "Publishing house "Contact" Mezhdurechensk "Contact" newspaper 2007, 2008.

REPORT

about the laboratory workshop

By discipline Information technology in construction

Test mark ..

Workshop leader

Yu.N. Belisov.

(position) (signature) (initials, surname)

Arkhangelsk 2014

Remarks sheet ________________________________________________________________________________________________________________________________________________________________________________________________

1 DEVELOPMENT OF INFORMATION TECHNOLOGIES IN CONSTRUCTION.. 4

2 WORKING WITH MICROSOFT EXCEL.. 5

3 INFORMATION SYSTEMS... 5

4 CALCULATION SOFTWARE COMPLEXES IN CONSTRUCTION.. 6

LIST OF USED SOURCES.. 9

DEVELOPMENT OF INFORMATION TECHNOLOGIES IN CONSTRUCTION

Smart home technology is becoming popular day by day for a number of reasons, but along with the advantages of this technology, there are also disadvantages (table 1.1).

Table 1.1 - Advantages and disadvantages of Smart Home technology

Information pollution of the Internet does not have the best effect on the development of information technologies in construction. Pollution on the Internet has the following manifestations:

– information saturation of the user. People who actively use the Web consume a large amount of various kinds of information every day;

- artificial stimulation of needs. This problem causes many negative consequences, from leading a self-destructive lifestyle to a critical level of mass consumption, which brings with it other, deeper problems that will affect humanity in the longer term;

- the problem of the veracity of information. A large amount of deliberately false information is posted on the network. The reasons for this can be various, ranging from simple ignorance and ignorance on any issue and ending with a specific goal pursued by a user or group of users by posting such information on the Web.

With so many negative consequences from information pollution, the Web does not provide enough quality tools to filter information flows. All filtering, as a rule, comes down to filtering out banner ads and pop-ups. These problems need to be resolved as soon as possible, since the Network, which has already firmly entered the life of almost every modern person, will only strengthen its position.

DIGITAL ARCHITECTURE

2.1 Fundamentals

Today, research aimed at studying and developing technologies in architecture is becoming increasingly popular among professional architects. What is the role of digital technologies in architecture? Is it possible to say that an architecture created with the help of digital technologies automatically becomes digital? The boundaries of these concepts are blurred, everyone understands them in their own way. Therefore, it is advisable to define digital architecture and propose a classification of its possible directions.

Four categories that are significant for defining digital architecture were taken as a basis: Issue (an architect’s belonging to the digital-virtual architecture trend), Concept (idea), Form (form), Technology (technology), discussed in the article by Evgeny Khilkevich "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 defining the hierarchy of these criteria and clarifying their characteristics.

First of all, the Issue category is not significant for attributing the project to a certain trend, since, firstly, not every author positions himself as a representative of one or another direction, and secondly, at this stage of architecture development it is impossible to draw a clear framework between the directions . Therefore, for the definition, we will rely only on the categories of "idea", "technology", "form". So, the idea is understood as the leading idea, the constructive principle of various types of activity, the technology - technological methods of design, means of implementation and operation of the object, the form - the geometric forms of space and their spatial characteristics.

In the triad "idea - technology - form" it is possible to identify the dependencies 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 implementation. The idea is fundamental, but the choice of technology for its implementation can lead to an adjustment of the concept. Further, the technology affects the form by the chosen method of shaping, and in the future - how the object will function. Technology is becoming defining in the understanding of digital architecture. The active introduction of technology does not imply the transformation of the creation of architecture into a mechanized process without human participation: technology is an intermediary between the architect and the implementation of his idea. The architect manages the whole process, obtaining an architectural space of a certain quality as a result.

Based on the characteristics and hierarchy of these categories, we will 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 digital architecture is a direction in architecture, which is based on digital technologies involved both at the levels of design and construction of an object, and during its operation.

An illustration of the "full cycle" digital architecture (using modern technologies at all stages of design) can be the work of the architectural bureau Gramazio & Kohler. Architecture based on precise computer calculations of complex grids, shapes and relationships of internal spaces, taking into account insolation and heat loss, is implemented using industrial construction robots. While these buildings are relatively small, as a rule, these are pavilions already implemented in Zurich, London, Barcelona, ​​New York and other cities (Table 1).

Table 1

In many digital architecture projects, the idea of ​​virtuality can be traced. It is expressed, first of all, in the creation of an interactive environment, that is, an environment that combines real and virtual reality, as well as in a departure from the traditional metric of space; thus creating a different, unusual environment. The main goal is to create the most calculated architecture, the most in contact with the person and the environment.

2.2 Technologies

Digital technologies are included in all stages of design: from pre-project to the stage of project implementation. At the pre-project stage, computer modeling is used for analysis, for the study of complex systems (computer experiment of forecasting or simulating processes). At the design stage, computer programs for shape modeling are used to evaluate and calculate loads, insolation, heat losses, as well as programs for optimizing structures (minimizing stress, minimizing deformation, ensuring maximum stability, etc.). In addition, connected computer software allows you to synchronize the process of creating working documentation. At the implementation stage, 3D printers, laser cutters and other methods of high-precision manufacturing of complex structures are used. The technology is also used in the functioning of the building (sensors and photosensors, "intelligent" systems, etc.).

2.3 Forms of representation

The appeal of architects to non-Euclidean geometry, topological geometry, the rejection of the usual metrics of space led to the emergence of new complex architectural forms, which became possible thanks to new technologies based on complex computing systems. However, despite the tendency to design curvilinear spaces and shapes, curvilinearity is not a fundamental characteristic of digital architecture. The form can also be classically rectangular, the main thing is the method in which it was created, how it was erected and how it functions.

The shape 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 shape.

Within the direction of digital architecture, a number of trends can be distinguished. The most striking of them are: 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 belong to the same phenomenon (Table 2).

table 2

GEOMETRIC FORMS IN MODERN ARCHITECTURE

Now it is modern architecture that shapes the look of the city. A person thinks about the beauty of his city, walking down the street, he looks not at his feet, but around. But how unpleasant it is to see simple rectangles of houses, because in nature there are many other intricate shapes: triangles, trapezoids, parallelograms, spirals ...

At the moment, architecture is developing, many talented architects are appearing, they are creating new buildings using all the variety of geometric shapes.

Modern architects: Norman Foster, Cedric Price, Richard Rogers, Nicholas Grimshaw - associate the image of science fiction with the possibilities of new technologies. Therefore, the style they created became known as "hi-tech". Another tradition of modern architecture is the so-called ecological architecture.

Architecture is called frozen music. Yes, it carries the harmony of forms, which reflects not only the spiritual life of generations, but also the eternal secrets of the human soul. Harmony that gives us aesthetic pleasure and continues to excite.

Architecture paradoxically combines the result of construction activity, geometric shapes and the pinnacle of artistic creativity. On the one hand, geometry, complex technologies, on the other - art. Engineering calculation, scientific knowledge and - the inspiration of the artist.

3.1 Norman Foster

Famous British architect, laureate of the Imperial and Pritzker Prizes. He was promoted by the queen, first to the knights, and then to the barons.

Born June 1, 1935 in Manchester, in a working-class family. From 1953-1955 he served as a pilot in the Royal Air Force. Then he entered the architectural department of the University of Manchester; having changed several universities, he eventually received a diploma from the Yale University School of Architecture in the USA (1962), where he received a master's degree and met Richard Rogers, with whom he created the Bureau of Four. From the bowels of this institution came a very widespread high-tech style.

Returning to England, he was a partner in Team 4, and in 1967 founded his own firm, Foster Assosiates.

Figure 2 - Norman Foster. Hearst Corporation Headquarters in New York

The building consists of glass blocks, which are regular triangles. Regular triangles make up regular hexagons.

Figure 3 - Norman Foster. Swiss Re headquarters in London, also known as "The Cucumber"

It consists of diamond-shaped glass panels of different shades, which in turn consist of smaller diamonds. All rhombuses form spirals.

Figure 4 - Norman Foster. Central Tower in Tokyo

Central Tower in Tokyo. A twenty-story building that fits well into the architectural environment of the city, but at the same time has its own character.

In the structure of the house, some geometric shapes are clearly visible: trapezoids, triangles and rectangles.

This building has two towers. Due to the fact that the building is built of glass, the minimum amount of concrete and iron ceilings, light enters the very heart. Thus, a contrast is created between the blank surface of the walls and soft rays of light, which is very fond of the Japanese.

Figure 5 - Norman Foster. Bank in Hong Kong

This building has symmetry and isosceles triangles.

Figure 6 - Norman Foster. Center for Microelectronics

The building has a cylindrical shape. The building is also symmetrical.

3.2 Zaha Hadid

Zaha Hadid was born in Baghdad in 1950. At the age of 11, during a trip to England, she decided that she wanted to become an architect. In 1972, after graduating from the American University in Beirut, Hadid moved to London and entered the architecture school of the Architectural Association.

The Soviet constructivists had a strong influence on her as an architect, but her creative language remains vividly original.

One of the first completed buildings was the fire station of Vitra, a manufacturer of designer furniture.

2006 - Hotel Puerta America, Madrid, Spain

2005 - Central building of the BMW plant, Leipzig, Germany

2005 - Science Center "Fano", Wolfsburg, Germany

2005 - Cable car stations, Innsbruck, Austria

2005 - Ordrupgaard Art Museum: new wing, Copenhagen, Denmark

2002 - Springboard Bergisel, Innsbruck, Austria

2001 - Hoenheim-North station and car park, Strasbourg, France

1998 - Rosenthal Center for Contemporary Art in Cincinnati, Ohio, USA

1994 - Fire brigade of designer furniture company "Vitra", Weil am Rhein, Germany

Figure 7 - Zaha Hadid. Fire Department.

This building consists of rectangular trapezoids.

Figure 8 - Zaha Hadid. Museum project in Perm

The project is an oval building, with glass on the roof, made in the form of an ellipse.

3.3 Friedensreich Hundertwasser

Austrian artist Friedensreich Hundertwasser (1928-2000). He became the most famous master of fine arts in Austria, combining Art Nouveau style, floral ornament with the principles of abstract art. In recent years, he was also fond of "ecological architecture", giving the natural forms of his paintings and drawings the monumentality of real buildings.

His Ideal Home is a safe, cozy burrow with grass on top, but a burrow with many eye-windows. In New Zealand, he built a house where the roof turns into a hill on the sides. Grass grows on it, which sometimes rams come to pinch.