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Building a house is the golden ratio. Golden section in domed houses - Sfera-Stroy

  1. What is important to know for calculations and what are the dangers of errors
  2. Types and forms of modern roofs
  3. Ridge run and slope angles
  4. Roof height calculations different forms
  5. Roof calculation using online resources
  6. What to consider when starting roof calculations

The final stage in the construction of any house (be it a spacious main dwelling or a small country house) is the arrangement of the roof. It is she who gives the exterior a presentable and complete look, but at the same time performs a very important function - it retains heat, creates a cozy, most comfortable and pleasant atmosphere inside. It is this element of any structure, without exaggeration, that is called one of the most important.

What determines the height of the structure and what is taken into account when performing pre-assembly calculations

It is especially important to know how to calculate the height of the roof for a house, and to understand exactly how to do it correctly. That is why you need to take some time to study this issue. Inaccuracies made in pre-wiring calculations lead to serious problems that are too difficult to deal with later. Often, to eliminate errors, you have to start work on arranging the roof again. For example, if the slopes are made with a small angle of inclination, then winter snowfalls will cause serious harm to such a design (due to the accumulation of snow, there is a risk that the roof will break). It is logical to assume that you can just make a high ridge and all problems will be solved, but this is not the case, because a roof that is too high is most vulnerable to gusts of wind.

Thus, when starting to calculate the roof and slope angles, as well as the arrangement of the roof, it must be remembered that its height is significantly influenced by:

  • the general square of the structure;
  • climatic conditions (as you may have guessed, in regions with snowy winters, sloping roofs are not recommended, which are optimal for warm continents);
  • material for arranging the roof, as well as battens;
  • selected form;
  • height of the main building;
  • personal preferences and tastes of the owner.

A number of other factors also largely affect the design parameters, for example, there is a direct dependence on the layer of insulation laid or the installation of snow retainers. The dimensions of the ridge are related to the features of the truss system, but at the same time they can increase the total area of ​​\u200b\u200bthe roof and the amount of materials required for its arrangement.

All of the above confirms the fact that the strength of the structure, the durability of its operation, aesthetics and harmony depend on the size of the roof. appearance the buildings.

What are the common types of modern roof structures


The type of roof has the most direct influence on the calculation and the formulas used for it, as well as on the amount and, therefore, on the consumption of the material that needs to be purchased for the roof. Today, the following structures are most often erected:

  • shed (it is preferable to use it for outbuildings);
  • gable (the most popular for residential buildings);
  • four-slope. Also a great choice for residential buildings. Various options are provided here: spectacular tented ones (a characteristic feature of which is the same size and shape of all slopes) or complex hips (their feature is the participation of two triangular hips and two slopes with a break (trapezoid shape));
  • attic (consists of two slopes, but always with a break). This fracture allows you to increase the area of ​​​​the attic.

Skate and determination of rational slope angles


For calculations of different forms of roofing, such a value as the size of the ridge is used. This name refers to the upper, horizontally located rib of the structure, which was formed at the intersection of two roof slopes (inclined planes).

There is a ridge on all types of roofs, except for hipped and domed ones. If the design is simple gable, then it is one, but if it is complex, then the skates are formed from two or more. During the construction of the roof, the rafter legs rest on the ridge runs, and based on which roofing material is chosen for the final coating, the base of the ridge is also selected.

Knowing how to calculate the roof height of a house correctly is also necessary for building a reliable and durable structure, as well as in order to predict the preliminary construction costs and plan a budget. In calculating the rational angle of inclination, the material from which it was decided to lay out the roof is taken into account: some roofing coverings can be laid at an angle of up to 90 degrees, while others can only be laid from 15 to 60 degrees.

When choosing which slope of the planes to choose a roof for your home, you need to take into account the functionality, the overall appearance of the resulting structure (after all, you want to get an aesthetic structure) and climatic conditions. As practice shows, for European countries, an angle of 35-40 degrees can be called an ideal solution.

Examples of calculations that are easy to do on your own

Basically, when it comes to simple designs roof, it will take quite a bit to calculate the height of the roof: a calculator and a few well-known principles from the basics of geometry, which are still taught in the school curriculum.

We take the basic principle of calculation from the rule that the length of one leg in a right triangle will be equal to the length of the other, if it is multiplied by the tangent of the angle formed with the base.

  • we measure the width of the building (let's say we have a four-meter house);
  • we accept the angle value equal to 35 degrees (as the recommended optimal option for European latitudes);
  • we calculate the tangent, it is obtained for a given angle of 0.7002;
  • 4 meters * 0.7002 = 2.8 meters.


The most complex calculations are accompanied by the arrangement of a mansard-type roof, feature which can be called the presence of two slopes with a break, which from the side makes its general appearance as if “broken”. Arrangement broken roof will increase the functional area of ​​​​the attic. The calculation of the hip roof is based on the above example of calculating the height of a gable roof, but do not forget that the roof has more than one angle of inclination, but several. Before moving on to settlement operations, you need to decide on them. Practice shows that it is best to choose the following angles:

  • for the lower - over 40 degrees;
  • for the rest - less than 40 degrees, but always more than 15.

To simplify the calculations, but at the same time to get the most accurate result quickly, experts prefer to use the “golden section” method; for this, the roof outline is inscribed in a circle in the drawing. By resorting to this successful rule, you can easily solve the question of how to correctly calculate the height of the roof, and most importantly, avoid inaccuracies in the calculation, which in practice will lead to the fact that the general appearance of the structure will be unaesthetic, inharmonious and simply ugly.

Where to go for help: online resource and consultants

If the roof being erected is of complex shape, then it also requires more voluminous, lengthy calculations. For calculations, data on the cross section of the rafters, the step between them, the size of the spans of the truss structure are used. In addition, the dimensions of the roof windows, chimneys, the presence of parapets and overhangs are taken into account, it will definitely be necessary to analyze the possibility of supports and the endurance of the foundation.

Today, anyone who does not know how to calculate the height of a roof can do this by contacting assistants who can be found on the Internet. These can be specialists who are ready to provide you with such services online, or a special Internet resource called a "calculator", in which case the site visitor enters the requested data and the system makes calculations based on them.

When choosing who to turn to for help, remember that the hip roof is an expensive design, so it does not tolerate mistakes and inaccuracies. The correctness of the calculations performed must be guaranteed. For beginners, the calculations of four-slope, hip and hipped roofs turn out to be quite complicated, so it is better to entrust them to a designer with experience in this field. On your own, you can only deal with calculations relating to single-slope structures for outbuildings and garages, or simple gable structures built to cover a small country house.

The classic roof of a Russian hut is a gable roof. The rafter system for it is quite simple, and this has ensured great popularity for this type of roof. A hip roof (four-pitched), for example, is geometrically more complex. It is more difficult to calculate and build, so let's take on the calculation of a symmetrical roof with two slopes. Its calculation consists in determining the length of the rafters that form pairs. Each of these pairs is attached to the adjacent roof trusses with the help of a crate. The ends of the roof are triangular gables. The length of the rafters, like the height of the roof, will be determined by its angle. How to choose it correctly? This will tell the weather prevailing in the area.

Skate height selection

Those who have been to the Baltic countries or Scandinavia could notice that the roofs of village houses there are pointed. It's connected with large quantity precipitation, which, in turn, is explained by the predominance of the maritime and temperate climate. Water immediately flows from such a roof, and snow does not linger at all. However, the neighborhood with forested hills reliably protects these settlements from strong winds, so the large windage of such roofs is not of great importance. Arab houses the roofs were flat because the amount of rainfall in the desert area is minimal. But strong dry winds do occur in such regions. In the same place where winds rage in the middle lane, you can find houses with completely different roofs - almost flat or arched, because just the lack of windage or good streamlining plays a big role. And if such houses used to be built intuitively, based on the experience of generations, today for different regions of Russia, sets of rules have been created that describe wind and snow loads on the roof. In particular, this is SP20.13330.2011, developed on the basis of SNiP 2.01.07-85* "Loads and Impacts". In the central region of the country, for example, it is recommended to choose the height of the ridge so that the angle of inclination of the slopes is approximately 30–45 °. It is this angle that will make it possible to calculate both the height of the roof ridge and the length of the rafters.



Let's turn to school geometry. Our roof must be presented in the form of a triangle, in fact, which is each of its gables. Such a triangle will be obtuse. We divide it along the axis of symmetry into two right-angled triangles. We received two legs, one of which (a) is known to us - this is half the width of the house. The second leg (b), which is not yet known, is the height of our roof.
b = a * tan α, where:
α - the angle of the roof, taken from the set of rules. The tangent of this angle can be calculated on an engineering calculator or use mathematical tables. The resulting leg b is the height of the roof. Knowing both legs, we can calculate the value of the hypotenuse. This is the approximate length of the rafters. However, since the roof often extends beyond the walls of the house, hanging over them, the length of the rafters can be increased. It all depends on the architecture of a particular building. Knowing the length of the rafters and the length of the roof itself, which in this dimension can also protrude beyond the edges of the house, hanging over the gables with a visor, we can already calculate its area, and therefore the amount of roofing material.

Calculation example

Let's say the house has a width of 6 m. Divide it in half and get 3 m. This is our leg a. The slope angle recommended for building a house in this area is 45 °.
b \u003d 3 * tg 45 ° \u003d 3 * 1 That is, even without tables and a calculator, it will become clear that the height of the roof will be 3 m, that is, half the width of the house.

The height of the roof affects the appearance of the house, the complexity of assembling the truss frame and technical specifications. Therefore, it is important to pay special attention to sizing and only then purchase material. In order to make calculations, it is not necessary to contact specialized organizations. In the article we will discuss how to correctly calculate the height of the roof, as well as what affects it.

What affects the height of a skate?

A ridge is a horizontal edge connecting the tops of two roof slopes. Overestimation and underestimation of the height negatively affects the operation of the roof, spoils the appearance of the building. Therefore, when calculating, it is not enough to be guided only by your own taste. Before calculating the height of the skate, it is important to pay attention to various technical conditions.

In the article, we will default to roofs with equal slopes in length and angle of inclination. This will make it easier to determine the height, although all the principles described apply to asymmetrical structures.

According to geometry, one of the slopes will be the hypotenuse, and the distance from the ridge to the base will be the leg.

Now let's go over each item in more detail.

Roofing

For different materials own requirements along the slope. The calculation of the height of the gable roof ridge will depend on this indicator. There is general principles choice of material depending on the angle of the slope:

  1. For small piece elements, the slope of the slope should be greater than for long ones. sheet materials. This is due to the fact that when moisture accumulates in the joints, leaks may appear. Therefore, ridges for a slate roof are higher than ridges for a metal roof. The fact is that the length of the wave slate is only 1.75 m, and the metal roofing material can occupy the entire length of the slope.
  2. The height of the ridge roof also affects the number of joints. With an underestimation of the angle, the number of joints and overlaps should also decrease. Therefore, large-sheet and roll materials are considered the most reliable options.
  3. Heavy roofing elements are placed on steep slopes. Roofs made of slate and ceramic tiles have a large mass, so they make a steep slope. So, they do not bend the rafter beams.

It is worth remembering that the steeper the slope, the more material will be needed to cover the roof. So, if we take as 100% the need for a slope angle of 7-10 °, then an angle of 45 ° will require 150% overrun, and an angle of 60 ° - all 200%.

The dimensions of the slopes relative to the width of the house will change along with the height of the ridge.

Attic space

There are two types of houses: with and without an attic. Each option has its own conditions for calculating the height of the ridge. If the attic is residential, then 30-40 cm is added to the height of the tallest owner. But it is better to think about the guests by making the ceiling at a height of 2.4 meters. But it is important to remember that this is only the ceiling, not the height of the roof. Here you will need to add another half a meter or more, depending on preferences.

If a attic space non-residential, then the height of the ridge is calculated under the influence fire safety. One of the points obliges the owners to provide a through passage under the roof with a height of at least 1.6 meters and a width of 1.2 m. With complex truss systems, these dimensions can be reduced by 0.4 m. This space will provide free air exchange and passage for repairs, inspection.

Barren buildings are built in such a way that additional walls are erected over the ceiling of the previous floor. For example, in semi-mansard buildings, the height of the walls is increased by 1.4 meters. In such structures, the height of the roof is measured from the lower edge of the Mauerlat. Such structures are suitable for climatic zones with strong winds. This makes it possible to reduce the slope of the slope.

Non-attic structures are popular in the construction of garages, warehouses and other small residential buildings. Usually they do not provide for an attic floor, thereby saving material and time.

atmospheric phenomena

Climatic conditions directly affect the height of the ridge. Therefore, in different cities there is a "golden" slope slope. Atmospheric factors include the following:

  1. Precipitation. The more snow it rains in your area, the more slope you need to do. Accordingly, the height of the roof also increases. If this condition is neglected, then the likelihood of leaks increases.
  2. Wind. For areas with medium and low winds, there is no difference in the height of the ridge. But so, where strong, gusty winds often blow, usually the roof slope does not exceed 10 °. This imposes certain restrictions on the materials used. Without taking into account the strength of the wind, you risk losing the entire roof structure.
  3. The amount of snow. There is a relationship between the steepness of the slope and the amount of snow. The more it falls in winter, the greater the angle you need to make. The reason is the increased load on the truss system. It is recommended to give preference to slopes with a slope of more than 45 °.

You can determine the features of the region of residence by contacting the local weather service or reference literature. The regulatory documentation SNiP 23-01-99 or SP 20.13330.2011 has weather maps and recommendations for construction.

Ways to calculate the height of the ridge

The calculation of the height of the roof largely depends on your preferences. There are two main ways:

  • mathematical;
  • graphic.

Let's deal with the mathematical method of counting. As already mentioned in the first subheading, a gable isosceles roof was taken by default. We have the ability to calculate the required height if we know the slope angle and the distance between the slopes. Now you need a Bradis table and a calculator. In the reference literature we find the value of the tangent of our angle, and then we multiply it by half the length between the slopes. The result is the height of the skate.

Consider the calculation for real example. Suppose that our building has dimensions of 7x10 meters. At the same time, we are in an area with medium winds, and we use metal tiles as roofing. We do not plan to equip the attic, but we take the slope equal to 20 °, so that rainwater flowed without problems.

It turns out that the length of the leg is 7/10 = 3.5 meters. According to the table, the tangent of 20° is 0.839. Now we multiply the resulting numbers: 3.5 * 0.839 \u003d 2.94. So the height of the skate gable roof, from the bottom of the Mauerlat, is 2.94 meters.

The graphical method is suitable for those who have a sheet of paper, a pencil and a ruler with a protractor at hand. All that is needed is to draw the roof in section, observing the scale. To do this, draw a horizontal line, mark the boundaries of the roof base on it. Determine the midpoint and draw a perpendicular. On one side, use a protractor to draw a line at the desired angle. The intersection point will show the height, you just need to measure it with a ruler.

The resulting result will be approximate, you also need to add 2/3 of the thickness of the rafter leg to it. Small deviations are acceptable and do not critically affect the operation of the roof. These errors are made up of the need to make ventilation under the metal tile and battens.

In order to mark the desired height in reality, it is enough to determine the middle of the building. Then nail a vertical bar or pole at the desired height. After the calculation has been made, try to transfer it as accurately as possible from paper to a real building. Then the roof will last for many years and will not leak on the rainiest days.

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. No wonder many learned minds call such an 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 the 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. Various 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 commensurate 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 old houses people feel comfortable and relaxed, not understanding what is the reason for this.

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”.

The use of these principles in practice will enliven any room, while contributing to good health and more comfortable and pleasant appearance dwellings.

We will be glad to see you among our clients!

Building according to the Golden Ratio from Center Country Construction"Asgard"- this is a reliable long-term cooperation on mutually beneficial terms in compliance with all the terms of the contract. Join the number of grateful customers who are already enjoying a comfortable stay in their country house.

Do you have any questions? Get a free consultation.

KNOW YOUR MEASUREMENT. Northern house building tradition

Interview with the master of wooden architecture Igor Tyulenev, who creates houses according to the principles of the old foundations of house building and sazhen proportioning. The interview was conducted specifically for the readers of the Pashkovka newspaper.

“The foundations of our Russian, Northern Tradition found a deep response in my heart,” says Igor Tyulenev. – Gradually I learned to perceive and understand and pass on the traditions of house building. And I continue to study. In Russia, everywhere they put an osmerik or six (a house with eight or six (like a honeycomb in bee hive) corners). And this is directly related to the harmony of the ascending and descending streams of force: the Earthly and Heavenly Yaris are alive (as it is now fashionable to call these streams - Yin and Yang, and the Ancestors called them - the nature of the Father and Mother, male and female energy) with their flow in a spiral. Towers and huts were mostly round in shape. Everything in house building has a certain importance, and the form is no exception.

For example, try, without changing the shape of the vessel or product, to fill a bottle of mineral water with ripe apples. Nothing will come of it, either you have to break the bottle, or finely chop the apples. A basket is better for storing apples, they will breathe easily in it, and, accordingly, they will be well stored, but it would never occur to anyone to store fresh honey or ripe kvass in a wicker basket. That is, everything needs a proper container.

Life is Force, and the form is activated by that Force, and the house is filling. For example, a "gasoline" car will not run on diesel fuel. Thus, the form may or may not be able to contain and perceive this or that energy, force. The well-known expression: “a house is a full bowl”, is now perceived as a house full of all kinds of “good” - things, furniture, but initially no one put such a meaning into this expression-wish. “A house is a full bowl” is a house filled to the brim with harmoniously intertwined flows of Earthly and Heavenly forces, which need a certain form for this, here the place of setting up the house is also of decisive importance.

I repeat, gradually, dwellings and other buildings took on a geometrically more “simple” shape, became square and rectangular. A right angle is formed at the intersection of the walls, but the Heavenly force tends to flow down, and the Earthly one rises. The Force, like water in a river, does not flow at a right angle, and therefore in the corners of today's brick, stone and panel houses, "negative" constantly accumulates, there the current of the Force is disturbed, without movement it “fades out”, the river turns into a swamp. A permanent minus point is formed in the corner. Subsequently, in order to avoid this process in wooden, already square houses, walls began to be hewn, thus giving a rounding of the corners, and allowing the flows of the Force to flow.

Why was wood preferred as a building material?

- The trunk of a tree is essentially a retinue (coil, spiral, and Vita - Life) structure of tubular systems, since the entire trunk from the butt to the top is permeated with bellies - channels through which, while the tree is growing, juice flows - from the roots up the trunk , and materialized sunlight from the leaves of the crown - also on the bellies, spreads throughout the tree. Depending on the purpose of the tree: to receive or give strength, its trunk acquired a left-handed or right-handed twist, the so-called swirl, in the process of growth, and because of this, the felled log became “right” or “left”.

Huts used to be cut down, combining these logs proportionally, or consciously giving the structure certain qualities, laying mainly right-handed or left-handed logs into the log house. Thanks to the method of stacking a log in a log house (butt - top), a continuous current of Zhiva and Yari was achieved in a spiral. In cups (places of cuts) the poles of energy change, a phase transition takes place by 90 degrees - plus to minus, the Force of the Father "becomes", is filled with the Force of the Mother, and vice versa. But this happens only if the core, the core of the tree, is not damaged. That's why earlier at home and chopped into okhryap - into the lower bowl. Today, experts criticize this method of logging, saying that moisture accumulates in the lower bowl, and the tree in the log house is more prone to decay, and they offer log cabins chopped into a hook - into the upper bowl. At the same time, they avoid making locks - fat tails, not realizing that the core of the tree broken in the log house in this case is a disservice to the residents of such houses.

The roof closes the entire contour of the house. And here the angle of the roof already matters, or rather the corners, since there are many options for them in the canon of housing construction. A house was built with one corner of the roof, and a barn with another ... Now few people think about this, approaching this issue from the concepts of aesthetics, or the possibility of material, nothing more. The house is designed to accommodate Life with certain qualities. Thus, it is necessary to take into account the place of setting (they heard the expression “the house must be placed on a stone”, this is because the current of force crosses differently). Do not build houses on sand, not only because it can collapse, but also because sand is not a conductor, there will be no power in such a house.

You also need to take into account the shape of the house, and the angle of the roof, as well as the material from which the house is built, and then the house can be given any properties - a Healing House, a Ritual House, a Residential House. All buildings and houses must have one hundred percent compliance with Form and Content.

By the way, the stove in the house, as its engine, must necessarily rely on the load-bearing beams of the floor, and not on an independent foundation - as is often the case now. Depending on how the stove stands in the house in relation to the entrance, to the right or to the left of it, the stove can be Straight and Unspun, respectively. So in your house, everything is either “rushing”, going well, or not very ... About the magic of the Russian stove, one can and should speak separately, its ability to give birth to bread, warm the house and keep the Fire of the hearth, in itself is priceless.

How were houses built in the old days?

- Home in old days they put the whole family, and often the whole world, such a term was - help, everyone gathered and built together. The ovens were adobe, and only immaculate girls and boys were invited to “beat” the oven, what strength they put into the oven! “In your own home, even the walls help” - so they say. Since we are talking about the house as a concept, about the essence of its purpose, so to speak, I can say more simply: the House is a place of Power that you create artificially. Home is a tool of evolution given by Rod. Your home, a universal tool with which you can do everything! This house has now been built, but we do not know how to interact with it. I mean with the house itself, with its space.

Of course, in order for the house to truly become yours, you must build it yourself, or at least take the maximum part in its construction. It is necessary to structure it for yourself, in the process of birth at home, water it, where it is salty with your sweat, and, maybe, where you get hurt with a little blood, the more valuable it will become for you, the more you put your strength into it, into your home. Previously, at least three generations of relatives Father, Mother, Grandfather and Grandmother and children lived in one hut. Knowledge was transferred naturally. There was a continuity in the transfer of knowledge, from grandfather and father to grandson and son.

- I heard that there used to be the concept of "Construction sacrifice"?

- Yes it is. Before a tree was cut down, gifts were brought to each tree and each tree was directly asked for permission to cut down. Promising him continued existence in new form, in the shape of a Dwelling. And if the tree gave such permission, then it experienced a state of supreme joy. As a result of the action of such a higher emotion, the entire molecular structure of wood changed, and now it was friendly to humans. In the new incarnation - a new measure, this expression is equal to all. A tree cut down in such a state will imprint it forever in its body, and a house built from such a log will constantly share this state of joy with its residents. And also will protect them from all misfortunes.

Now almost no one does this. But what I want to say: the attitude of a person himself to the house, to Life can change everything down to the atomic level. It is very important what you have inside, with what mood you live and act. Even a house built of railway sleepers soaked in creosote can become a source of positive power if a bright person full of the Joy of Life lives in it...

House, Family Homestead as an artifact.

The estate is not only hedge, a garden, a kitchen garden, a forest, a clearing, a pond, but also a variety of buildings - a house, a pantry, a barn, a bathhouse, a gazebo.

Nature and man himself should be a model and measure for the structures created on the estate. Then all the buildings will be harmonious and beautiful, life will flow in them in the most favorable way for the psyche and health, and it will be possible to reveal and realize many of the abilities inherent in a person.

Today in architecture there are:

1. Estates and houses built according to living dimensions.

These houses are inherent in the properties of all living beings - they were created taking into account the golden ratio and the so-called wurf coefficients. Wurf is a three-member division of the human body (it will be discussed in more detail below). This includes houses created using the old Russian system of sazhens. This is how houses are built for a comfortable and pleasant life.

Basic fathoms in meters:

City police 2,848
Large 2,584
Great 2,440
Greek 2,304
Treasury 2,176
Pharaoh 2,091
Piletsky 2,055
Royal 1,974
Church 1,864
Folk 1,760
Chernyaeva 1,691
Egyptian 1,663
Masonry 1,597
Simple 1,508
Small 1,424
Lesser 1.345

All 16 fixed sazhens, according to which it is proposed to design structures, are calculated based on the size of historical buildings - cultural monuments. Fathoms increase in accordance with the coefficient of harmony of the musical series - 1.059.
I would like to emphasize that fathoms are a tool for creating volume, and not just a unit of length. From any size you can make a sazhen.

Harmonious dimensions give buildings and structures the following properties:

1. Beauty;
2. Durability;
3. Strength;
4. Excellent acoustics;
5. Health effect for people;
6. Harmonization of space.

Before the introduction of design by meters, not only houses, but also parks, cities were created according to sazhens, the name of one of the sazhens reminds us of this - the city.

The land in the estate was changed by tithes - 1 tithe - 109 acres. There are 2400 square fathoms in one tithe. 4,548 sq. m - square sazhen.

2.848x1.597=4.548 sq. m;
2.548x1.76 = 4.548 sq. m;
2.44x1.864=4.548 sq. m;
2.304x1.974=4.548 sq. m;
2.176x2.090=4.548 sq. m;
1.508x2x1.508=4.548 sq. m;

When creating a house according to sazhens, it is taken into account that in nature there are no identical figures - diversity pleases the eye, pacifies the psyche.

Amazing yields were also noted on the ridges, marked by sazhens.

Separately in the estate is the theme of creating a "living pond", i.e. such a reservoir, where the water is maximally self-purifying (does not overgrow), everything is favorable for the life of fish, crayfish and, at the request of the owners, for swimming. Of course, for the construction of a pond, it is first of all important to have a source of water (green grass, willow, alder are indicators of the source), a bed of clay, and the location of the banks along geodetic lines. And only then is the marking of the pond by fathoms.

The depth of the bottom should be different, and it is desirable that the reservoir be deeper in the north, shallower in the south. For convenience, it is possible to build 1 or 2 terraces deep into the pond with a width of about 0.5 m for planting aquatic plants, such as water lilies, reeds. It is desirable to stretch the banks of the pond in the direction of the wind. The combination of natural forms and geodesic lines is important. For example, a pond shaped like a shrimp or a snake will not self-clean if built on a plain. But this form is great for a reservoir at the foot of a mountain or in a ravine.

The paths in the estate do not have to be straight. The energy goes tortuously. A striking example is the streets of old Moscow. Standing at the beginning of such a street, you will not see its end - it is so crooked. It is necessary to follow nature, and there are no straight lines in it, especially parallel ones. Likewise with the ridges. It is better when long ridges are arranged in the form of a meander or snake.

2. Dead estates and houses.

These structures slow down natural processes, therefore, they are used to preserve inanimate products and bodies, like refrigerators, storehouses, crypts. Such houses are based on regular geometric shapes that are not found in nature - a square, a circle, an isosceles and an equilateral triangle. The exception here is a hexagon - a honeycomb, a regular geometric figure, but alive.

The earth is measured in squares - square meter, square hundred, square hectare.

Ponds are created in the form of regular geometric shapes, regardless of geodetic lines, cardinal points and wind direction.

The paths are straight, turns at clear angles.

3. Other facilities.

Not "living" and "dead" estates and houses. Such structures are created by amateurs or are intended for some unknown, space purposes. These include new building, city apartments. The topic has not been studied, you can write a dissertation ....

Used Books:


2. Seminar July 6-10 by Sepp Holzer at the Krameterhof.
3. Site sazheni.ru
4. Forum http://forum.anastasia.ru/topic_47351_90.html

Rationale for the use of fathoms

God has arranged the World, and in the Harmony of the World God's perfection is remotely reflected. God gave people reason and feelings capable of perceiving the Harmony of the World. Moreover, Harmony is inherent in the Man himself. And Man can not only perceive, but also reproduce the Harmony of the World in his works.

Harmony is measurable. One of the measures of Harmony is a human measure - a sazhen. Creating something by sazhens, Man gives Beauty and Harmony to his works. As much as it is organic for a Human to live in the nature created by God, it is natural for a Human to live and use the creations that reflect this Harmony.

It is natural for a person to live in a harmonious environment created by him. This so-called "cultural" environment. It is a secondary habitat artificially created by Man. However, this secondary nature must also comply with the laws of Harmony and be favorable for a person. Such a correspondence can be provided by a sazhen.

The uniqueness of the system of ancient Russian sazhens lies in the fact that “fundamentally, there is no single standard measuring unit for sazhens, and the measurement system itself is not Euclidean.

For many centuries, the lack of a single standard did not interfere, and moreover, it contributed to the construction of magnificent structures that were aesthetically proportional to nature, also because in ancient Russian architecture all articulations were three-part, notes A. F. Chernyaev in the book Golden Fathoms of Ancient Russia .

For example, fingers, toes, hands (shoulder-forearm-hand), legs (thigh, lower leg, foot), etc. - have a three-membered structure. Moreover, a two-term limb did not exist in nature.

The ratio of 3 lengths make up a proportion called wurf. Wurf values ​​for the human body vary, averaging 1.31.

Moreover, the coefficient of the golden section squared, divided by two, is equal to the wurf. (1.618x1.618): 2=1.31.

At present, most architects in Russia have undeservedly forgotten the method of designing by sazhens and use the metric system.

Consider the history of the meter. Meter was first introduced in France in the 18th century and originally had two competing definitions:

As the length of a pendulum with a half-period of swing at a latitude of 45° equal to 1 s (in modern units this length is m).

As one forty-millionth part of the Paris meridian (that is, one ten-millionth part of the distance from the north pole to the equator along the surface of the earth's ellipsoid at the longitude of Paris).

The modern definition of the meter in terms of time and the speed of light was introduced in 1983:

A meter is the length of the path traveled by light in a vacuum in (1/299,792,458) seconds.

It turns out that the meter is an artificially derived unit of measurement that is not directly related, and, accordingly, does not reflect the Harmony of the World and Man. A meter is a standard that forms a line. Fathoms are a natural measure for Man. They form a three-part (3 is a sacred number) system, according to which the area and volume are harmoniously formed.

Peter the Great, as D.S. Merezhkovsky, in his work "The Antichrist", abolished the natural measures: a fathom, a finger, an elbow, an inch, which were present in clothes, utensils and architecture, making them fixed in the Western manner. It is not just that the meter was introduced in France and Russia during the revolutions. The destroyers knew why it was necessary to forget the wisdom and traditions of the ancestors, to destroy the roots...

Ancient people felt Harmony intuitively, without thinking about measurements. But the connection with God was weakening, and therefore rigidly fixed sizes of sazhens arose, rules for building various structures according to sazhens appeared.

Our ancestors carefully preserved and passed on the age-old wisdom and beauty, embodying them in the temples of Ancient Russia. Life in estates and houses built according to sazhens allowed not to lose the feeling of the Harmony of the World, reminded Man of God.

Now we visit estates miraculously preserved after collectivization and urbanization. For example, in Moscow, near Red Square, the family estate of the Romanovs, where now only the house-museum remains, “The House of the Romanov Boyars”. The house-museum and part of the estate of the artist Vasnetsov in the former Troitsky Lane near the Sukharevskoye metro station have been preserved.

On Novy Arbat, a piece of the estate and the family home of the Lermontovs are hidden behind skyscrapers. Everyone knows Boldino - the family estate of the great Russian poet Pushkin. A charming corner is the estate of the artist Polenov in Tarusa, a museum run by his descendants.

The family estate of the “father of Russian aviation”, the memorial house-museum and the estate of Zhukovsky are located in the village of Orekhovo, which is 30 km from Vladimir, on the Vladimir-Alexandrov highway. And there are many such examples.

The revival of the ancient traditions of creating estates and estates will undoubtedly serve the socio-economic upsurge and improvement of life in the country, the development of the spiritual, creative forces and abilities of the new landowners.

Used Books:

  1. A.F. Chernyaev "Golden fathoms of Ancient Russia".
  2. Forum http://forum.anastasia.ru/topic_47351_90.html
  3. Wikipedia.

Variety of fathoms

Consider various options the use of sazhens in the design of a residential building. Common to all methods: when building a house according to sazhens, the external dimensions of the house should have different sizes along 3 coordinate axes, and only an even number of sazhens is set aside. Similarly, the space inside the house is planned, only an even number of half-sazhens, elbows, spans, metacarpuses or vershoks is taken.

Details such as windows and doors rounded at the top, a high roof, various terraces and porches, asymmetric elements and parts of the house make it original and memorable. A separate topic is the decoration of the house with carvings, the so-called "patterning". This is a whole language of various figures, telling about the family living in the house. The furniture is made in accordance with the size of the house and the owners. Complements inner space home decoration color: curtains, carpets, paintings.

Design for 16 fixed fathoms

An even number of fathoms is plotted along the 3 axes, which must be different and not be next to each other in the list.

1. Piletsky 2.055
2. Egyptian 1,663
3. Lesser 1.345
4. Treasury 2.176
5. Folk 1,760
6. Small 1.424
7. Greek 2,304
8. Church 1,864
9. Simple 1,508
10. Great 2,440
11. Royal 1,974
12. Masonry 1,597
13. Large 2,584
14. Pharaoh 2,091
15. Chernyaeva 1,691
16. Policeman 2,848

So, the external dimensions of the house can be as follows: length - 6 church fathoms, height - 4 royal fathoms, width - 4 people's fathoms. If the house is round or polygonal, then the outer diameter is equal to an even number of fathoms, for example, 4 masonry fathoms.

Fathoms according to the golden proportions of the owner.

It is proposed to take five consecutive numbers of the golden ratio 0.382/0.618/1/1.618/2.618. These coefficients must be multiplied by the growth of the owner - as a result, a number of fathoms is obtained, proportional to its growth. For example, with a height of 1.764 m, the scale will be as follows: 0.674 / 1.090 / 1.764 / 2.854 / 4.618 m. The indicated row is successively multiplied by 2, 4, 8, 16 ... - a table is formed, according to which the sizes of individual fathoms are determined. The fathoms calculated by this method are divided into 2, 4, 8, 16, 32 ... parts, respectively. As a result, we get independent units: half a sazhen, elbows, spans, metacarpuses, vershoks.

Types of "human" fathoms.

The most famous "human" fathoms:

- flywheel. This is the length of outstretched arms;

- growth. Just the height of a man;

- oblique. The height of a person with his arm raised up.

According to the indicated sazhens, a house is designed, taking into account the size of the owner and hostess. The external dimensions of the house are calculated according to the size of the owner, and the internal dimensions are calculated according to the size of the hostess. There is a certain meaning hidden here: such a correspondence is intended to reflect the relationship between the roles of men and women in the family.

In conclusion, it should be noted that regardless of the units of length (distance can be measured in feet, meters or parrots), when designing according to fathoms, we create a “living”, harmonious space for a Person for Love, creativity and relaxation.

Used Books:

1. A. F. Chernyaev “Golden fathoms of Ancient Russia”.

Review of the hostess of the house, built according to the system of ancient Russian sazhens, about her house

My house is really built according to Russian sazhens. But only outside. Inside - how it happened. It is comfortable to live in it, we don’t want to leave it - we perceive it as a living being, very friendly and cheerful.

Whether the reason for this sazhen, or the fact that it was built with love by our like-minded person, a very clean and kind person with extensive construction experience, is hard to say.

Most often I hear such words about my house: “what a nice one you have!”. It seems small, but it seems - not very, moderately high, moderately - wide, so strong - in a word - okay. But in this, I think, the merit of fathoms.

He is pleasing to the eye with his proportions, well, smart, of course (after all, we love him - so we dressed him up). Guests, entering for a moment, do not leave for hours - they just sit on the steps or the terrace. This is especially noticeable in children, the mother of the baby will lower the baby to the ground to go home, and he again climbs the stairs to the house - and he is so happy.

Six months after the construction of the house, I attended Chernyaev's seminar in Lipetsk. There I learned an important thing that everyone should take into account when building a house, even if the construction is not in sazhens.

Ceiling height in the house furnace heating should be as large as possible - superheated air rises and hangs from the ceiling. If the ceilings are 3 meters (Chernyaev says 3.20 is better), then everything is fine. If it is lower, then our head is always in the discomfort zone.

Indeed, during the heating season, my son could not sleep upstairs. bunk bed(the height of our ceilings is 2.5 meters) - it is very hot and stuffy up there.

I am for the fact that the houses of the settlers were solid, beautiful and well-ordered. Extra costs“for beauty” pay off a hundredfold - how many times my eyes catch my eye

Examples of the golden ratio in architecture can be found everywhere when you know how to see it. Even a schoolboy can figure it out. In 2013, 10th grade student Elena Sivakova conducted her own research on buildings from the 19th and 20th centuries. Let's follow how she did it, and learn how to see and identify it in architectural structures in 5 minutes. After reading the article, there will be no questions left about what it is and whether its unusual properties can be used in your life.

7+ Examples of the Golden Ratio in Russian Architecture

St. Petersburg

The buildings of the historical center of St. Petersburg were built in different styles, such as baroque, empire, eclectic, neo-baroque, neo-gothic. Do they obey the golden rule?

Saint Isaac's Cathedral

The court architect of Alexander I, Auguste Montferrand, built this cathedral from 1819 to 1858. Late style, in which the features of the neo-Renaissance and eclecticism are already manifested. Elena wondered: “What is the reason for the harmony of a rather bulky building?”

The first row is determined by the width of the building, which is taken as 400 units. and represents such numbers as 400, 247, 153, 94, 58…

If we divide 400 by the number ≈1.618, we get approximately 247; repeat the action with the following number: 247: 1.618≈153.

And so we find all the numbers. Now let's look at the picture. The main part with columns fits into a rectangle with sides 400 and 247. Since the sides are in the ratio Ф≈1.618, they form a Golden Rectangle.

The next row is represented by the height of the building: 370, 228, 140, 87, 53, 33, 20, 12. These dimensions are built into smaller details. St. Isaac's Cathedral is vertically divided by the Golden Section at the base of the dome, which makes the ratio of the main part and the dome harmonious.

The third row of sizes starts from 113, and shows the width of the base of the main dome: 113, 69, 42, 26, 16. The numbers of this series are found in the sizes of windows, in the heights of columns and other details of the cathedral.

Golden rectangular and isosceles triangles take place in the building of St. Isaac's Cathedral, as can be seen from the figure.

Kunstkamera

The building of the Kunstkamera, founded in 1718 under the leadership of the German architect Georg Mattarnovi, stands on the University Embankment of Vasilevsky Island: Petrovsky baroque, two 3-storey buildings and a complex multi-tiered domed tower.

The study begins with the main values: the height and length of the building, from which the golden row is built. Length - 450 units, then 277, 170, 105, 65, 40, 24. Such dimensions can be seen in the height and breadth of different levels of the tower, the length of the buildings. The tower part itself is inscribed in a golden isosceles triangle from the base to the top. The golden section is seen to a greater extent in this main element, which is correct from the point of view of architecture. Conclusion: the basis of the Kunstkamera obeys the golden rule and preserves compositional harmony.

The new golden row begins with the height of the building: 211, 130, 80, 49, 30. Looking at the dimensions of the drawing, it becomes clear that the choice of a three-story type of buildings is due to the proportionality with the tower.

Trading house "Esders and Scheifals" at the intersection of Moika and Gorokhovaya

Built in 1907 according to the design of Vladimir Alexandrovich Lipsky and Konstantin Nikolaevich de Rochefort (Rochefort). In 1905, the Belgian S. Esders and the Netherlander N. Scheyfals applied for permission to build a five-story building with a dome and a spire on the corner tower for their trading house instead of the old one.

From a building length of 671 units. the Golden Ratio series begins, observed in sizes: 671, 414, 256, 158, 98, 60, 37, 23. Pay attention to the main element - the spire. We are convinced that the compositional solution is completed by a harmonious combination of height values.

Built in 1941 according to the design of Noy Abramovich Trotsky. The building of the Soviet period is considered as a creative interpretation. The central portico with fourteen columns completes the sculptural ensemble on the theme of building socialism and the coat of arms of the Russian Soviet Federative Socialist Republic.

Five-story buildings are symmetrically located on the sides. The length of the House reaches 1472 units, from which, by dividing by the F number, a number of dimensions of the building elements are obtained: 1472, 909, 562, 34, 214, 132, 81, 50 (Appendix 21): the height of the structure, the height of the entrance, etc.

The top of the Golden Isosceles Triangle coincides with the top of the building, and its sides pass through the top points of the main entrance. A right-angled golden triangle is formed by vertices at the top of the building and at the end of the inside of the side wing. The proportionality is obvious, although it does not have much compositional significance.

Moscow

Moscow State University on Sparrow Hills

A team led by B.M. Iofan, who was later removed from the post of chief architect, worked on his project. An example of post-war Soviet architecture was built from 1949 to 1953.

BM Iofan proposed a composition of five components with a central tower. During the years of construction, it was the tallest building in Europe.

The length of the building is 1472 units. and begins the series: 909, 562, 347, 214, 132, 81, 50. The golden section obeys, mainly height dimensions. Another row follows from the width of the tower: 538, 332, 205, 126, which is visible in latitudinal dimensions.

The golden right triangle with its hypotenuse passes through the corner of the building and captures the outbuildings.

Thus, in all the buildings studied, the student discovered the Golden Section, which preserves harmony.

5 additional examples

To simplify the task of finding the SP, you can take rational fractions 3/2; 5/3; 8/5; 13/8; 21/13; 34/21; 55/34; 89/55; and so on. The pattern is clear: 3+2 =5; 5+3=8; 8+5=13… Or even easier. Make yourself a compass to determine the proportion according to the instructions in the video. It will take about 10 minutes. How to use this compass to determine the proportionality of the elements will also be told and shown.

Applying this method, we find the golden proportion of the Russian architect Matvey Kazakov in the Kremlin building of the Senate, and in all other works: the Prechistensky Palace in Moscow, the Noble Assembly, the Golitsyn Hospital (named after Pirogov) ...

Created by another great architect Vasily Ivanovich Bazhenov, the Pashkov House in Moscow (Russian State Library) is considered to be an example of perfect architectural monuments, in which it is easy to identify the ZS.

Terrible symbol of Paris and the golden ratio

When the metal Eiffel Tower was assembled in Paris, many French people were outraged. Critics wrote about her as "the ugliness of the city", "the shame of Paris", "a skinny pyramid of metal stairs". Among them were Emile Zola, Dumas Jr., Guy de Maupassant. Now this most visited monument is the pride of the Parisians. Maybe the “divine” proportion is to blame?

It is also observed in the most famous French cathedral Notre Dame de Paris.

The whole truth about the ancient builders

Intuitively or consciously did great architects build buildings with these proportions in mind? Ancient mathematicians have known about the golden ratio since the time of Pythagoras. There are more and more confirmations of its application in architectural proportions. However, not a single ancient record is found with a direct recommendation to use the "divine proportion". Vitruvius (1st century BC), who wrote the Ten Books on Architecture, in which he also considered proportionality, does not have one. Strange fact, isn't it?

Maybe all the above studies are an adaptation to a known result? It is not so difficult to choose from a variety of architectural elements those that confirm the hypothesis, since no one requires absolute accuracy. It is logical to think about the question: “What if the Greeks did NOT use golden ratio?»

As a matter of fact, for Luca Pacioli, who wrote the work “Divine Proportion” in 1509, its applied value was not so important. It was important to substantiate its mystical nature. And they began to use it consciously only from the moment the book was published.

Mystery of ancient Greek architecture

Beautiful and harmonious objects always comply with the AP rule, and this proportionality is determined in the analysis of magnitudes. Art critics carefully studied the Greek Parthenon, erected in honor of the victory over the Persians - the temple of the goddess Athena. The ratio of the length of the temple to the width gives the golden number with a small error. If you subtract 14 cm from the length of the structure and add to the width, you get a complete match with mathematical value. The façade of the building tapers slightly upwards, deviating from a rectangular shape. Given the visual perception, this is done by the builders consciously. Therefore, it is not entirely correct to consider it a rectangle of the golden section. But the proportions are observed, so it is logical to assume that the architects Iktin and Kallikrates deliberately laid the rule in the project?

Myths and outlandish facts about the pyramid

The pyramid of Cheops was also built taking into account this condition. Without going into the mathematical proof of the presence of the golden formula, we will only say that it contains a right-angled golden triangle, the sides of which are the height and half of the side of the base of the building. Nothing surprising?

But then the question arises about the level of ancient Egyptian mathematics. It turns out that the Pythagorean theorem was known to them two millennia before the birth of the scientist himself. Attention is drawn to the fact that the heirs of Cheops built their pyramids with different proportions. Why?

It has been established that pyramidal structures with APs have a phenomenal effect on those in them: plants grow better, metals become stronger, water stays fresh for a long time. Scientists have been working with these riddles for many years, but the mystery remains.

It is noticed that the pyramid brings the structure of space into a harmonious state. Everything that falls into the zone of action is also organized in a similar way: the psycho-emotional state of people improves, radiation harmful to humans decreases, and geopathogenic zones disappear. The Internet claims that if the size of the figure doubles, then the influence of the pyramid increases a hundred times.

How, after all, to build a “Golden” house for yourself?

The correct distribution of energies inside the house, harmonious designs, combined with the environment and the safety of building materials encourage contemporary architects and designers to use the principles and concepts of the Golden Ratio. This increases the estimate and creates the impression of a deep study of the project. The cost increases by 60-80%.

For talented artists and architects, the rule remains intuitive during the creative process. However, some of them consciously implement this provision.

In nature, such proportionality is found everywhere. Anyone who feels the harmony of space will create a proportional building without special efforts for this.

For example, our ancestors built mansions proportionate to a person. They measured height and length in sazhens, cubits, arshins, spans. Does anyone object that the golden ratio is observed in the human body? The length of the arm from the fingertips to the armpit is related to the distance from the same point to the elbow as this value is to the size of the palm.

The famous French architect Le Corbusier used the height of the owner as a starting unit to calculate the parameters of the future house and interior. All his works are truly individual and harmonious.

5 ways to follow the rule in the interior

  1. In a house built without taking into account the ratio, you can redevelop the rooms so that the proportions match.
  2. Sometimes it is enough to rearrange the furniture or make an additional partition.
  3. Similarly, the height and length of windows and doors change.
  4. In color design, obtaining a simplified ratio is achieved due to 60% of the main color, 30% - shading, and the remaining 10% - enhancing the perception of tones.
  5. The height and length of the furniture should be commensurate with the height of the ceilings and the width of the walls.

The application of this norm in, as an architecturally designed space, is combined with the concepts of self-organization, recursion, asymmetry, and beauty.

About the golden ratio in simple words

What is it? Segments of the golden ratio are expressed by an infinite irrational fraction, the decimal value of which is approximately equal to the number Ф≈1.618 or Ф≈1.62. In other words: if we take a whole and divide it into two parts so that one of them is 62% and the other is 38%, we get the Golden Ratio.

Golden rectangle: when we divide the length of the larger side by the length of the smaller one, and we get the F number. When dividing the smaller by the larger, we get the inverse value of φ ≈ 0.618.

Golden isosceles triangle: if the ratio of the size of one side and the size of the base is the golden number Ф; the angle between equal sides is 36°.

Kepler's golden right triangle combines the Pythagorean theorem and 3C: the ratio of the squares of its sides is 1.618.

Watch an informative video on the topic