Mazlova Ekaterina, Mishkevich Albina Grade 6 MOBU secondary school No. 5 Meleuz RB

Scientific - research work on the topic: in architecture cities of Meleuz »

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Scientific - research work on the topic: "Geometric shapes and figures in the architecture of the city of Meleuz"
Completed: students of 6th grade MOBU secondary school No. 5g. Meleuz Mishkevich Albina and Mazlova Ekaterina

The purpose of our work: to find out how geometry decorates the city of Meleuz; explore what geometric shapes, bodies and figures are found on the streets of our city. Tasks: 1. Study the variety of geometric shapes and figures. 2. Consider options for using geometric shapes and bodies in individual architectural objects of our city. why.

Objects of study: architectural buildings and structures, streets of the city of Meleuz. Subject of study: geometric shapes and figures in the architecture of the city of Meleuz. Research hypothesis: geometric figures, being ideal objects, find their visual embodiment in a variety of architectural structures.

Research methods: 1. Analyze the literature on the topic under study. 2. Consider the variety of architectural structures in the city of Meleuz. 3. Show what form or set of geometric shapes the selected structures have.4. Questioning.5. Experiment.6. Formulation of research results. Relevance of work 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.
1) Polygons, types of polygons
BASIC GEOMETRIC FIGURES AND FORMS
2) Round shapes
BASIC GEOMETRIC FIGURES AND FORMS
3) Polyhedra
BASIC GEOMETRIC FIGURES AND FORMS
4) Bodies of rotation
IS EVERYTHING SUITABLE FOR YOU IN THE ARCHITECTURE OF OUR CITY?
WHAT ARCHITECTURAL BUILDINGS WOULD YOU LIKE TO SEE IN OUR CITY?
WHAT GEOMETRIC FIGURES AND FORMS ARE USED IN THE ARCHITECTURE OF OUR CITY?
WHAT GEOMETRIC SHAPES AND FORMS MAKE BUILDINGS MORE CLEAR AND EXPRESSIVE?
EXPERIMENTAL APPLICATION "IF I WERE AN ARCHITECT"
The work was done by 30 students (grade 1 b) 28 students used polygons (rectangle, square, rhombus) 2 students used a circle and an oval.
FIRST DIRECTION
SECOND DIRECTION
SLIDE-SHOW "GEOMETRY OF OUR CITY"
CONCLUSION:
All architectural structures of the city of Meleuz consist of geometric figures and their combinations (mainly polyhedrons).
LE CORBUSIER:
“…… 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.

Preview:

Municipal educational budgetary institution

secondary school No. 5

municipal district Meleuzovsky district

Republic of Bashkortostan

Research work

on the topic:

"Geometric shapes and figures

in architecture

Meleuz cities »

Completed:

6th grade students

MOBU SOSH No. 5

municipal district

Meleuzovsky district

Republic of Bashkortostan

Mishkevich Albina and

Mazlova Ekaterina

Leader: math teacher

MOBU SOSH No. 5

Melkova Anzhelika 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) bodies of revolution…………………………………………………………………. ten

II. Overview of the architectural structures of the city………………………….... 11

a) questioning…………….………………………………………………… 12

b) experiment………………………………………………………………… 13

c) review of architectural structures ……………………………….……… 13

Conclusion. ………………………………………………………………....... 17

Literature..…………………………………………………………………… 19

Applications.… ……………………………………………………………….. 20

Introduction

We live in Meleuz, Republic of Bashkortostan. The city of Meleuz is a regional center. It is located at the confluence of the Meleuz River with the Belaya River.

Cities are like people ... sometimes they suffer from their own imperfection, make mistakes, rejoice - there is a holiday on their streets. Sometimes it seems that the city is sad or even crying.

Modern residential complexes, stylish shopping centers and beautiful shops - the architectural appearance of Meleuz is changing every year, the city is getting prettier before our eyes.

We love our city and proudly say to all non-residents: "I am a Meleuzian." We, we assure you, we have something to be proud of - our city has blossomed and become a real beauty. Clean paved streets, beautiful flower beds, fountains and buildings of various shapes.

Observing the architectural structures of our city, we were interested in the following: is it possible to determine the relationship of geometric shapes with architectural structures.

We decided to consider such a question as the geometry of the city and whether it affects its image, because each city has its own structure and each city has its own aura.

The purpose of our work: find out how geometry decorates the city of Meleuz; explore what geometric shapes, bodies and figures are found on the streets of our city.

Tasks:

1. Explore the variety of geometric shapes and figures;

2. Consider options for using geometric shapes and bodies in individual architectural objects of our city;

3. Find out which geometric shapes are more common and why.

Research objects:architectural buildings and structures, streets of Meleuz.

Subject of study:geometric shapes and figures in the architecture of the city of Meleuz.

Research hypothesis:geometric figures, being ideal objects, find their visual embodiment in a variety of architectural structures.

Place and dates of the study:Republic of Bashkortostan, Meleuz, September 2013 - February 2014

Research methods:

1. Analyze the literature on the topic under study.

2. Consider the variety of architectural structures of the city of Meleuz.

3. Show what shape or set of geometric shapes they have

Selected buildings.

4. Questioning.

5. Experiment.

6. Registration of research results.

The relevance of our workthat 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.

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

The main part consists of two chapters. The first deals with the basic geometric shapes and forms. The second section presents an overview of the remarkable architectural structures of the city of Meleuz with comments on their forms.

Main Intended Outcome of the Study- collecting material for use in geometry lessons in high school, designing a slide show "The geometry of our city".

I. Basic geometric shapes and forms

Amazing country - Geometry!

Figures and lines live in it,

Measure, draw and find out:

perimeter, area, length, width,

Diameter, radius and height.

Hurry up and collect your knowledge baggage!

Prepare a simple pencil as soon as possible!

Triangles, squares, rhombuses, circles… every student comes across them at school in geometry lessons.

Geometric figures occupy a central place in the school curriculum.

The first geometric concepts arose in prehistoric times.

For primitive people, the shape of the objects around them played an important role. By shape and color, they distinguished edible mushrooms from inedible ones, trees suitable for buildings from trees that can only be used for firewood. Sometimes they found crystals of minerals, from which they made devices for hunting and at home. So, mastering the world around them, people got acquainted with the simplest geometric shapes.

And when people began to build houses, it was necessary to understand more deeply what form to give to 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 indications 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 to 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" - I measure.

This section of geometry studies figures that are located on a plane: a point, a line,square, rectangle, triangle, rhombus, pentagon and other polygons, circle, 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

Polygon - This 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 triangle , from four segments -quadrilateral, from five segments - 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.

A triangle is the simplest closed rectilinear figure, one of the first whose properties a person learned in ancient times, since this figure has always been widely used in practical life.

b) Quadrangles

quadrilateralis a flat geometric figure consisting of four points (vertices of the quadrilateral) and four consecutive segments connecting them (sides of a quadrilateral). They have four corners and four sides. A quadrilateral never has three vertices on the same line.

Quadrangles are divided into:

If opposite sides are pairwise parallel

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

Since childhood, the square and rectangle familiar to us turned out to be a special case of a parallelogram.

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.

2) if only two sides are parallel

Trapeze A quadrilateral with exactly one pair of opposite sides parallel.

The trapezoid is calledisosceles (or isosceles),if its sides are equal.

A trapezoid with one right angle is called rectangular.

Rectangular trapezoid Isosceles 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 a part of a plane bounded by a circle.

The circumference is only part of the circle, its boundary, while -

Me as a circle is a more extensive and complete figure.

Oval - it 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.

Based on: triangular prism, quadrangular prism, pentagonal prism, etc.

According to the location of the lateral ribs:

tilted prism– the side rib is inclined to the base at an angle other than 90º.

straight prism - the side rib is located perpendicular to the base.

Pentagonal oblique Triangular oblique Pentagonal straight

b) Parallelepiped

A parallelepiped is a prism with a parallelogram at its base.

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

Inclined box- this is an inclined prism, at the base of which there is a parallelogram (Fig. a).

Right parallelepiped- this is a straight prism, at the base of which there is a parallelogram (Fig. b) or a 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 (ora straight prism whose base is a rectangle).

Cube is a right parallelepiped, all faces of which 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) 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 sphere.

A 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 is the Latin form of the Greek word (sfire) - ball.

A ball is a 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.

II. Overview of the architectural structures of the city

Some may think that various intricate lines, figures, surfaces can only be found in the books of mathematicians. However, it is worth looking around, and we will see that many objects have a shape similar to geometric shapes already familiar to us. It turns out there are a lot of them. We just don't always notice them.

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.

So, in the construction of both modern buildings and buildings of past centuries, knowledge of geometry is necessary. Architectural shaping with the help of geometric constructions is preserved in all cases. This problem faced the architects of past centuries, and it has not disappeared even today.

Of course, one can speak about the correspondence of architectural forms to geometric figures only approximately, digressing from small details. Each geometric figure has a unique, in terms of architecture, set of properties.

In modern architecture, a variety of geometric shapes are boldly used. The house approximately has the form of a rectangular parallelepiped. At the same time, many residential buildings and public buildings are decorated with columns.

The circle as a geometric figure has always attracted the attention of artists and architects. Solemnity and aspiration upward - this effect in the architecture of buildings is achieved by using arches representing arcs of circles. The architecture of Orthodox churches includes domes, arches, rounded vaults as essential elements, which visually enlarges the space, creates the effect of flight, lightness.

And how many geometric shapes can be found in bridge designs. Lifebuoys are often attached to the parapet of the bridge. They are very close in shape to a torus.

In our work, we explored what geometric shapes and bodies surround us, and made sure how many different geometric lines and surfaces people use in their activities - in the construction of various buildings, bridges, fences and barriers. They are used not out of simple love for interesting geometric shapes, but because the properties of these geometric lines and surfaces make it possible to solve various problems with the greatest simplicity.

A) the results of the survey

Before starting to work on the topic, we conducted a sociological survey among the students of our school. The survey involved 54 students of the 6th grade.

During the survey, students were asked to answer the following questions:

Questionnaire

1. Are you satisfied with the architecture of our city?

and all -

b) partially -

c) would like to change -

2. What architectural structures would you like to see in our city?

a) suit these -

b) more modern -

c) fundamentally change the architecture of the city -

3. What geometric shapes and forms are used in the architecture of our city?

b) pyramid -

c) a triangle -

d) circle -

e) polygons -

4. What geometric shapes and forms make buildings clearer and more expressive?

a) a rectangular parallelepiped -

b) pyramid -

c) a triangle

d) circle -

e) polygons -

5. The most beautiful building in our city?

The results of the survey are given in Annex 1.

Many of the guys surveyed would like to see the city as a modern metropolis, and many would like to radically change its architecture.

The guys believe that the use of various geometric shapes will make the city more attractive not only for residents, but also for guests.

To the question which building in the city they consider the most beautiful, 38 students answered that they consider the City Palace of Culture the most beautiful building in our city.

The city, urban space can be reduced to a certain set of elements. In fact, everything that surrounds us in the city is a set of geometric shapes. This "geometrism" is practically not perceived at the everyday level from the point of view of a city dweller, a passer-by, a tourist.

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".

b) experiment.

Each of us played the game "Cubes" in childhood, came up with designs for buildings and built them, considering ourselves a builder or architect. Most often, we used a cube, a parallelepiped, a cone and a cylinder in construction. In the form of the first two, bricks and concrete blocks were made from which buildings were erected, cones - roofs, cylinders - columns.

One of the questions of the questionnaire was the question: What geometric shapes and forms are used in the architecture of our city? Most of the guys answered that it was a rectangular parallelepiped and various types of polygons.

To test the assumption that the cube, parallelepiped, cone and cylinder are most commonly used in construction, an experiment was conducted.

Pupils of grade 1b were asked to make an application out of paper on the topic: "If I were an architect"(Appendix 2) .

The guys were offered a set of geometric shapes (rectangle, square, pyramid, cone, circle, cylinder). It turned out that the majority (28 students out of 30) used only the triangle, rectangles and squares. Only 2 guys additionally used a circle and an oval.

This experiment confirmed the hypothesis that geometric figures, being ideal objects, find their visual embodiment in a variety of architectural structures.

c) an overview of the architectural structures of the city

In the modern world, we are surrounded by many buildings consisting of complex geometric shapes, most of which are polyhedra. There are a lot of examples of this, just look around and we will notice that the buildings in which we live, the shops we go to, schools and kindergartens, etc. presented as polyhedrons.

Let's turn to the modern urban landscape. There are two directions here.

1) buildings of public, cultural purpose

These buildings are designed to attract the attention of people, create positive emotions in them. When designing them, the architects used combinations of various geometric shapes and bodies. And our gaze most often stops at buildings that combine various geometric shapes.

For example, in Meleuz these are the buildings of the city Palace of Culture, an Orthodox church and a mosque(Appendix 3 photo 1, photo 2, photo 3).

The word TEMPLE is of Russian origin (from the word mansion - a festive building). The temple is God's house on earth. Every detail of the temple has a deep meaning and significance.

The construction of a new Orthodox church for the city of Meleuz began in the era of Perestroika - in 1990 on the site of the large Trinity-Nikolskaya Church, demolished shortly before (the building existed from ~ 1898, and before that the old Trinity Church stood here).

In 1994, the construction of a new brick church, named in memory of the last functioning church of Meleuz "Kazan-Bogorodsky", was completed.

Temple 7-domed with a three-tiered bell tower.

The architectural style is modern eclecticism with distant Eastern Romanesque motifs.

The "bulbous" shape of the dome was not chosen by chance. It resembles a flame sharpening upwards, a burning candle, which is lit during prayer. This shape of the dome symbolizes spiritual uplift and striving for perfection.

The onion is a part of the sphere, smoothly transitioning and ending with a cone.

Domes - a hemisphere or simply a part of a sphere bounded by a plane. The figure lying at the base of the dome is a regular six-, octagonal prism.

The spiers are either pyramids or cones.

The architecture of the church includes arches and rounded vaults as obligatory elements, which visually enlarges the space, creates the effect of flight and lightness. Round dormer window at the end of the wall in the shape of a circle.

The mosque is a very unusual building in appearance.

It is decorated with an octagonal minaret (regular octagonal straight prism), which ends with a high pyramidal (regular octagonal pyramid) tent. The spire of the minaret is usually crowned with a crescent moon.

2) residential buildings

High-rise buildings are structures made of rectangular parallelepipeds. The predominant geometric shapes are squares and rectangles (cubes and parallelepipeds). And upon closer examination, one can notice such geometric shapes as cylinders, cones, with which the facades of houses are decorated. In modern architecture, a variety of geometric shapes are boldly used. Many residential buildings, public buildings are decorated with columns.(Appendix 3 photo 4, photo 5, photo 6).

One of the most "strong", "stable" and "confident" geometric shapes is the well-known square, in other words, an absolutely regular rectangle. The shape of a rectangle has a brick, board, slab, glass - that is, everything that we need to build a building has a rectangular shape.

For example, a rectangle is the basic part of the building, and cylinders and cones are the components of the porch, railing.

Without geometry, there would be nothing, because all the buildings that surround us are geometric shapes. First - simpler ones, such as a square, rectangle, ball. Then more complex ones: prisms, tetrahedra, pyramids, etc. But we do not always pay attention to the buildings around us.

3) fences, front gardens

Geometric figures of various shapes can also be found in other remarkable structures erected by builders and architects.(Appendix 4).

The circle as a geometric figure has always attracted the attention of artists and architects. Delight and surprise is caused by "cast iron lace" - garden fences, bridge railings, balcony railings and lanterns. Clearly visible against the backdrop of the facade of buildings in summer, in frost in winter, it gives a special charm to the city.

As independent structures, cones are not used in construction. Almost always they make up some part of the building, such as roofs and architectural decorating details. Conical piles are also used in construction.

The expressive contrast of the triangle and the rectangle on the façade attracts attention. Round, rectangular, square - all these shapes coexist perfectly 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 at the same time, it should be noted that construction is currently actively developing in our city. In recent years, architects in development have been attracted to more modern designs. Buildings with unusual shapes attract much more attention than buildings with standard shapes.

The "youngest" buildings are the Arkaim shopping mall, the Sweet Dream shopping mall, and the Solnechny market. These structures have modern, non-standard forms, radically different from the already familiar “buildings - parallelepipeds. These new objects will be a kind of “visiting card not only of Meleuz and the Republic of Bashkortostan, but also of the time in which we live.

More and more objects under construction have regular geometric shapes, and glass prevails in facade solutions (stained glass, panoramic, frameless, continuous and structural glazing of facades)

The widespread use of steel and glass, metal and plastic, many floors, ultimate functionality and laconism - these are the features of the city of Meleuz in the 21st century.

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 architectural structures of cities, and comparing the geometric forms included in their designs, one can notice 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 it severity, individuality and beauty.

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

Thus, the following conclusions can be drawn:

The use of various geometric shapes in architectural structures makes it possible to change the traditional architecture of the city.

Building the city with abstract, modern structures makes it more attractive.

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.

Conclusion: All architectural structures of the city of Meleuz consist of geometric figures and their combinations (mainly polyhedrons).

We believe that our work is consistent with the goals and objectives stated earlier.

Results of our workcan be used as a teaching aid in geometry lessons or optional classes in the study of this subject.

how main result of our researchwas the creation of the slideshow "Geometry of our city".

What did we achieve at work?

First, we got acquainted with the educational material on geometry.

Secondly, we did painstaking work and collected working material to study the relationship between architecture and geometry.

Thirdly, we have 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 for new buildings, include various geometric shapes in their designs;

2) the beauty of buildings in our city lies in their symmetry and dissymmetry;

3) the use of various geometric shapes in architectural structures makes it possible to change the traditional architecture of the city;

4) the development of the city with abstract, modern structures makes it more attractive to residents and visitors.

The purpose of this work was to highlight the main geometric shapes (on the example of modern architecture).

To achieve the goal:

The main geometric shapes were identified.

An experiment was conducted to study the most frequently used geometric shapes in the application.

The main features of the use of various geometric shapes in architecture are analyzed.

The features of the modern architecture of Meleuz are characterized.

Man gradually reduces the number of geometric forms used, in particular in architecture, in favor of rectilinear ones (cubes and parallelepipeds), thereby impoverishing the world around him.

Thus, several questions arise that may be topics for future research. How will the reduction of geometric shapes surrounding a person in favor of rectilinear ones, for example, affect people's health, in particular, vision. Who invented polygons and polyhedra, where are they used?

And we would like to end our work with the words of the great French architect, creator of international style architecture, artist and designer of the 20th century, Le Corbusier (1887-1965): “I think that we have never lived in such a geometric 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.

One can only agree with Le Corbusier's thought. Years and centuries pass, but the role of geometry does not change.

LITERATURE

1. A.V. Voloshinov. "Mathematics and Art".

M.: Enlightenment. 2000.

2. Journal "Mathematics at School" - 2005. - No. 4.

3. A.V. Ikonnikov. "The Artistic Language of Architecture".

M: Stroyizdat. 1992.

4. A.V. Pogorelov. " Geometry grade 10-11.

M.: Enlightenment. 2009.

5. L.S. Atanasyan. "Geometry grade 7-9"

M.: Enlightenment. 2011.

6. Internet resources: http://ru.wikipedia.org

slide 1

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

slide 2

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

slide 3

“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

slide 4

In this photo you see the clock tower, which is a mandatory attribute of any American university. Abstracting from some details, we can say that it has the shape of a right quadrangular prism, which is also called a rectangular parallelepiped. The geometric shape of a building is so important that there are cases when the names of geometric shapes are fixed in the name or name of the building. So, the building of the US military department is called the Pentagon, which means pentagon.

slide 5

The name of the tombs of the Egyptian pharaohs also uses the name of a spatial geometric figure - pyramids. Often, various geometric figures are combined in an architectural structure. For example, in the Spasskaya Tower of the Moscow Kremlin, at the base you can see a straight parallelepiped, turning in the middle part into a figure approaching a cylinder, but it ends with a pyramid.

slide 6

Slide 7

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

Slide 8

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

Slide 9

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.

Slide 10

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.

slide 11

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

slide 12

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.

slide 13

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

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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 photo (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 totality of buildings and structures that create a spatial environment for human life and activity. Architecture certainly creates a materially organized environment that people need for their life and activities, in accordance with their aspirations, as well as modern technical capabilities and aesthetic views. In architecture, functional, technical and aesthetic properties of objects are interconnected.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Geometric shape as a guarantor of the strength of structures.

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

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

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

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

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

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

b) Cone

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.

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.

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

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

Unusual architecture

Skyscraper DC Tower One

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

"Innovation Tower"

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

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

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

Aspen Art Museum

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

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

Louis Vuitton Foundation

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

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

Inside the building, covered with a dozen glass plates, there are 11 rooms 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 legacy of the film studio of the same name. The building is located in the 13th arrondissement of Paris, significantly rebuilt during the modernist experiments of the 1960s, but despite its radical form, it does not break the preserved historical buildings. The architect placed the spherical volume of the office, reminiscent of the armadillo shell due to its decoration, in a small courtyard hidden behind the historic facade. The contrast of old and new only emphasizes the sophistication of the solution.

4.Conclusion.

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

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

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

Conclusion.

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

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/.

3. Geometry in architecture

The house approximately has the form of a rectangular parallelepiped. In modern architecture, a variety of geometric shapes are boldly used. Many residential buildings, public buildings are decorated with columns.

The circle as a geometric figure has always attracted the attention of artists and architects. In the unique architectural appearance of St. Petersburg, "cast-iron lace" - garden fences, railings of bridges and embankments, balcony railings and lanterns - arouses delight and surprise. Clearly visible against the backdrop of the facade of buildings in summer, in frost in winter, it gives a special charm to the city. The gates of the Tauride Palace (created at the end of the 13th century by the architect F.I. Volkov) are given special airiness by circles woven into an ornament. Solemnity and aspiration upward - this effect in the architecture of buildings is achieved by using arches representing arcs of circles. We see this on the building of the General Staff. (St. Petersburg). The architecture of Orthodox churches includes domes, arches, rounded vaults as essential elements, which visually enlarges the space, creates the effect of flight, lightness.

And how beautiful the Moscow Kremlin is. Its towers are beautiful! How many interesting geometric shapes are based on them! For example, Nabatnaya tower. A smaller parallelepiped with openings for windows stands on a high parallelepiped, and a quadrangular truncated pyramid is erected even higher. It has four arches topped with an octagonal pyramid. Geometric figures of various shapes can also be found in other remarkable structures erected by Russian architects.

The expressive contrast of triangle and rectangle on the facade attracts the attention of visitors to the Groningen Museum (Holland). Round, rectangular, square - all these shapes coexist perfectly in the building of the Museum of Modern Art in San Francisco (USA). The building of the Center for Contemporary Art named after Georges Pompidou in Paris is a combination of a giant transparent parallelepiped with openwork metal fittings. The main elements of the hospital building in Berlin (Germany) are rectangles and circles. The geometric shape of the railway station at the airport of Lyon (France) resembles an ancient giant bird and at the same time the structure is ultra-modern.

And how many geometric shapes can be found in bridge designs. Lifebuoys are often attached to the parapet of the bridge. They are very close in shape to a torus.

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