The golden section method in the construction of a harmonious country house

When arranging your home, undoubtedly, one of the main points is Harmony and Coherence in the use of housing space. However, this is not feasible without a clear understanding of the basic principles in this difficult matter. For centuries, people have accumulated experience in using these principles both in the construction of individual houses and buildings, and in the construction of large-scale settlements. After all, not only the person himself and the arrangement of his life, but also the arrangement of everything in the Universe is an example of harmony, perfection and coherence. It is not for nothing that many learned minds call such impeccable coherence a truly “divine sign”. The principle of the “Golden Ratio”, which will be discussed below, is precisely based on the use of such harmony and its transfer to the sphere of arranging a human dwelling.

The Golden Section (Golden Ratio) is a division of any value in relation to 62% and 38% (Ф = 1: 1.618).

Man as the standard of the "Golden Ratio"

No matter how surprising it may sound, but in those days when there were no instruments for spatial measurements, the measure for the ancestors of the modern Slavs was the man himself. To be convinced of this, it is enough to recall many of the names in the Slavic measuring system: elbow, span, flywheel and oblique fathom, metacarpus, foot. Thus, the use of such measures of length already laid the foundation for the “golden” correspondence of the measured objects to the proportions of the human body. And it is not surprising that buildings erected according to such natural principles, were examples of harmony with the outside world and the surrounding nature.

Some of the features of ancient Russian sazhens

The most common in architectural planning in Ancient Russia there was a system of measurements by means of the so-called "sazhens", of which there were a great many. Different localities used their sazhens, which was reflected in their names: Vladimir, Moscow, Novgorod. How can such a difference be explained? Most likely, the fact that people from different areas and regions often differed in their height, size and body proportions. Moreover, many craftsmen could invent and use various personal fathoms in their work, which is quite natural - after all, any construction should be carried out according to the needs of a particular owner. If a person selects clothes taking into account the height, size and shape of the body, it would be logical to adhere to the same principles in the construction and home improvement. A low house is clearly not suitable for a giant, and a short person does not need high ceilings at all. A thin man does not need too wide doorway, while a person with large dimensions simply needs it. Matching the size to the needs of the owner provides coherence, harmony and comfort.

However, as various studies confirm, Old Russian sazhens were not proportionate and multiple of each other. That is why many experts consider their use irrational and devoid of convenience, preferring to resort to classical reference units, such as the meter.

However, how to explain such a wide practice of using irrational measures among our ancestors? Unfortunately, a strictly material perception of the surrounding reality has taken root in modern official science, and as a result, many of these questions remain without an intelligible answer.

The world around us is full of numerous movements and processes, far from each of which is able to see the human eye. Many waves, vibrations, microscopic vibrations permeate outer space every moment. This is a kind of "pulsation of nature" - not only living, but also inanimate. And what has been said fully applies to various elements of a human dwelling, whether it be walls, floors or ceilings. Microscopic wave motions, elusive even for many sensitive devices, continuously affect the human body, which cannot remain without consequences for it. As researchers in this field note, in those rooms that are built on the basis of a standard metric system, the waves take on a monotonous, “standing” character, adversely affecting human health. The body resists constant and uniform wave action, which weakens and tires it, contributing to exhaustion.

Secrets of harmony in the house

Not being commensurate and multiple values, ancient Russian sazhens are devoid of strict physical rationality. The absence of multiplicity in distances leads to imbalance of “standing” wave oscillations. At the same time, the coherence of the proportions of the dwelling with the proportions of its inhabitants is accompanied by the emergence of other waves vibrating in unison with microscopic fluctuations in the human body. It is this room that is the best for people to live, and therefore in many ancient houses people feel comfortable and relaxed, not understanding what is causing it.

Of course, accurate measurement systems are essential and have a wide range of applications, including in construction, but planning proportionality and proportions based on them is not a good option.

If the dwelling has already been built, then it can be improved by visually breaking it down into parts and premises that meet the conditions of the “golden proportion”.

Putting these principles into practice will bring any space to life while promoting well-being and a more comfortable and enjoyable experience. appearance dwellings.

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Designing a house according to the golden section

golden ratio in the design of residential buildings

For many centuries, the golden ratio has been the basis of architecture, painting and other arts. The golden section is a natural harmony, proportionality, which can be found in a variety of living structures - in the pattern of wood fibers, in the arrangement of flower petals, in the structure of shells and the human body. That is why since ancient times mankind has been striving to use this harmony in everyday life, including in construction.

The very concept of the golden section was introduced by the Greek philosopher Pythagoras, who managed to derive the formula of the so-called "divine" proportion. He defined it as the division of the whole into two unequal parts, with the smaller part related to the larger one in exactly the same way as the larger one to the common whole. If a unit is taken as a whole, then its greater part will be 0.618, and the smaller one - 0.382. These numbers can be used for designing houses according to the golden ratio.

How to use the golden ratio in construction?

All important features of the future building should be incorporated into it at the design stages. Construction planning according to the golden section begins with the definition of the main module of the building, which will act as a conditional unit. It is to it that all other dimensions of the object will subsequently be attached, and taking into account it, the internal space of the object will be divided into sections.

As a module, the most important value of the future structure, you can take the average human height or a number approximately corresponding to the growth of the future owner. Thus, the owner will be able to plan the construction of an object that will best suit him.

Other ongoing design and construction works will depend on the purpose of the owner. The golden section rule can be used not only in the construction of objects, but also in the design of interior and exterior decoration of houses.

Where can the golden ratio be used?

Wanting to build the most functional and attractive residential building, the owner can use the golden section rule when determining the ratio of colors for decorating the facade or interior cladding. Considering this rule, it becomes clear that two colors will need to be used to decorate a room or the entire building, moreover, one of them will be dominant, occupying about 60% of the entire space being designed, and the second - accompanying, occupying from 30% to 40%. An additional color can also be introduced into the interior, which should be no more than 10%, it can be used to emphasize individual decorative elements or structural details of the building.

As for the colors themselves, they are chosen taking into account the style of architecture and design. The main, accompanying and additional colors do not have to be very different from each other. Sometimes you can use several shades of the same color to decorate rooms, making soft transitions of tone and thus achieving the desired visual effect.

The golden section rule can also be used when creating a general design composition for external or interior decoration. In this case, the main detail of the composition is chosen, the most important focal point of lighting, furniture and decor. The surrounding space is filled with accompanying elements that emphasize the chosen style, the main constructive or design solutions. Experienced designers know that in any interior there should be dynamics and development. Single-colored and uniform houses do not attract attention, look gray and completely uninteresting.

You can also use the golden ratio when dividing walls into levels. To do this, you can use various physical elements, such as skirting boards. If the owner wants to make the division soft and less noticeable, then the wall can be left as a whole by applying the principle of the golden section in the arrangement of furniture or in hanging panels. With this method of interior design, it is better to use the most neutral main color, highlighting bright spots. decorative elements and all kinds of decorations.

It is very important when designing a building to maintain the correct ratio of furniture and available space. Taking into account the rule of the golden section, the furniture in each room should occupy no more than 60% of the total composition, otherwise the rooms will look cramped and cluttered. You can maximize the attractiveness and harmony of interior spaces by designing custom-made furniture. In this case, the owner will be able, taking into account the rule of the golden section, to determine the dimensions and characteristics of each individual element of the interior.

The 2/3 rule can be used in almost every issue regarding the design of the rooms of a residential building. So, when choosing a pendant lamp, you need to take into account that it should be located at a height of about 2/3 of the height of the room, the sofa should occupy no more than 2/3 of the partition allocated for it, the coffee table should be more than 2/3 of the size of the sofa, next to with which he is located.

The golden section rule can be used in the design of adjacent territories of apartment buildings and private buildings, however, such work is extremely difficult to perform, which is why it is recommended to involve experienced designers in their implementation. To determine the cost of services of specialists, you can use the calculator.

Golden Ratio - Harmonic Proportion

In mathematics, proportion (Latin proportio) is the equality of two ratios: a: b = c: d.

Line segment AB can be divided into two parts in the following ways:
into two equal parts - AB: AC = AB: BC;
into two unequal parts in any ratio (such parts do not form proportions);
thus, when AB: AC = AC: BC.

The latter is the golden division or division of the segment in the extreme and average ratio.

The golden section is such a proportional division of a segment into unequal parts, in which the entire segment relates to the larger part in the same way as the larger part itself relates to the smaller one; or in other words, the smaller segment is related to the larger one as the larger one is to everything

a: b = b: c or c: b = b: a.

Practical acquaintance with the golden ratio begins with dividing a straight line segment in the golden ratio using a compass and ruler.

From point B, a perpendicular equal to half AB is restored. The resulting point C is connected by a line to point A. On the resulting line, a segment BC is plotted, ending with point D. The segment AD is transferred to the straight line AB. The resulting point E divides the segment AB in the ratio of the golden ratio.

Segments of the golden ratio are expressed as an infinite irrational fraction AE \u003d 0.618 ..., if AB is taken as a unit, BE \u003d 0.382 ... For practical purposes, approximate values ​​\u200b\u200bof 0.62 and 0.38 are often used. If the segment AB is taken as 100 parts, then the larger part of the segment is 62, and the smaller one is 38 parts.

The properties of the golden section are described by the equation:

x2 - x - 1 = 0.

Solution to this equation:

The properties of the golden section created a romantic aura of mystery and almost mystical worship around this number.

The second golden ratio

The Bulgarian magazine "Fatherland" (No. 10, 1983) published an article by Tsvetan Tsekov-Karandash "On the second golden section", which follows from the main section and gives a different ratio of 44: 56.

The division is carried out as follows. The segment AB is divided in proportion to the golden section. From point C, the perpendicular CD is restored. Radius AB is point D, which is connected by a line to point A. Right angle ACD is bisected. A line is drawn from point C to the intersection with line AD. Point E divides segment AD in the ratio 56:44.

The figure shows the position of the line of the second golden section. It is located in the middle between the golden section line and the middle line of the rectangle.

Golden Triangle

To find segments of the golden ratio of the ascending and descending rows, you can use the pentagram.

To build a pentagram, you need to build a regular pentagon. The method of its construction was developed by the German painter and graphic artist Albrecht Dürer (1471...1528). Let O be the center of the circle, A a point on the circle, and E the midpoint of segment OA. The perpendicular to the radius OA, raised at point O, intersects with the circle at point D. Using a compass, mark the segment CE = ED on the diameter. The length of a side of a regular pentagon inscribed in a circle is DC. We set aside segments DC on the circle and get five points for drawing a regular pentagon. We connect the corners of the pentagon through one diagonal and get a pentagram. All diagonals of the pentagon divide each other into segments connected by the golden ratio.

Each end of the pentagonal star is a golden triangle. Its sides form an angle of 36° at the top, and the base laid on the side divides it in proportion to the golden section.

Draw straight line AB. From point A we lay off on it a segment O of arbitrary size three times, through the resulting point P we draw a perpendicular to the line AB, on the perpendicular to the right and left of point P we put off segments O. The resulting points d and d1 are connected by straight lines with point A. We put the segment dd1 on line Ad1, getting point C. She divided the line Ad1 in proportion to the golden ratio. The lines Ad1 and dd1 are used to build a "golden" rectangle.

History of the golden section

It is generally accepted that the concept of the golden division was introduced into scientific use Pythagoras, ancient Greek philosopher and mathematician (VI century BC). There is an assumption that Pythagoras borrowed his knowledge of the golden division from the Egyptians and Babylonians. Indeed, the proportions of the Cheops pyramid, temples, bas-reliefs, household items and decorations from the tomb of Tutankhamun indicate that the Egyptian craftsmen used the ratios of the golden division when creating them. French architect Le Corbusier found that in the relief from the temple of Pharaoh Seti I in Abydos and in the relief depicting Pharaoh Ramses, the proportions of the figures correspond to the values ​​​​of the golden division. The architect Khesira depicted on a relief wooden board from the tomb of his name, holds measuring instruments in which the proportions of the golden division are fixed.

The Greeks were skilled geometers. They even taught arithmetic to their children with the help of geometric shapes. The square of Pythagoras and the diagonal of this square were the basis for constructing dynamic rectangles.

Plato(427...347 BC) also knew about the golden division. His dialogue " Timaeus» is dedicated to the mathematical and aesthetic views of the school of Pythagoras and, in particular, to the issues of the golden division.

In the facade of the ancient Greek temple of the Parthenon there are golden proportions. During its excavations, compasses were found, which were used by architects and sculptors of the ancient world. The Pompeian compass (Museum in Naples) also contains the proportions of the golden division.

In the ancient literature that has come down to us, the golden division is first mentioned in " Beginnings» Euclid. In the 2nd book of the "Beginnings" a geometric construction of the golden division is given. After Euclid, Hypsicles (II century BC), Pappus (III century AD) and others were engaged in the study of the golden division. In medieval Europe with the golden division We met through Arabic translations of Euclid's Elements. The translator J. Campano from Navarre (3rd century) commented on the translation. The secrets of the golden division were jealously guarded, kept in strict secrecy. They were known only to the initiates.

During the Renaissance, interest in the golden division increased among scientists and artists in connection with its use in both geometry and art, especially in architecture. Leonardo da Vinci, an artist and scientist, saw that Italian artists had great empirical experience, but little knowledge. He conceived and began to write a book on geometry, but at that time a monk's book appeared Luca Pacioli, and Leonardo abandoned his venture. According to contemporaries and historians of science, Luca Pacioli was a real luminary, the greatest mathematician Italy between Fibonacci and Galileo. Luca Pacioli was a student of the artist Piero della Francesca, who wrote two books, one of which was called On Perspective in Painting. He is considered the creator of descriptive geometry.

Luca Pacioli was well aware of the importance of science for art. In 1496, at the invitation of the Duke of Moreau, he came to Milan, where he lectured on mathematics. Leonardo da Vinci also worked at the Moro court in Milan at that time. In 1509, Luca Pacioli's Divine Proportion was published in Venice, with brilliantly executed illustrations, which is why they are believed to have been made by Leonardo da Vinci. The book was an enthusiastic hymn to the golden ratio. Among the many advantages of the golden ratio, the monk Luca Pacioli did not fail to name its “divine essence” as an expression of the divine trinity of God the Son, God the Father and God the Holy Spirit (it was understood that the small segment is the personification of God the Son, the larger segment is the personification of God the Father, and the entire segment - the god of the holy spirit).

Leonardo da Vinci also paid much attention to the study of the golden division. He made sections of a stereometric body formed by regular pentagons, and each time he obtained rectangles with aspect ratios in golden division. Therefore, he gave this division the name of the golden section. So it is still the most popular.

At the same time, in the north of Europe, in Germany, he worked on the same problems Albrecht Dürer. He sketches an introduction to the first draft of a treatise on proportions. Durer writes. “It is necessary that the one who knows something should teach it to others who need it. This is what I set out to do."

Judging by one of Dürer's letters, he met with Luca Pacioli during his stay in Italy. Albrecht Dürer develops in detail the theory of the proportions of the human body. Dürer assigned an important place in his system of ratios to the golden section. The height of a person is divided in golden proportions by the belt line, as well as by the line drawn through the tips of the middle fingers of the lowered hands, the lower part of the face - by the mouth, etc. Known proportional compass Dürer.

Great astronomer of the 16th century Johannes Kepler called the golden ratio one of the treasures of geometry. He is the first to draw attention to the significance of the golden ratio for botany (plant growth and structure).

Kepler called the golden ratio self-continuing. “It is arranged in such a way,” he wrote, “that the two junior terms of this infinite proportion add up to the third term, and any two last terms, if added together, give the next term, and the same proportion remains until infinity."

The construction of a series of segments of the golden ratio can be done both in the direction of increase (increasing series) and in the direction of decrease (descending series).

If on a straight line of arbitrary length, set aside segment m, next we set aside segment M. Based on these two segments, we build a scale of segments of the golden proportion of the ascending and descending rows.

In subsequent centuries, the rule of the golden ratio turned into an academic canon, and when, over time, a struggle began in art with the academic routine, in the heat of the struggle, “they threw out the child along with the water.” The golden section was “discovered” again in the middle of the 19th century. In 1855, a German researcher of the golden section, professor Zeising published his work Aesthetic Investigations. With Zeising, exactly what happened was bound to happen to the researcher who considers the phenomenon as such, without connection with other phenomena. He absolutized the proportion of the golden section, declaring it universal for all phenomena of nature and art. Zeising had numerous followers, but there were also opponents who declared his doctrine of proportions to be "mathematical aesthetics".

Zeising did a great job. He measured about two thousand human bodies and came to the conclusion that the golden ratio expresses the average statistical law. The division of the body by the navel point is the most important indicator of the golden ratio. The proportions of the male body fluctuate within the average ratio of 13: 8 = 1.625 and approach the golden ratio somewhat closer than the proportions of the female body, in relation to which the average value of the proportion is expressed in the ratio 8: 5 = 1.6. In a newborn, the proportion is 1: 1, by the age of 13 it is 1.6, and by the age of 21 it is equal to the male. The proportions of the golden section are also manifested in relation to other parts of the body - the length of the shoulder, forearm and hand, hand and fingers, etc.

Zeising tested the validity of his theory on Greek statues. He developed the proportions of Apollo Belvedere in most detail. Greek vases, architectural structures were studied different eras, plants, animals, bird eggs, musical tones, poetic meters. Zeising defined the golden ratio, showed how it is expressed in line segments and in numbers. When the figures expressing the lengths of the segments were obtained, Zeising saw that they constituted a Fibonacci series, which could be continued indefinitely in one direction and the other. His next book was entitled "Golden division as the basic morphological law in nature and art." In 1876, a small book, almost a pamphlet, was published in Russia, outlining Zeising's work. The author took refuge under the initials Yu.F.V. Not a single painting is mentioned in this edition.

At the end of XIX - beginning of XX centuries. a lot of purely formalistic theories appeared about the use of the golden section in works of art and architecture. With the development of design and technical aesthetics, the law of the golden ratio extended to the design of cars, furniture, etc.

Fibonacci series

The name of the Italian mathematician monk Leonardo from Pisa, better known as Fibonacci (son of Bonacci), is indirectly connected with the history of the golden section. He traveled a lot in the East, introduced Europe to Indian (Arabic) numerals. In 1202, his mathematical work The Book of the Abacus (Counting Board) was published, in which all the problems known at that time were collected. One of the tasks read "How many pairs of rabbits in one year from one pair will be born." Reflecting on this topic, Fibonacci built the following series of numbers:

A series of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc. known as the Fibonacci series. The peculiarity of the sequence of numbers is that each of its members, starting from the third, is equal to the sum of the previous two 2 + 3 = 5; 3 + 5 = 8; 5 + 8 = 13, 8 + 13 = 21; 13 + 21 \u003d 34, etc., and the ratio of adjacent numbers of the series approaches the ratio of the golden division. So, 21:34 = 0.617, and 34:55 = 0.618. This ratio is denoted by the symbol Ф. Only this ratio - 0.618: 0.382 - gives a continuous division of a straight line segment in the golden ratio, increasing it or decreasing it to infinity, when the smaller segment is related to the larger one as the larger one is to everything.

Fibonacci also dealt with the practical needs of trade: what is the smallest number of weights that can be used to weigh a commodity? Fibonacci proves that the following system of weights is optimal: 1, 2, 4, 8, 16...

Generalized golden ratio

Fibonacci series could have remained only a mathematical incident if it were not for the fact that all researchers of the golden division in the plant and animal world, not to mention art, invariably came to this series as an arithmetic expression of the law of golden division.

Scientists continued to actively develop the theory of Fibonacci numbers and the golden ratio. Yu. Matiyasevich solves Hilbert's 10th problem using Fibonacci numbers. There are elegant methods for solving a number of cybernetic problems (search theory, games, programming) using Fibonacci numbers and the golden section. In the USA, even the Mathematical Fibonacci Association is being created, which has been publishing a special journal since 1963.

One of the achievements in this area is the discovery of generalized Fibonacci numbers and generalized golden ratios.

The Fibonacci series (1, 1, 2, 3, 5, 8) and the "binary" series of weights 1, 2, 4, 8, 16 discovered by him... are completely different at first glance. But the algorithms for their construction are very similar to each other: in the first case, each number is the sum of the previous number with itself 2 = 1 + 1; 4 \u003d 2 + 2 ..., in the second - this is the sum of the two previous numbers 2 \u003d 1 + 1, 3 \u003d 2 + 1, 5 \u003d 3 + 2 .... Is it possible to find a general mathematical formula from which " binary series, and the Fibonacci series? Or maybe this formula will give us new numerical sets with some new unique properties?

Indeed, let's set a numerical parameter S, which can take any values: 0, 1, 2, 3, 4, 5... separated from the previous one by S steps. If we denote the nth member of this series by φS (n), then we obtain the general formula φS (n) = φS (n - 1) + φS (n - S - 1).

Obviously, with S = 0, from this formula we will get a “binary” series, with S = 1 - the Fibonacci series, with S = 2, 3, 4. new series of numbers, which are called S-Fibonacci numbers.

In general terms, the golden S-proportion is the positive root of the golden S-section equation xS+1 – xS – 1 = 0.

It is easy to show that at S = 0, the division of the segment in half is obtained, and at S = 1, the familiar classical golden section.

The ratios of neighboring Fibonacci S-numbers with absolute mathematical accuracy coincide in the limit with the golden S-proportions! Mathematicians in such cases say that golden S-sections are numerical invariants of Fibonacci S-numbers.

The facts confirming the existence of golden S-sections in nature are given by the Belarusian scientist E.M. Soroko in the book "Structural Harmony of Systems" (Minsk, "Science and Technology", 1984). It turns out, for example, that well-studied binary alloys have special, pronounced functional properties (thermally stable, hard, wear-resistant, oxidation-resistant, etc.) only if the specific weights of the initial components are related to each other by one of golden S-proportions. This allowed the author to put forward a hypothesis that golden S-sections are numerical invariants of self-organizing systems. Being experimentally confirmed, this hypothesis can be of fundamental importance for the development of synergetics, a new field of science that studies processes in self-organizing systems.

Using golden S-proportion codes, any real number can be expressed as a sum of degrees of golden S-proportions with integer coefficients.

The fundamental difference between this method of encoding numbers is that the bases of new codes, which are golden S-proportions, turn out to be irrational numbers for S > 0. Thus, the new number systems with irrational bases, as it were, put the historically established hierarchy of relations between rational and irrational numbers “upside down”. The fact is that at first the natural numbers were "discovered"; then their ratios are rational numbers. And only later - after the Pythagoreans discovered incommensurable segments - irrational numbers appeared. For example, in decimal, quinary, binary and other classical positional number systems, natural numbers - 10, 5, 2 - were chosen as a kind of fundamental principle, from which, according to certain rules, all other natural, as well as rational and irrational numbers were constructed.

Kind of an alternative existing ways calculus is a new, irrational system, as the fundamental principle, the beginning of which is chosen as an irrational number (which, we recall, is the root of the golden section equation); other real numbers are already expressed through it.

In such a number system, any natural number is always representable as a finite number - and not infinite, as previously thought! are the sums of powers of any of the golden S-proportions. This is one of the reasons why "irrational" arithmetic, with its amazing mathematical simplicity and elegance, seems to have absorbed best qualities classical binary and "Fibonacci" arithmetic.

Principles of shaping in nature

Everything that took on some form formed, grew, strove to take a place in space and preserve itself. This aspiration finds fulfillment mainly in two variants - upward growth or spreading over the surface of the earth and twisting in a spiral.

The shell is twisted in a spiral. If you unfold it, you get a length slightly inferior to the length of the snake. A small ten-centimeter shell has a spiral 35 cm long. Spirals are very common in nature. The concept of the golden ratio will be incomplete, if not to say about the spiral.

The shape of the spirally curled shell attracted the attention of Archimedes. He studied it and deduced the equation of the spiral. The spiral drawn according to this equation is called by his name. The increase in her step is always uniform. At present, the Archimedes spiral is widely used in engineering.

Even Goethe emphasized the tendency of nature to spirality. The spiral and spiral arrangement of leaves on tree branches was noticed long ago. The spiral was seen in the arrangement of sunflower seeds, in pine cones, pineapples, cacti, etc. The joint work of botanists and mathematicians has shed light on these amazing natural phenomena. It turned out that in the arrangement of leaves on a branch (phylotaxis), sunflower seeds, pine cones, the Fibonacci series manifests itself, and therefore, the law of the golden section manifests itself. The spider spins its web in a spiral pattern. A hurricane is spiraling. A frightened herd of reindeer scatter in a spiral. The DNA molecule is twisted into a double helix. Goethe called the spiral "the curve of life."

Among the roadside herbs grows an unremarkable plant - chicory. Let's take a closer look at it. A branch was formed from the main stem. Here is the first leaf.

The process makes a strong ejection into space, stops, releases a leaf, but is shorter than the first one, again makes an ejection into space, but of less force, releases an even smaller leaf and ejection again. If the first outlier is taken as 100 units, then the second is equal to 62 units, the third is 38, the fourth is 24, and so on. The length of the petals is also subject to the golden ratio. In growth, the conquest of space, the plant retained certain proportions. Its growth impulses gradually decreased in proportion to the golden ratio.

Rice. 13. Chicory

Rice. 14. Viviparous lizard

In the lizard, at first glance, proportions that are pleasing to our eyes are caught - the length of its tail relates to the length of the rest of the body as 62 to 38.

Both in the plant and animal worlds, the shaping tendency of nature persistently breaks through - symmetry with respect to the direction of growth and movement. Here the golden ratio appears in the proportions of parts perpendicular to the direction of growth.

Nature has carried out the division into symmetrical parts and golden proportions. In parts, a repetition of the structure of the whole is manifested.

Rice. 15. Bird egg

The great Goethe, a poet, naturalist and artist (he painted and painted in watercolor), dreamed of creating a unified doctrine of the form, formation and transformation of organic bodies. It was he who introduced the term morphology into scientific use.

Pierre Curie at the beginning of our century formulated a number of profound ideas of symmetry. He argued that one cannot consider the symmetry of any body without taking into account the symmetry of the environment.

The patterns of "golden" symmetry are manifested in the energy transitions of elementary particles, in the structure of some chemical compounds, in planetary and space systems, in the gene structures of living organisms. These patterns, as indicated above, are in the structure of individual human organs and the body as a whole, and are also manifested in biorhythms and the functioning of the brain and visual perception.
Golden ratio and symmetry

The golden ratio cannot be considered in itself, separately, without connection with symmetry. The great Russian crystallographer G.V. Wulff (1863...1925) considered the golden ratio to be one of the manifestations of symmetry.

The golden division is not a manifestation of asymmetry, something opposite to symmetry. According to modern concepts, the golden division is an asymmetric symmetry. The science of symmetry includes such concepts as static and dynamic symmetry. Static symmetry characterizes rest, balance, and dynamic symmetry characterizes movement, growth. So, in nature, static symmetry is represented by the structure of crystals, and in art it characterizes peace, balance and immobility. Dynamic symmetry expresses activity, characterizes movement, development, rhythm, it is evidence of life. Static symmetry is characterized by equal segments, equal magnitudes. Dynamic symmetry is characterized by an increase in segments or their decrease, and it is expressed in the values ​​of the golden section of an increasing or decreasing series.

Information sources: Kovalev F.V. Golden section in painting. K .: Vyscha school, 1989. Kepler I. About hexagonal snowflakes. - M., 1982. Durer A. Diaries, letters, treatises - L., M., 1957. Tsekov-Karandash Ts. About the second golden section. – Sofia, 1983. Stakhov A. Codes of the golden ratio.	see also: Ernst Neufert. Building design. Measurement system

The one-story, horizontally developed house consists of two rectangular blocks standing at an angle. The central part in the form of a circle segment connects both blocks. This original plan made it possible to conveniently place the house on the site and deploy it with a wide facade towards the garden.

Contrary to popular belief, in the design of houses, the artistic ambitions of the architect are by no means the main role. The value of a home primarily depends on its functionality and durability.

House design It's more of a craft than art. The house should be beautiful, solid and comfortable. It is impossible to perceive it as a work of art - this can lead to misunderstandings between the customer and the architect. Often the reason for disagreement is the excessive ambitions of the architect, while it is the requirements of the customer that should be at the forefront. The task of the architect is to find solutions that satisfy both parties.

And remember - the numerous changes made by the customer to the project, as a rule, indicate a lack of understanding between him and the architect. Therefore, you should not blame the customer for interfering with the author's vision, but it is better to think about whether his needs are taken into account? If the architect is not able to implement them, then he should not make a project for him.

A strikingly simple roof is an important element of the house's architecture. Despite the fact that the main life in the house takes place on the ground floor, skylights provide additional illumination of the space under the roof.

Proper house architecture

A house with a successful architectural solution will look good even without additional conspicuous details. But the lack of clear proportions is ugly, even if the house is decorated with many spectacular elements. Designing new house, we strive to architectural solution was balanced. If it is orderly and well proportioned, the house has a chance to look good. Even if its decoration is not the most successful, repairs can always put the house in order.

Low-set windows and almost reachable eaves create an atmosphere of close connection between the house and the garden.

Proportions (the ratio of the height of the walls and the size of the roof, the ratio of the sizes of various elements, etc.) play a major role in the architecture of the house. Naturally, there is no single principle, but some specific principle in the image of each house should be clearly traced. If a one-story house is low and horizontal, then the shape of its architectural details should be consistent with its proportions. For example, horizontal windows, quite appropriate in this case, would look strange in a tall house.

The terrace adjacent to the dining room is shifted into the depths of the house, forming a wide gallery. It is hidden from view and represents, rather, one of the many nooks in the garden.

About the benefits of a hip roof

A very important element of the architecture of the house is the roof. Its shape depends, among other things, on the size of the span, that is, on the width of the house. You should strive to ensure that the spans are not too large. With a width of 12 m, even a roof with a small angle of inclination of the slopes looks cumbersome. And with a width of 9 m, the same roof can be higher and more noticeable, while its design will be simpler. We especially like the hipped roofs with wide eaves and a slope angle of about 40°.

A two-story house with a hipped, simple roof was designed for a site with an entrance from the south side.

In order not to "lose" the sunny area, the garage and the utility part were placed behind the house.

The hip roof perfectly completes the volume, crowning all the walls. A house with such a roof looks calm and uniform from any point. Here is the house with gable roof looks different from different points: from the side of the gable wall - this is one image, from the side of the facades - another. Sometimes these images differ in such a way that they create an impression of dissonance. The hip roof is an indicator of the balance of the project: if its contour is a closed rectangle, and the edges of the slopes converge at the appropriate point, this is the best evidence that everything is in order with the shape of the house. Naturally, the hip roof has its drawbacks. She needs more supports, the location of which needs to be thought out, taking into account not only the design requirements, but also the convenience of the layout of the premises. Numerous skylights and chimneys look bad on such a roof.

There are more slopes in the attic under a hip roof than under a gable roof, so the design of the interior space will be more complicated. It is not easy to design and implement. However, it is precisely thanks to this shape of the roof that the house has a closed volume, a calm and orderly image.

About a not quite one-story house

In our opinion, living in one-story houses is much more comfortable. And although the staircase often serves as an interior decoration, its absence is a big advantage. In addition, in a house with an exploited attic, there are often problems with temperature changes. Attic rooms, even though well insulated, can become excessively hot in summer, and in winter warm air collects in the upper part of the house, and it becomes too hot in the attic, while on the ground floor it is quite cool.

An example is not quite one-story house. Favored by architects simple hip roof with large slopes covers the attic, which represents a reserve of space and allows you to create in one-story house high interiors and mezzanines

In addition, the roofs in one-story houses often have a slight slope of the slopes. And although the proportions of the facade may seem correct on the drawing, in reality, when viewed from a height of human growth, the slopes are not visible, the roof “disappears”, but the eaves and gutters are striking.

Therefore, in one-story houses, for aesthetic reasons, we try to design a higher roof. It must be visible, because it may well become a decoration of the house. Well, if the roof is made high enough, then the question always arises of how to use the attic. Sometimes the best option is a two-level living room. It gives the room an appropriate status and diversifies the interior space.

Entrance to the house. The atmosphere of openness is created by a corner window through which you can look into the kitchen. Variety in the image brings a combination finishing materials: red-brown brick, light plaster, natural wood and dark blue tiles.

About projects and design

People who have plots of a simple shape and do not plan to build super-original houses should buy ready-made projects. They are constantly being improved and among them you can find a good option. It is worth stopping at a typical project, instead of buying an individual one, and then endlessly changing and modifying it. For an architect, changes in a prepared project are a difficult and thankless job: modern building codes impose a huge responsibility on the author of the adaptation. He must check all calculations and certify their correctness with his own signature. If he does not notice any mistake, he may be held legally liable. Therefore, project adaptation is not a mere formality. Very often it turns out that a small change at first glance leads to the following and as a result leads to such chaos that it would be better (and sometimes cheaper) to start all over again.

The architects tried to make the border between what is inside and what is outside be hardly perceptible. Apart from large windows this purpose is served by the same decoration of the ceiling of the dining room and the terrace. It seems that the space of the dining room continues outside the walls of the house. Even on a hot summer afternoon, you can take shelter in the cool shade on the eastern terrace. The western terrace is located near the kitchen and dining room. Two terraces are located one opposite the other on two sides of the house. Thanks to this position, through the living room you can see through the house.

Finished projects are sold many times, hence the low price for them. The execution of an individual project requires considerable effort, and the architect sells it only once, so a carefully executed individual project will be many times more expensive than a finished one. But there are private developers who are not satisfied with any finished project, there are situations when the finished project is not applicable, and at the same time there are too non-standard houses. It is not clear why they have, for example, two kitchens or three staircases. In fact, it turns out that there is nothing illogical in such eccentricity: the strange layout meets specific needs or is born from family history. This must be kept in mind when it comes to design principles. Principles are principles, and the project is ruled by life. However, there are time-tested rules that we apply. For example:

Good Entry Principle. It matters what we see when we enter a house. It must be some important element in the interior. The guest, having crossed the threshold, should immediately know where to go. Space itself must guide it.

Division into zones. It is a standard dictated by necessity. In order for the house to be comfortable, the part in which all household members gather must be clearly separated from the private one. The interior space should be organized in such a way that a guest, for example, in search of a bathroom, does not accidentally end up in the bedroom of the mistress of the house. Such separation is relatively easy to design in two-storey houses, where the natural boundary is a staircase, but in a one-story house it requires more ingenuity from the architect.

Everyone living in the house should have their own personal space. Some people need it more, some less. However, everyone needs to ensure that privacy is maintained. We must not forget about the hobbies and hobbies of the household.

Children should have big rooms. Certainly not smaller than the parents' bedroom. The parents have the whole house at their disposal, the children have only their rooms in which they play, do their homework and sleep.

Unnecessary inventions

There are many houses that lack signs of professional architectural work, but at the same time, the designer’s claims for “unusualness and exclusivity” are visible. house built by good project, easy to recognize: it does not strike the imagination. He's not weird. It looks like a house, not a church or a castle. In architecture, borrowing from other images is often annoying.

Irritating is also the discrepancy between the costs of the result. Very often there are, for example, meaningless triangular bay windows, strangely shaped roofs, incomprehensible ledges on the facades - expensive elements that have no functional justification, but were created only for the sake of effect. When you understand how much effort and money they cost, you wonder why it was necessary?

The house must remain stylish for at least 100 years. It should neither surprise nor shock. It must be functional, beautiful and reliable. If all architects and customers set themselves only such goals, the world around us would be beautiful. Art does not always require sacrifice.