The golden ratio is the power of the Cheops pyramid. The secret relationship between the “Golden Ratio” and “pyramids” The Golden Ratio of the pyramid can be used at home

Kholodnykh Vladimir Yurievich

Pyramids of the golden ratio

Preface

This is a story about the world of forms. Look around you, everything around us has a form. We are so used to this that we don’t seem to notice it. Well, maybe we’ll get excited about pretty legs running past or clearly defined crimson lips seen on the subway. Then our instinct tells us that interesting content may be hidden behind these forms. Thus, we subconsciously penetrate two laws of nature at once. The first is that content is hidden inside each form. That is, the processes occurring inside the form are different from the processes occurring outside the form. Second - different forms corresponds to different contents. This means that the interaction of substances, fields, energy flows within one form occurs differently than in a form different from it. Then, by changing the shape, you can change the interaction. These principles form the basis for the construction of the pyramids. Why pyramids? For now, let’s make the assumption that based on the sum of the features, ease of construction plus effectiveness of impact, the shape of the pyramid, in modern terms, turned out to be more competitive.

The pyramids were built a long time ago. Every developed ancient civilization in America, northern Africa, and Asia considered it necessary to install at least a dozen pyramids. Since they were built from stone, a large number of pyramids have been well preserved to this day. Various scientific and non-scientific studies were carried out in the pyramids. But no one was able to answer the question of how the pyramids influence the surrounding nature and what is the impact on the subsoil located under them. After all, to do this it would be necessary to destroy the pyramids and see what would happen then. You can go another way. First, see what is there. Then build a pyramid and wait to see what happens. Russian Alexander Golod managed to go this way. He built several golden ratio pyramids in Russia ranging in height from 12 to 40 meters. What happened after the construction of the pyramids? One pyramid was built on the shore of Lake Seliger. After its construction, the ecology of the lake began to quickly improve, although before that the opposite happened. The construction of a group of pyramids in Bashkiria in oil fields had a strong impact on oil-bearing formations, reducing the viscosity of oil, thereby increasing its production from wells. This means that the impact from the pyramids extends not only across the surface of the earth, but also deep beneath it. Due to what changes occur in the space surrounding the pyramids, because in the pyramids of A. Golod there are no energy sources, only four inclined walls. It turns out that the pyramids interact with the Earth. More precisely, with the flows of energies flowing in the Earth and on its surface. The effects that occur around the pyramids are a kind of feedback from the interaction of the energies of the Earth inside the pyramidal form. And as we see, the effects of the golden ratio pyramids built by A. Golod have a very beneficial effect on nature. What are the golden ratio pyramids? But first, let's talk a little about the golden ratio.

We learned about the golden ratio proportion from Leonardo da Vinci, who lived in the Middle Ages. He told us that the dimensions of the human body, that is, arms, legs, head, torso, are in a ratio determined by the number 1.618 or its derivative numbers 0.618, 0.382. He called this ratio “golden.” Before this, the mathematician Fibonacci discovered a sequence of integers arranged in ascending order. The result from dividing two adjacent numbers in this sequence gradually approached 1.618. It turned out that numbers of this sequence are found everywhere in the living world. For example, leaf cuttings are attached to the plant stem in a spiral. Hazel leaves are located every 1/3 of a turn, oak - 2/5 of a turn, poplar - 3/8 of a turn, willow - 5/13 of a turn. The numbers 1,2,3,5,8,13 are the numbers in the Fibonacci sequence. When studying the signs of divisibility of numbers in this sequence, it turned out that the number 5 plays a special role in it. However, even earlier, Pythagoras showed us how, using geometric constructions, we can divide a straight line segment into two parts that are in the ratio of the golden ratio. Pythagoras was not so much a mathematician as a philosopher. He connected the numbers of the decimal counting system with the principles of building the world and the Universe. Each number has its own philosophical meaning. In order to understand where the golden ratio came from, let's try to plunge into the world of Pythagoras.

Number one

The number one, according to Pythagoras, corresponds to something primary, the most important, primordial, and from which the entire Universe will subsequently be created. This primary contains everything and rests within itself. From our dictionary, the word “god” that best suits this primary one. And God could rest within himself as much as he likes, but since he contains everything within himself, including living things, then he himself, in his own way, is alive. And all living things have an inherent desire. What can God strive for if he has everything? Perhaps, only to one thing - to knowing your capabilities. How can God know his capabilities? After all, knowledge is movement, but God is at rest. And then God has a plan or program. Let's call it the Divine Word or Logos. We are not given the opportunity to understand this program, only God knows, but it is possible to assume that God needed conditions to manifest himself for the purpose of knowledge. So God creates the Universe, including the living world, and, at the same time, you and me. He endows the living world with feelings and intelligence so that you and I can feel and be aware of God, that is, the world around us, and also retain this information until our life ends. After which God takes this information into himself, as people say - God tidied it up.

God had no questions about what to build the Universe from. Only from yourself. There was no other, as they say, by definition. The method of construction, or rather its beginning, is one. It is the separation of a part or division into parts.

Let's try to choose a geometric figure corresponding to the number 1, that is, the image or symbol of God before the moment of separation. All religious sources suggest a circle or circle. In a three-dimensional image, a circle will correspond to a ball or sphere. Take a closer look at the circle. All its points are the same distance from its center. Complete symmetry, complete balance, complete peace. And if you look at the rotating ball, you get the impression that it is standing still. However, with all this unity, a hidden duality is already emerging. The diameter of the ball is equal to two radii.

This means that the most primary element in the construction of the Universe will be the sphere. The whole world around us also consists of spheres, manifested or hidden. How can you build from spheres? There aren't many options. Since a sphere has only one parameter - diameter or radius, they can differ in the size of the radius. You can make sequences from spheres of the same or different sizes by directing them in a straight line, as if putting balls on an axis. If two or more sequences with balls intersect at one point, then a spatial structure of balls is formed. And if you now move the balls a little apart from each other, then a painfully familiar picture appears before your eyes in the school chemistry classroom. This is a spatial model of the crystalline structure of matter, consisting of wires and multi-colored balls. Atoms can be thought of as spheres whose size is limited by electron clouds. Then the properties of substances are determined both by the sizes of the spherical atoms included in them and by their relative position in space.

Number two

The number two according to Pythagoras corresponds to the process of dividing God into two parts opposite to each other. We call these poles. Positive and negative, male and female, yang and yin. The separation occurs due to the initial impulse of energy embedded in the program - Logos. The separated poles are part of the whole and therefore they contain an eternal striving towards each other. I was unable to find a geometric figure corresponding to the number 2. Maybe readers will have better luck. The process of dividing into two gave rise to mirror symmetry. Everything in the universe has mirror symmetry, obvious or hidden.

Here I would like to draw your attention to right triangles. All but one right triangle do not have mirror symmetry. However, the presence right angle suggests that this triangle can be rotated around a leg and complete itself, creating a symmetrical figure called an isosceles triangle. Right triangles act as a tool for studying isosceles triangles and pyramids. Pythagoras paid due attention to right triangles, leaving us, among other things, a theorem on the ratio of sides in this triangle - the famous “Pythagorean Pants”.

Let's talk a little about the method of our study of the pyramids. It was said above that the primordial forms from which everything that exists is built are spheres. All other forms, including pyramids, will be secondary. The inner essence of the pyramid, its purpose, is determined by the sequence of spheres inscribed in it. If you cut a pyramid in half with a vertical plane passing through the apex, an isosceles triangle will form on the cut. The sequence of circles inscribed in a triangle will correspond to the sequence of spheres inscribed in a pyramid. An isosceles triangle has the property that the size of each circle inscribed in it in the direction of height differs from the size of the next circle by the same number of times. That is, there is a number that can be multiplied by to calculate the radius of any circle in the sequence. This number will be the main characteristic of both an isosceles triangle and a circle.

In order to build a pyramid, you need to know the ratio of its sides. As we have already said, a pyramid cut by a vertical plane turns into an isosceles triangle. If you draw an altitude in this triangle, it will divide it into two right triangles. Each of these right triangles will describe an isosceles triangle, defining a pyramid. Knowing the aspect ratio of a right triangle, you can easily build a pyramid. Therefore, as the study progresses, we will depict these triangles.

Number three

The number three corresponds to the state of god after division into poles. The poles have a mutual desire to merge, since they emerged from a single whole. In order for them not to merge, some process must take place between the poles, as a result of which something qualitatively new appears, allowing the poles to remain separated and be in a state of equilibrium with this third one. This is how the divine triad, the holy trinity, appears: Father, Mother and Son. In Christianity, the Holy Trinity corresponds to the Father, Son and Holy Spirit. It sounds beautiful and mysterious. From this definition it follows that God the Father and the Holy Spirit are opposite poles. Maybe it is so. But the idea arises that Christian theosophists could not afford to elevate the feminine principle to the divine rank, since they considered it sinful. Peculiar echoes of patriarchy.

The symbol of the Holy Trinity is an equilateral triangle. When you are on Nevsky Prospekt, go to the Kazan Cathedral. On its pediment there is an image of a gilded equilateral triangle with shining rays diverging to the sides. This is a symbol of God in Christianity. It means that God is triune, that is, one in three persons: Father, Mother and Son. God is still in a state close to unity. Look at the equilateral triangle. All its corners are at the same distance from each other. The figure is balanced, there is a sense of lack of internal tension in it.

Only the architect of the Kazan Cathedral cheated a little. For the sake of the proportions of the pediment, he nevertheless reduced the height of the equilateral triangle and made it into an isosceles one.

The tetrahedron corresponds to the image of the Holy Trinity in volume. This is a three-sided pyramid, all of whose faces are equilateral triangles. How to build a tetrahedron? Take an equilateral triangle, divide all its sides in half and connect the midpoints with straight lines. The original triangle split into four smaller equilateral triangles. Now we will bend the corners of the triangle along the lines towards each other. We have a tetrahedron. It was said earlier that the world is built from spheres. Let's try to fit a sequence of spheres into a tetrahedron. We will use a right triangle as a tool. I would like to say in advance that most of the mathematical calculations are missing from the brochure due to their considerable simplicity, monotony and tedious repetition. In addition, the Pythagorean theorem and the similarity of triangles were all taught in school, and a meticulous reader will be able to check me at any time.

Let's cut the tetrahedron in half with a vertical plane passing through two vertices and the middle of the edge. We will get an isosceles triangle lying on its side. Let us draw a height in this triangle, which will also be the height of the tetrahedron. The result is two right triangles. One of them has an aspect ratio of 1:2:Ö3, the other 1:2Ö2:3. If a sequence of circles is inscribed in the last of them, then they will correspond to the sequence of spheres inscribed in the tetrahedron. Here it is necessary to clarify that the sequence of circles fits into an isosceles triangle, half of which will be a right triangle with an aspect ratio of 1:2Ö2:3. Since the pyramid is trihedral, the second half of the isosceles triangle is rotated around side 2Ö2 by 120 degrees and lies in another plane, not shown in the figure. The radius of the first inscribed circle is R=1/Ö2. Let's recalculate the sides of the triangle so that the radius of the first circle is equal to 1. To do this, divide all the sides of the triangle by 1/Ö2, then the length of the lower leg of the triangle will be equal to Ö2. The common factor of the sequence of inscribed circles will be the reciprocal of the square of the length of the lower leg, that is, 1/2. Now we can write the sequence of radii of the inscribed spheres of the tetrahedron: 1, 1/2, 1/2 2, 1/2 3, 1/2 4 ... Each subsequent sphere is half the size of the previous one. This means that the number 2 is hidden inside the tetrahedron. Let's see what sequence of circles is inscribed on the face of the tetrahedron. As mentioned earlier, the face of a tetrahedron is an equilateral triangle. The height dropped from the vertex will divide it into two identical right triangles with an aspect ratio of 1:Ö3:2. The radius of the first inscribed circle will be 1/Ö3. Let's recalculate the sides of the triangle so that the radius is equal to one. The length of the lower leg will then be Ö3 and the sequence of radii of the inscribed circles of the equilateral triangle will be: 1, 1/3, 1/3 2, 1/3 3, 1/3 4 ..., that is, each subsequent circle is three times smaller than the previous one. This means that the number 3 was discovered on the edge of the tetrahedron.

Let's try to draw the first conclusion. A triangular pyramid, called a tetrahedron, reveals on its faces the number 3 - a symbol of the Holy Trinity. Hidden inside the tetrahedron is the number 2 - a symbol of the previous stage, when God is divided into two poles.

When we built the tetrahedron, our equilateral triangle was divided into four smaller similar triangles. This suggests that inside the number 3 there is still an unmanifested number 4.

Number four

The number four according to Pythagoras corresponds to the material world. Matter that is not living, "dead" or inanimate. In order to move to the number 4, it is necessary to destroy the divine trinity of the Holy Trinity. And to prevent a reverse merger from happening, something new must appear that resists the merger. This new one will be “solid earth” or matter, then 3+1=4.

In geometric figures it looks like this. We break the equilateral triangle in one of the corners and insert a straight line segment equal to the side of the triangle. We get a square. In a square, the vertices of the corners are at different distances from each other, the balance is disrupted. There is already tension in the square. In volume, the number 4 corresponds to a cube. If you unwrap a cube, that is, unfold its six faces on a plane, you will get a cross - a symbol of Christianity. But Christians still have Jesus Christ chained to the cross, that is, the crucifixion. In other words, how to find the divine that is hidden in dead matter. Take a cube, draw a diagonal line on the upper base or connect two opposite vertices of the square with a straight line. On the opposite side of the cube we will also draw a diagonal, but in a different direction. Now let's connect the ends of these diagonals to each other. To do this, we will draw four more lines, which will also be diagonals of other faces of the cube. The result is a tetrahedron - a symbol of the Holy Trinity. This means that matter cannot exist without divine filling and is inextricably linked with it.

Let's try to find the sequence of radii of spheres inscribed in a cube. To do this, let's place the cube on one of the vertices, and direct the opposite vertex straight up. Now you can better see that the cube consists of two trihedral pyramids connected by “bases,” as it were. Only the line connecting these bases will be broken and located in different planes. For greater simplicity, let's turn the double pyramid into a single pyramid with a flat base. To do this, draw a horizontal plane through the three vertices of the cube, that is, cut off the top of the cube. We get a trihedral pyramid, at the base of which lies an equilateral triangle. Next we proceed as with a tetrahedron. Let's cut the pyramid with a vertical plane passing through two vertices and the middle of one of the edges. Let us draw the height in the resulting triangle. We have two right triangles with an aspect ratio of 1:Ö2:Ö3. We have already seen such a triangle in a tetrahedron. This is another confirmation that the number 3 is hidden in the number 4. The sequence of circles inscribed in a smaller triangle will determine the sequence of spheres inscribed in a cube. The radius of the first inscribed circle will be R=(Ö3–1)/Ö2. Let us reduce the inscribed circle to a unit radius by recalculating the sides of the triangle. Now we can write the sequence of radii of spheres inscribed in a cube: 1, [(Ö31)/Ö2] 2 , [(Ö31)/Ö2] 4 , [(Ö31)/Ö2] 6 ,...After converting to brackets, we get: 1, 2Ö3, (2Ö3) 2, (2Ö3) 3,... This is the sequence of “dead” matter. Its total multiplier will be 2-Ö3. The result was a combination of numbers: 2 - from the division into poles, 3 - from the holy trinity. Inside the cube, information about two previous processes is hidden. Based on these processes, “dead” matter is created.

Let's move on to tetrahedral pyramids. There is another regular polyhedron - the octahedron. It is composed of eight equilateral triangles and consists of two tetrahedral pyramids connected by their bases. The connecting line of the pyramids lies in the same plane. Let's see what sequence of radii of inscribed spheres the octahedron has. To do this, take the upper part of the octahedron and cut it with a vertical plane passing through the vertex and the midpoints of the opposite sides. It’s easier to cut the pyramid in half from top to bottom. The result is an isosceles triangle. Now let's draw the height and get two identical right triangles. Let us denote half the side of the octahedron as 1. Then the hypotenuse of the right triangle coincides with the height of the face of the octahedron and is equal to Ö3. The remaining leg of a right triangle, according to the Pythagorean theorem, is equal to Ö2. That is, a right triangle has an aspect ratio of 1:Ö2:Ö3. The same right triangle describes the sequence of inscribed spheres of a cube. This means that the sequence of radii of inscribed spheres near the octahedron coincides with the sequence of radii of inscribed spheres near the cube and is a sequence of “dead” matter. The difference between a cube and an octahedron is that the sequences of inscribed spheres are located in space at different angles.

I deliberately do not represent the number 2+Ö3 as a decimal number with a comma and will do so in the future. A decimal number with a comma shows only the quantitative characteristics of the number, but hides the history of the origin of this number. The curious reader can calculate this himself using a calculator.

The principles of the cube and octahedron are embedded in the internal structure of most substances that make up material solids. The atoms are located both at the vertices of these polyhedra and in the middles of the faces, as well as in the center of the internal volume.

How does a person perceive the energy of “dead” matter in sensations? To describe this feeling, the expression “grave cold” is used, a feeling of loneliness, abandonment, a terrible cold penetrating inside. If you want to feel it better, then dress warmly, go down into the cellar for 15-20 minutes and turn off the lights. Just don’t show off, but try to be calm researchers. A dark basement of an abandoned house would also work. The bravest ones can try to go down into the cemetery crypt. In normal circumstances, an adult does not notice this sensation.

Young children are much more sensitive than adults. They can sense the energies of “dead” matter in an ordinary room. Previously, there was a punishment for naughty children - they were placed in the corner of the room. The little man immediately felt a sense of loneliness, although his peers were very close and frolicking in the center of the room. After some time, this feeling captured the baby so much that he often began to cry. We can say that this is a purely psychological technique. The child was deprived of the opportunity to communicate in a team where he, as the most active, was the leader and he is offended. But what is a collective? This is, first of all, “living heat” emanating from people, that is, energy flows emanating from living matter. When a child is removed from a group of peers, he is deprived of this energetic support. This is already a punishment. However, it is further aggravated by the fact that the child is placed in the corner of a rectangular parallelepiped, this is the usual shape of the room, from which, like from the corner of a cube, a flow of energies of “dead” matter emanates.

Old people, like children, also often have increased sensitivity. My late grandmother, being at a very old age, pestered everyone at home with the fact that in her room she was “drafting from the corners,” that is, blowing drafts from the corners of the room. We were all perplexed, since in her room the window and door were sealed almost hermetically and no air movement was felt even with a candle. They believed that grandma was imagining something in her old age. Now I realized that she already felt the cold of “dead matter” too well and very accurately determined where it was coming from.

Number five

The number five according to Pythagoras is the number of living matter. How does living matter appear? To do this, it is necessary to spiritualize “dead” matter, that is, add a little more of the divine to it. Let's try to do this using geometry. Let's take the symbol of “dead” matter - a square, put it on a horizontal plane and divide it in half with a straight line into two equal rectangles. On top of the middle line of the square we will place the symbol of the Holy Trinity - an equilateral triangle. Now we connect the vertex of the triangle with the corners of the square with straight lines and get a tetrahedral pyramid. The sequence of radii of inscribed spheres for this pyramid is the same as for an equilateral triangle: 1, 1/3, 1/3 2, 1/3 3,... Let's see what kind of isosceles triangle the face of the pyramid is. Let's take half the side of the square as one, then half the base of the face is also equal to 1. The height of the face will coincide with the side of the equilateral triangle and is equal to 2. We will find the length of the side of the face from a right triangle, which is half of the face. One of its legs is equal to 1, the other is equal to 2, and the hypotenuse, according to the Pythagorean theorem, is equal to Ö5. Here we have come close to the golden ratio.

Let's use the experience of Pythagoras. Let's take a right triangle with a leg ratio of 1:2, that is, one side at a right angle is twice as large as the other. The third side of this triangle or hypotenuse according to the Pythagorean theorem is equal to Ö5. Now subtract the length of the shorter leg from the length of the hypotenuse. The result was Ö5–1. Now we divide the length of the larger leg by the length of the resulting segment. It turned out 2/(Ö5–1)= 1.618...= F. This is the number of the golden section. It was named with the letter “F” in honor of the ancient Greek sculptor Phidias, who used the golden ratio proportion in his creations. In order to bring this expression to a more familiar form, we multiply the numerator and denominator of the fraction by Ö5+1. We get: 2/(Ö51)= 2(Ö5+1)/(Ö51)×(Ö5+1)= 2(Ö5+1)/ (Ö5 2 1)= 2(Ö5+1)/ (51)= (Ö5+1)/2= 1.618... The number Ф is an infinite non-periodic fraction, which is similar to the number “Pi”.

Why is everything so simple? Pythagoras took the triangle, manipulated the sides and presented us with that golden mean, which is the “cornerstone”, the foundation of the entire living world. Well, first of all, it’s not that simple. How long have we been approaching this number? And, secondly, Pythagoras knew exactly where to look for the golden ratio. A right triangle with a leg ratio of 1:2 is half of an isosceles triangle. And this triangle gives birth to life. Let us inscribe a sequence of circles into it. The radius of the first circle is equal to (Ö5–1)/2 = 0.618=1/F. Let's recalculate the triangle to unit radius. Now you can write a sequence of radii of inscribed circles: 1, 1/Ф 2, 1/Ф 4, 1/Ф 6,... This is the life-giving sequence. Why life-giving? Remember the example of tree leaves at the beginning of the brochure. Let's rewrite these fractions: 1/3=0.3333; 2/5=0.4; 3/8=0.375; 5/13=0.385. You see these fractions are getting closer and closer to the value 1/F 2 =0.382. Life itself tells us this.

Based on the life-giving sequence, let's build a pyramid of life - one of the first pyramids of the golden ratio. To do this, take an isosceles triangle of life, install it on a square base and connect the top of the triangle with the corners of the square with straight lines. The result is a pyramid of life. The ratio of its height to the side of the base is H/L=1. The sequence of radii of inscribed spheres is: 1, 1/Ф 2, 1/Ф 4, 1/Ф 6,...

Let's take a closer look at the golden ratio sequence. In its full form it looks like this: ...1/Ф 3, 1/Ф 2, 1/Ф, 1, Ф, Ф 2, Ф 3,... or...0.146; 0.236; 0.382; 0.618; 1; 1.618; 2.618; 4.236; 6.854... The number Ф has properties broader than decimal numbers. For example: 1 + Ф = Ф 2, Ф + Ф 2 = Ф 3. That is, each subsequent member of the golden sequence can be obtained either by summing the two previous members or by multiplying the previous member by the number F. Let us compare the sequence of inscribed spheres in the pyramid of life with the complete sequence. It can be seen that in the sequence of spheres of the pyramid of life there are only members with even degrees at the number F. Let's try to build a pyramid of the golden ratio, including all the members of the golden sequence. To do this, we will construct an isosceles triangle, place it on a square and connect its vertex to the corners of the square with straight lines. We obtain a pyramid with the ratio of height to base length H/L=2.058=ФОФ. Our compatriot Alexander Golod is building such pyramids. Since the pyramids bear the names of their builders, we will call this pyramid of the golden ratio the pyramid of A. Golod. He built several pyramids ranging from 12 to 44 meters in height and is conducting research to study the properties of such pyramids. In addition to a whole host of beneficial properties for humans (see the list of references), it was noticed that the pyramid influences the moral and ethical qualities of people in a positive sense.

Let's pause and try to understand one issue. Why does the number Ф 2, and not Ф, give birth to life? We spiritualized “dead” matter precisely following esoteric rules. They created a pyramid based on “dead” matter; the hidden essence of the pyramid is the divine image of the Holy Trinity. What appeared on the edge was not the number 5, nor the number F created with its help, but the second power of the number F, that is, F 2. This is not at all accidental. It is F2 that gives birth to life in all its richness of colors and diversity life forms. However, giving birth to and raising a living being is only one stage of life. It is very important how it will develop in the future. Is it possible that living beings will destroy each other in the struggle for life? This is where the role of the first power of the number F comes into play. The number F is a regulator of the development of life. It “ensures” that living beings carry out their life tasks within clear limits. Reasonable limitation of one's needs is a necessary condition for the coexistence of life forms. If a living being crosses these boundaries, then sooner or later there will be retribution, which is often expressed in the form of death. Do you think this is fiction? Let's consider an example from zoology. In some years, for some reason, the number of field mice increases catastrophically. The mice, which bred in huge numbers, quickly ate the cereal plants in their area, thereby depriving themselves and their offspring of food. They could no longer store the required amount of grain for the winter and died from lack of food in the winter. The following year, the mouse population was much lower than in normal years.

While researching the properties of his pyramid, A. Golod carried out one experiment. With the consent of the officials, a ring of crystals that had undergone crystallization in the pyramid was laid out around the colony of prisoners, and the prisoners themselves were given ordinary salt for food, which was kept in the pyramid. Over eleven months of observation in the colony, mortality decreased, serious crimes disappeared, and the number of violations of the regime decreased several times. This suggests that A. Golod’s pyramid, which contains the number F, affects, among other things, the moral qualities of people. This means that the fulfillment of moral laws is a necessary condition for people’s lives, since these laws are within the sphere of influence of the golden ratio. Failure to comply with moral laws is punished in the same way as in the above example with mice. It is no coincidence that some historians consider the collapse of the Romans to be the cause of the collapse of the Roman Empire.

Now let's try to select from the sequence of the golden section members whose exponents are divisible by three, that is: 1, Ф 3, Ф 6, Ф 9,... Let's build such a pyramid of the golden ratio. The result is a pyramid with a ratio of height to base length H/L=0.636. This is the proportion of the Cheops pyramid - the largest pyramid in Egypt. The pyramid is built using a right triangle with an aspect ratio of 1:ÖF:F. This triangle is called the golden triangle. The main property of this pyramid is maintaining the stability of living matter. Let us also write the ratio of the sides of the right triangle describing the faces of the Cheops pyramid 1:Ф: 4 5ÖФ.

Now let's look at the corners of these pyramids. The angle at the top of the Cheops pyramid becomes the angle at the base of A. Golod’s pyramid. The angle at the top of the face of the Cheops pyramid becomes the angle at the base of the pyramid of life. The pyramids seem to exchange angles.

1, 1/F 4, 1/F 8, 1/F 12,…

1, 1/F 5, 1/F 10, 1/F 15,

1, 1/F 6, 1/F 12, 1/F 18,…

As you can see, with increasing degree at the number F, the height of the pyramids decreases, but, as before, they bear the main property of the pyramids of the golden ratio - to be conducive to life. The choice of proportions for golden ratio pyramids is quite wide and it is quite possible to choose a suitable pyramid, for example, for designing the roof of a house. With such a roof, the energy situation in the house will be favorable for people to live in.

We have been discussing the four-sided pyramids associated with the number 5 for quite some time, but have not yet said anything about the five-sided pyramid. The symbol of the number 5 is also a regular pentagon. But the pentagram is better known - a five-pointed star, which can be built by connecting the vertices of a pentagon through one another with straight lines. From a pentagram it is surprisingly easy to get a five-sided pyramid. To do this, it is enough to bend the five rays of the pentagram along the lines inward until the vertices connect with each other. You say that such pyramids were not built. On Earth - no, but on Mars - yes. After processing photographs taken by American interplanetary probes, it turned out that on Mars there are not only tetrahedral pyramids, but also pentahedral ones. Moreover, their height is several times higher than the Cheops pyramid.

Let's return to the five-sided pyramid. It turned out that it has a sequence of radii of inscribed spheres: 1, 1/Ф 2, 1/Ф 4, 1/Ф 6,..., that is, this is the pyramid of life and the pyramid of the golden ratio. The face of this pyramid is an isosceles triangle with base angles of 72 degrees. This is one of the sacred or sacred numbers in ancient Egypt. The sequence of radii of the inscribed circles of an isosceles triangle: 1, Ö5/Ф 3, 5/Ф 6, 5Ö5/Ф 9,... The aspect ratio of a right triangle that describes such an isosceles triangle is 1:ФОФ× 4 Ö5:2Ф. Using this triangle, we will build another tetrahedral pyramid of the golden ratio. We will place this isosceles triangle on a square, connect the vertex of the triangle with the corners of the square with straight lines and get a pyramid with a ratio of height to base length H/L = 1.539. Let's call this pyramid the pyramid of flourishing life, since to construct the isosceles triangle that defines this pyramid, we used the number 5 twice.

We will build the next tetrahedral pyramid of the golden ratio using a triangle taken from a regular pentagon. To do this, connect any two vertices of its corners with a straight line. The smaller part of the pentagon is an isosceles triangle. The angle at the base is 36 degrees. By the way, it is also a sacred number. A right triangle describing an isosceles triangle has an aspect ratio of 2:Ф: 4 Ö5/ОФ. A tetrahedral pyramid built on this triangle has a sequence of radii of inscribed spheres: 1, 1/(Ф 3 ×Ö5), 1/(Ф 6 ×5), 1/(Ф 9 ×5Ö5),... Ratio of height to base length H/L=0.363.

We have described only some of the pyramids of the golden ratio, which have the simplest expressions for the sequence of radii of inscribed spheres. There are pyramids with more complex expressions of radius sequences. For example, let's take two regular polyhedra. A pentagondodecahedron is a dodecahedron whose faces are regular pentagons. An icosahedron is a twenty-sided structure whose faces are regular triangles. They are also associated with the number 5, and therefore with living matter. The sequence of radii of inscribed spheres for these polyhedra is the same: 1, (2/[Ö(Ф 4 +4) – Ф 2 ]) 2 , (2/[О(Ф 4 +4) – Ф 2 ]) 4 , (2/[Ö(Ф 4 +4)Ф 2 ]) 6,... The right triangle describing this sequence has an aspect ratio of 2:Ф 2:Ö3× 4 Ö5×ÖФ. This triangle is interesting because if you construct an isosceles triangle on it, then the angle at its vertex equal to angle between the bonds of hydrogen and oxygen in a water molecule near the freezing point. The pentagondodecahedron and icosahedron differ in that their sequences of inscribed spheres are located in space at different angles. A situation similar to a cube and an octahedron.

Number six

The number 6 according to Pythagoras corresponds to the balance of living matter and the divine. This is the moment when life has completely mastered the material world and is ready to return to the divine realm.

It is possible to construct a tetrahedral pyramid with a sequence of inscribed spheres: 1, 1/6, 1/6 2,1/6 3,... The right triangle that describes this pyramid has an aspect ratio of 2Ö6:5:7. But the hexagonal pyramid is of greater interest. Let's take an isosceles triangle of life with a sequence of inscribed circles: 1, 1/Ф 2, 1/Ф 4, 1/Ф 6,... Let's place it on a regular hexagon so that the angles at the base of the triangle lie at the midpoints of the opposite sides of the hexagon. Now we connect the vertex of the triangle and the corners of the hexagon with straight lines and get a hexagonal pyramid. The sequence of radii of inscribed spheres is the same as that of the pyramid of life: 1, 1/Ф 2, 1/Ф 4, 1/Ф 6,... That is, this is a pyramid of the golden ratio.

Let us cut the hexagonal pyramid with a vertical plane passing through the top of the pyramid and two opposite corners of the base. The result is an equilateral triangle - a symbol of the divine trinity. On the faces of the pyramid you will also get interesting isosceles triangles. A right triangle describing an isosceles triangle has an aspect ratio of 1:Ö15:4. The sequence of radii of inscribed circles is: 1, 3/5, (3/5) 2, (3/5) 3,..., 3 - corresponds to the divine trinity, 5 - corresponds to life. Then this isosceles triangle can be called the triangle of balance of life and spirit. By the way, the hexagonal pyramid is used in the tent of the Church of the Savior on Spilled Blood.

Number seven

The number seven according to Pythagoras corresponds to the release of the divine from “dead” matter, 7=4+3. If we talk about a person, then at this stage of development his mind and personality can already exist independently of the body. And if a person is in it, then only of his own free will to perform some important task. This is the number of great initiates: Buddha, Krishna, Jesus Christ, Pythagoras.

To build a seven-sided pyramid, you need to divide the circle exactly into seven parts. This is somewhat difficult, since the result is a long decimal fraction 360/7 = 51.42857143... We will make do with a tetrahedral pyramid with a sequence of radii of inscribed spheres: 1, 1/7, 1/7 2, 1/7 3,... Rectangular the triangle describing this pyramid has an aspect ratio of Ö7:3:4. Let's look at the edge of this pyramid. The right triangle that describes the isosceles triangle of its face has an aspect ratio of 3:4:5. The sequence of radii of the inscribed circles of a face: 1, 1/4, 1/4 2, 1/4 3,... A right triangle with an aspect ratio of 3:4:5 is called an Egyptian triangle, and in ancient Egypt it was called sacred. In Egyptian mythology, this triangle was a symbol similar to the Holy Trinity in Christianity. The vertical side of the triangle corresponded to the god Osiris, who personified the masculine principle. The horizontal side corresponded to the goddess Isis, who personified the feminine principle. The role of the Son was played by the god Horus, who according to mythology was the son of Osiris and Isis. It corresponded to the hypotenuse of the triangle. The Egyptian triangle received such a high sacred rank because of its close proximity to the number 7. But this is a more “earthly” symbol, since it also carries the number 4. The Egyptian triangle was not only a symbol. In everyday life, with its help, surveying work was carried out to mark out crop areas in the Nile Valley. The Egyptians attached such importance to this triangle that they built a pyramid in proportion to the Egyptian triangle, which bears the name of Pharaoh Khafre. Although it does not belong to the pyramids of the golden ratio, but, being a derivative of the number 7, it also has a beneficial effect on humans. It can also be noted that the angle of inclination of the faces of this pyramid is only 3 percent greater than the corresponding angle of the pyramid of the golden triangle, and is equal to the angle at the apex of the pyramid of life.

Egyptian triangle has something to do with music. With its help, basic chords are built. The range from a sound, for example, A of one octave to the sound of A of the next octave corresponds to a decrease in the wavelength of the sound by 2 times or an increase in the oscillation frequency of the sound wave by 2 times. It is divided into 12 identical half-tone intervals. The oscillation frequency of the sound wave corresponding to each subsequent semitone can be calculated by multiplying the oscillation frequency of the sound wave of the semitone from which we started counting the octave by a factor of 12 2 = 1/1.059463...(by the way, 12 2 is almost equal to F 3 / 4= 1.059017…). A full octave contains 12 intervals, then (12 2) 12 =2.

Let's take a major triad, for example C major. It consists of the sounds Do, Mi, Sol. Let's add another C sound to cover the full octave. From Do to Mi there are 4 semitones, from Mi to Sol – 3 semitones, from Sol to Do – 5 semitones. The interval ratio is 4:3:5. Let's take a minor triad, for example, A minor. It consists of the sounds La, Do, Mi. Let's also add the following sound La. From A to Do there are 3 semitones, from Do to Mi – 4 semitones, from Mi to A – 5 semitones. The interval ratio is 3:4:5. Minor chords are obtained if we go around the sides of the Egyptian triangle, for example, clockwise. Major chords are obtained by going around the triangle in the opposite direction.

If the Egyptian triangle is placed on the other side, then the sequence of semicircles inscribed in it will take the form: 1, 1/9, 1/9 2, 1/9 3,... That is, this triangle is directly related to the number 9. This is the number of the God-man . It is implied that you and I will someday become like this. You've probably heard that the number 999 is the number of a person. But not the modern man, but the man of the future. We've settled on number 5 for now.

Perhaps a small part of God's plan, which is carried by the program - Logos, is to enter matter, create a person, endowing him with will and the desire for creativity - truly divine traits, to provide him with freedom to study and understand the world around him. And when a person embraces with his mind everything that exists around him, understands all the relationships in the Universe (number 8), becomes like God and immortal (number 9), he will be able to return to him again - God (number 10, also number 1), bringing with him a conscious image of the Universe.

Egyptian pyramids

Let's now try to compare these theoretical developments with actually existing pyramids. Naturally our gaze will turn towards Egypt. The ancient Egyptians built both step and smooth pyramids. We are more interested in smooth pyramids. In addition, they are superior to stepped ones both in quantity and in size. The largest pyramids are located in Giza, a place on the banks of the Nile near Cairo. The pyramid of Pharaoh Cheops or Khufu has a size of 233 meters at the base and 146.6 meters in height. Its proportions are described by a golden triangle, the aspect ratio of which is 1: ÖF: F. Or rather, not the pyramid itself, but its body without cladding. This is how it stands now. The sequence of radii of inscribed spheres: 1, 1/Ф 3, 1/Ф 6, 1/Ф 9, ...

The Fibonacci number sequence will help us understand the purpose of this pyramid: 1,1,2,3,5,8,13,21,34,55,... In this sequence of numbers, every third term is obtained by adding the two previous ones. This sequence has another property. The result of dividing each subsequent term by the previous one tends to the number of the golden ratio Ф=1.618... For example: 13/8=1.625, 34/21=1.619. As mentioned above, the numbers of this sequence can be found in the proportions of organs of plants, animals, and humans. However, the chosenness of the Fibonacci sequence is that it tends to the number F the fastest. There are a large number of sequences, the ratio of two adjacent terms of which tends to the number F. For example: 1,3,4,7,11,18,29,47, 76,123,199,... 29/18=1.611, 76/47 =1.617. The first term does not have to be one: 2,7,9,16,25,41,66,107,173,l99,... 66/41=1.610, 173/107=1.617. This means that the order in which the sequence is constructed is important: every third term is the sum of the previous two. Now let's imagine that the terms of these sequences are squares of numbers. Let's rewrite the last row of numbers: Ö2 2, Ö7 2, Ö9 2, Ö16 2, Ö25 2, Ö41 2,... or Ö2 2, Ö7 2, 3 2, 4 2, 5 2, Ö41 2,... If we now take three numbers in a row, then the relationship between them will be the same as in the Pythagorean theorem: Ö2 2 + Ö7 2 =3 2 ; Ö7 2 +3 2 =4 2 ; 3 2 +4 2 =5 2 ;... The result is a sequence of right triangles. Each subsequent triangle follows from the previous one. The legs of the subsequent triangle become the hypotenuse and the longer leg of the previous one. As the number of members of a numerical sequence increases, three of its members will differ by the number Ф. This means that in a sequence of triangles these terms will differ by the number Ф. There is only one right triangle whose sides differ by ÖF. This is the golden triangle. The remaining triangles will be similar to it. This means that all sequences of right triangles will tend to the golden triangle. Or vice versa, all right triangles flow from the golden triangle. Since a right triangle is half of an isosceles triangle, and they, in turn, determine the parameters of tetrahedral pyramids, all pyramids follow from the pyramid built on the golden triangle. That is, such a pyramid will be the original pole. And since the pyramid contains the principle of the golden ratio, which is a necessary condition for the existence of life, the pyramid of the golden triangle is a stabilizing pole living matter. According to A. Lukashev, the Cheops pyramid stabilizes the characteristics of space and time in which living matter exists. However, our planet did an excellent job of stabilizing the conditions necessary for the existence of life even before the construction of the pyramids. Why is there a need in Egypt to create structures that help our planet and duplicate its functions? Most likely, this is due to the appearance on the banks of the Nile of too much thinking living matter, that is, people. After all, the most active construction of the pyramids took place during the creation of a single state in Egypt with a centralized economy and power. People with their contradictory thoughts, desires and aspirations worsened the “ecology of space.” There are many examples in history when a person, with his thoughts, embodied in reality, destroyed not only himself, but everything around him, including entire states.

The presence of a pole of stability is a necessary condition for the existence of life, but it is not sufficient. For the development of life, another pole is needed, in the direction of which development will be directed. This role is as important as the previous one. This means that the pyramid playing this role should be close in size to the Cheops pyramid. You don't have to go far. To the south of the Cheops pyramid is the pyramid of Khafre or Khafre. The length of its base is 215.5 meters, height 143.7 meters. The Pyramid of Khafre is slightly smaller than the Pyramid of Cheops. However, if we take into account that the Pyramid of Khafre stands on a hillock about 11 meters high, then its top will be 8.5 meters higher than the Pyramid of Cheops. The proportions of the pyramid of Khafre are described by a right triangle, the aspect ratio of which is 3: 4: 5 and the base is 3. The sequence of radii of the inscribed spheres of the pyramid: 1, 1/4, 1/4 2, 1/4 3,... Here the attentive reader will say, that there is a problem. The number 4, a symbol of “dead” matter, cannot be the direction of life development. Absolutely right. But here it is necessary to take into account that the isosceles triangle that determines the proportions of the Khafre pyramid is the face of the pyramid with a sequence of radii of inscribed spheres: 1, 1/7, 1/7 2, 1/7 3,... Number 7 is the number of human spiritual development. However, the energies of such a pyramid are available only to especially enlightened people. For the rest of the mortals, it’s like a poultice for the dead, that is, it’s still ineffective. You need to coarse the energies a little, to “ground” them, as it were. Then they will become more accessible to people. To do this, you need to build a pyramid using the pyramid face of the number 7.

However, the pyramid of Khafre plays not only a guiding role. It is also a pyramid that gives birth to life. The clue that confirms this is literally right under our feet. This is our planet - Earth. It has the shape of a pentagondodecahedron, although highly rounded. Pentagons are visible on its surface. Their sides overlap mountain ranges and crustal faults. The pentagondodecahedron, as mentioned earlier, contains the number 5 - the number of living matter. This is a living polyhedron, that is, it contributes to the origin of life. Perhaps life on our planet appeared only when it changed its spherical shape to a pentagondodecahedron, and the ratio of energies inside the Earth began to correspond to the golden ratio.

The pentagon dodecahedron is interesting for one property. If a beam perpendicular to the edge is directed inward through its face, it will be reflected repeatedly from the faces, intersecting with itself. The intersection angles between the reflected rays are 73.7398... degrees and 53.1301... degrees and, together with the incoming ray, form two groups of isosceles triangles. One group is the triangles of life, the sequence of radii of the inscribed spheres of which is: 1, 1/Ф 2, 1/Ф 4, 1/Ф 6,... The other group of triangles corresponds to an isosceles triangle that determines the proportions of the pyramid of Khafre, the angles at the base of which are equal to 53.1301 ... degrees. It turns out that the corners of the Khafre pyramid correspond to the directions of energy flows operating in the pentagondodecahedron - the polyhedron that gives birth to life.

The situation with the pyramid of Mikerinus or Menkaure, the third great pyramid at Giza, is somewhat confusing. This pyramid is located south of the Pyramid of Khafre. The length of its base is about 108 meters, height 66.4 meters. The angle of inclination of its faces, according to different sources, lies within 50.71...51.5 degrees. An interesting idea was expressed by the Englishman David Furlong. Its essence is that the ratio of the sides of the triangles that define all the pyramids of the Giza complex are associated with the numerical sequence: 1,3,4,7,11,18,29,47,... The Pyramid of Khafre is determined by the numbers 3 and 4, the Pyramid of Cheops - numbers 7 and 11, and the Mikerin pyramid - numbers 11 and 18. This number sequence is built on the principle of the Fibonacci sequence, that is, every third member of it is the sum of the two previous members. If you look closely at this sequence, you will notice that its terms are, rounded to the nearest integer, numbers in the golden ratio sequence. According to Furlong's idea, the isosceles triangle that determines the proportions of the Mycerinus pyramid has a ratio of height to base length of 11:18. Such a triangle is the face of a pyramid with a sequence of inscribed spheres: 1, 1/10, 1/10 2, 1/10 3,... That is, carrying the number 10. From the point of view of esotericism, 10= 1+0= 1. This means a pyramid , carrying the number 10, is a divine pyramid. Then the pyramid of Mikerin, built on the edge of the divine pyramid, should be for people the earthly embodiment of the ideal, the ultimate goal of human development.

Among other Egyptian pyramids, the pyramid of Pharaoh Niuserra also has the proportion of the Cheops pyramid. The length of its base is 78.8 meters, height 50.1 meters. But, at least seven other pyramids have a proportion close to that of the pyramid of Khafre. I was unable to find any other pyramids with the proportions of Mikerinus’s pyramid in printed sources. The predominant number of pyramids of spiritual development over stabilizing ones most likely indicates that the pharaohs and priests of ancient Egypt were very careful about the spiritual growth of their people.

Is there a pyramid of life among the Egyptian pyramids? Probably no. However, there is an unfinished pyramid of Pharaoh Rajedef. The length of its base is 104.5 meters, the angle of inclination of the sides is 60 degrees. This is the angle of an equilateral triangle. Then the sequence of radii of the inscribed spheres of this pyramid will be: 1, 1/3, 1/3 2, 1/3 3,..., and its face will be a triangle of life. But the pyramid is unfinished and, in addition, somewhat destroyed. Therefore, the accuracy of its measurement raises some doubts. If the error is negative by 3.5 degrees, then this may already be a pyramid of life.

As you can see, accuracy is very important when building pyramids and when measuring them. After all, a mistake of just a degree can change the perception of the inner essence of the pyramid. Unfortunately, the accuracy of measurements of the remaining smooth Egyptian pyramids is questionable, also due to their serious destruction. Therefore, one can only guess about their true proportions.

Life range

Living matter on our planet exists due to processes occurring in aqueous solutions. The amount of water in the human body is 80% of its total mass. Other living organisms may have even more. The task of maintaining the stability of living matter, first of all, will mean maintaining the stability of the aquatic environment of the body. This applies not only to temperature stability, but also to structural stability. The properties of water are largely determined by the presence of hydrogen bonds between its molecules. Thanks to them, water can exhibit the properties of solids - crystals. That is, water is a liquid crystal. The transfer of information from one organ of a living organism to another can occur through the transfer of chemical substances, for example, hormones, by a flow of liquid (blood), or by the formation of a bond based on the principle of a chain of water molecules oriented in a certain way. That is, the creation of a certain spatial structure from liquid crystals. The speed of information transfer along such a chain will be much greater. Since water is a liquid and not a solid, these chains of liquid crystals will be destroyed quite quickly and need to be renewed. A temperature of 36...37 degrees Celsius is, as it were, a critical point. At this temperature and just below this temperature, liquid crystals are quite stable, and just above it, the rate of decomposition of liquid crystals increases significantly. Then an increase in a person’s body temperature during illness can be explained by the need to destroy unnecessary or dangerous information structures for the body in order to then create new ones that are necessary for the body to continue life.

The angles of inclination of the edges of most smooth Egyptian ones are in the range of 50...55 degrees. If these values ​​are multiplied by two, you get 100...110 degrees. This range includes all values ​​of the angle between the bonds of oxygen and hydrogen in a water molecule in all states of aggregation. That is, from steam to ice 104.45...109.5 degrees. It remains unclear why multiply by two. The fact is that in nature crystals exist in the form of double pyramids. This is determined by various reasons, including the law of conservation of energy. The tetrahedral pyramids represent half of a crystal, albeit man-made, the second part of the pyramid will be an energy double, which is located under the pyramid with the top down. Therefore, the angle between the physical and energetic edges of the pyramid will be twice as large as the angle between the physical edge and the base. It turns out that almost everything Egyptian pyramids, like antennas, are tuned to influence water molecules. Let's see between which pyramids the water molecule is located. Let us once again draw the triangles that determine the proportions of the pyramids, and place a water molecule in different states of aggregation between them. It turns out that the water molecule in vapor and liquid states is located between the pyramid of Cheops and the pyramid of Khafre, between the poles of life. But ice is already “dead” matter and the angle in the water molecule becomes slightly larger than the angle between the faces of the octahedron - the pyramid of “dead” matter.

About scaling issues

We are now so accustomed to the decimal system of measurement that the statement that an Egyptian cubit is 0.635 meters and one ten-millionth of the radius of the Earth is taken for granted. However, if we live in a world of the golden ratio, then the principles of scaling or comparison of sizes should be determined by it. In Russia, the measuring system of fathoms, based on the ratio of the golden section, existed for quite a long time. My father told how his grandfather, who died in the late fifties, taught him how to lay Russian stoves, using fathoms and vershoks as a measuring device. Between fathoms, and in Rus' there were more than 17 names, there was a ratio of F 3/4 and F/2. Within a fathom, the size was reduced by dividing by two. The last one was an inch. It was equal to 1/2 5 fathoms.

The idea of ​​taking the size of the globe as the primary standard turned out to be very popular. The unit of length, derived from the size of the Earth, the meter, is gradually occupying a dominant position in all countries. Why is the meter so popular and does it have anything to do with the golden ratio? It turned out that yes. And, although one meter, by definition, is equal to one forty-millionth of the circumference of the Earth passing through the poles, at the same time, 1 meter is equal to 1/F 34 of the equatorial diameter of the Earth. Moreover, 34 or 3+4= 7 is a sacred number, that is, it carries a hidden divine meaning. There is a great subconscious desire among people for the golden ratio.

When I found information about the size of a water molecule, I wanted to check whether the ratio of the sizes of the Earth and water is described by the golden ratio. Let's draw a water molecule in the form of a triangle, complete it and inscribe a circle. It turned out that the diameter of this circle and the equatorial diameter of the Earth have the ratio: Dwater × Ф 83 = Dearth. Moreover, this value corresponds to a water temperature of about 30 degrees Celsius. And the number 83=8+3=11 also turns out to be sacred.

I really wanted to test the same idea on the Egyptian pyramids. Here it turned out to be more difficult. Pyramid researchers have already reached a consensus regarding the composition of the pyramids at Giza. The pyramid of Cheops corresponds to Venus, the pyramid of Khafre corresponds to Earth, and the pyramid of Mikerin corresponds to Mars. If this is so, then the diameter of the sphere inscribed in the pyramid of Khafre and the diameter of the Earth should have a relationship described by the golden ratio. We will measure the height of the Chefren pyramid from the level of the base of the Cheops pyramid. This is justified by the fact that when comparing pyramids, relative sizes are used, not absolute ones. Then the height of the Khafre pyramid will be 143.7 + 11.2 = 154.9 meters and the diameter of the inscribed sphere will be 116.2 meters. The relationship with the diameter of the Earth will take the form Dchaphrene × Ф 24 × Ф 3 /4 = D earth. That is, in the ratio of diameters there is additionally a value similar to the ratio in Russian fathoms Ф 3 /4.

If the reader wants to make copies of the Egyptian pyramids, for example, for use as greenhouses, then instead of the scale in decimal system, in my opinion, it is more logical to use the golden ratio scale: 1:11, 1:18, 1:29, 1:47, 1:76, 1:123, 1:199.

Why do we need pyramids

The influence on a person’s sensations of his location on the earth’s surface, the shape of the building next to which he stands, and the shape of the room where he is located has been known for a long time. On this occasion, in people’s speech there are such expressions as “a bad place”, “an unsightly house”, “the walls are pressing”, etc. However, even in our age of pragmatic materialism, when there is a concept of maximum permissible doses of concentrations of chemicals, electromagnetic field radiation, radioactive doses, it is difficult to measure these sensations in some units in order to say how important it is for the preservation of human health to stay in a particular place, house, room. This means that if such units have not been invented, then it is not so necessary for modern man. Seems Yes. There are more important questions. However, the word “comfort” has existed in the Russian language for many centuries. The explanatory dictionary explains it as convenience, well-being in a home environment, in everyday life, comfort, a sense of peace. Think about the word livability. This means such a structure of the world surrounding a person that leads to good or prosperity in everyday life. This means that the degree of prosperity of a person directly depends on how comfortable he feels in life. Then comfort becomes the most important measure for a person, and finding the law by which comfort is created is extremely necessary. Let's try to define the concept of comfort in the language of physics. Then comfort is a certain set of energy flows acting on a person, the properties, intensity of influence and direction of which are in a certain combination, corresponding to the laws of the universe. Or, simply put, these energy flows must be in harmony.

Humanity is already familiar to some extent with harmony. The fundamental number that reflects the harmony of the entire living world is the number of the golden ratio. This means that if in a certain space this very set of energy flows influences a person according to the law of the golden ratio, then a person in this space or, simply, place will feel comfortable and live in the most favorable way for himself. Are there such places on Earth? Yes there is, but not much. In our northwestern regions, such places are most famous on Valaam and Kizhi. In these places, people have been improving their health since ancient times, and some even received great wisdom, or, in church terms, enlightenment. The features of these places are associated with the geological structure, which allows the energies of the Earth to reach the surface in a powerful flow. Moreover, the combination of these energies is beneficial for humans. But the same energies come out of the Earth over its entire surface, albeit not in such strong flows and not in such a combination. If you don’t set yourself the ultimate goal of immediate enlightenment, but try to at least create the necessary energetic comfort in a small space, then the problem will be solved more easily. People have long found a way to create energetic comfort. This method is associated with the construction of pyramids and temples.

As you know, the largest ancient civilizations built pyramids. The ancient Mayans built step pyramids, the Egyptians built smooth and stepped ones. A large number of pyramids were found in China and Tibet. Those peoples who did not possess such powerful knowledge built conical mounds. The idea of ​​building pyramids is quite elegant. If there is a certain place with an area from one square meter to a hectare that is not harmful for a person, in other words, there is no geopathogenic zone, which is usual, then it is possible to concentrate the energy flow coming out of the Earth in this area and balance it in accordance with the law of the golden ratio and direct it along the surface of the earth. You can change the direction of the energy flow using an inclined plane. You can distribute it evenly using a cone. A similar problem can be solved using a dome. But the most effective energy concentrator, as it turned out from research, turned out to be regular pyramid. This is a pyramid whose base is a regular polygon, in particular a square, and the side faces are in the shape of an isosceles triangle. The ratio of energy flows can be modified by constructing these geometric bodies in accordance with the proportion of the golden section.

The property of concentrating and transforming energy with the help of appropriate building architecture is still used today in religious buildings to bring people into a special state of bliss. This state itself is favorable for people; they become more open and friendly. Surfaces: cone, dome, pyramid are the main elements of churches and cathedrals. You don’t have to look far for an example. Everyone knows the domes of St. Isaac's and Kazan Cathedrals. The multifaceted pyramid is used in the architecture of the Church of the Savior on Spilled Blood and in the spire of the Peter and Paul Cathedral. A cone and a tetrahedral pyramid crown the Church of the Baptist on Kamenny Island.

How do pyramids work?

Let's try to figure out how pyramids “work”. Let our pyramid be hollow, that is, filled with air. The walls of the pyramid will be formed by a thin film. This assumption is interesting in a practical sense, since personal funds are still not enough to build a decent-sized monolithic pyramid. We assume that the right triangle describing the pyramid has an aspect ratio of 1:F:F. That is, the proportions of our pyramid correspond to the proportions of the Cheops pyramid. The pyramid is oriented with its faces to the cardinal points.

Let's cut the pyramid in half with a vertical plane directed from north to south. We get an isosceles triangle. The main energy flow will come from the earth, perpendicular to its surface. Other energy flows will affect the pyramid in the direction of the parallel and the meridian. They are parallel to the surface of the earth. Getting inside the pyramid, energy flows are partially reflected from its walls, and partially pass through the wall-faces. The pyramid begins to radiate with its edges.

In our pyramid, the flow of energy emanating from the earth is reflected from the walls twice. Streams of energy flowing parallel to the surface of the earth are reflected from the walls once. The interaction of the primary flows with the reflected ones creates a redistribution of energy inside the pyramid, the so-called interference pattern. It has three zones. The first zone is formed by the flows of energies of the left and right halves of the pyramid from the primary flow emanating from the earth and two reflected ones. The second zone is formed by the energy flows of the left and right halves of the pyramid from the primary flow emanating from the earth and the second reflected flow. The third zone consists of many pieces in which some reflected energy flows are missing. Now let’s add another interference zone to the figure, which is formed by energy flows flowing in the direction of the meridian (the zone inside the rays AM and AK). A similar picture will appear if we consider the pyramid in an east-west section. Now we have outlined the most energetically saturated places in the pyramid. Let's try to superimpose a picture with the location of the internal chambers of the Cheops pyramid on our interference picture of the pyramid. The cameras in the figure are marked with circles. At the bottom of zone “1” is the king’s chamber. The level of this chamber corresponds to the level of 1/3 of the height of the entire pyramid. In the middle part of zone “2” there is an underground chamber. Its level corresponds to the level of 1/3 of the height of the triangle VDS (base BC). Just below point E is the queen's chamber. Its level corresponds to 2/3 of the height of the triangle WEIGHT (base BC).

The locations of the cameras in our film pyramid very clearly correspond to the locations of the cameras in the real Cheops pyramid. However, the linear principle of the movement of energy flows, which was used to determine the locations of the cameras, cannot describe the presence of a vertical flow of energy in the pyramid, coming from the base through the top. Such a flow, consisting of ionized particles, is observed above the pyramid of A. Golod. An upward flow of ions more than two kilometers high was discovered by a radar operating in the centimeter range during studies of a pyramid built near Lake Seliger. In fact, according to the flow movement in our model, only one ray can pass through the top, emanating exactly from the center of the base. Accordingly, there is no need to talk about any high-density energy flow. This means that there is another process in the pyramid that leads to the formation of a powerful vertical flow of energy.

The book by V. Babanin describes the observations of the psychic T. Syrchenko. When visiting Egypt in 1994, she “registered” the presence of powerful pillars of some kind of energy above all the pyramids in Giza. However, above the Egyptian pyramids, locators do not detect the presence of a high-density ion column, like that of A. Golod’s pyramid on Seliger. One could be very skeptical about this “observation”, if not for one little thing. The psychic describes that a donut-shaped ring was twisted between the columns of energy. There was one incident regarding such a bagel.

Once a professional stove maker made a bet with his neighbor that the smoke from the chimney of his house would come out in rings. I don’t know what the stove maker argued, but soon the whole town watched how, in calm weather, the chimney puffed out rings of smoke. The secret was very simple. The stove maker rearranged the pipe in such a way that as it rose, it was tightened with a screw. That is, it forced the upward flow of smoke in the chimney to spin around its own axis. As a result, smoke donuts were obtained at the outlet of the pipe. This effect was observed by a psychic over the feasts in Giza.

This suggests that the energy flows emanating from the tops of the pyramids are twisted around the longitudinal axis, that is, a vortex tube is obtained. A rotating flow in the form of a vortex tube is described by flow theory. Its peculiarity is that the smaller the cross-section of the tube compared to the original one, the greater the flow speed. In the case of a pyramid, the flow of energy entering it through the base, as it moves upward, will reduce the cross section due to the inclination of the faces of the pyramid and increase the speed of rotation. At the top of the pyramid, the flow will turn into a narrow tube with a high energy density, since in this case most of the energy entering through the base of the pyramid will pass through its top. The result will be a tornado “upside down”. The trunk of the tornado will be directed upward, like a column. At the same time, the transverse dimensions of the tornado will not extend beyond the boundaries of the pyramid shape.

I would venture to note that the flow of ions exists to one degree or another above all the pyramids. Ions are formed not in the pyramid, but in the surrounding area. During research on Seliger, instruments recorded a zone of increased air ionization within a radius of 150 kilometers around the pyramid. This is the Earth's reaction to the action of the flow of energy inside the pyramid. Ions are drawn to the pyramid from all surrounding areas, layered on the vertical flow of energy of the pyramid and thrown upward by it. The amount of ions formed near the pyramid is determined by the Earth according to some other program related to the restoration of the ozone layer. After all, before the appearance of A. Golod’s pyramid, the Earth replenished ozone layer, although not as active. A. Golod's pyramid is another mechanism in the system of its replenishment.

The question arises why such a dense ion flow is formed above the pyramid of A. Golod, and not above the pyramids of Cheops or Khafre. Most likely this is due to the purpose of A. Golod’s pyramid - to create proportionality between the processes taking place on Earth. Where necessary - add, where not necessary - subtract. The purpose of the pyramids of Cheops and Khafre is different. This is written in a corresponding number sequence within their forms.

It remains to solve the issue of the flow of energy coming from space. Scientists have long discovered the property of pointed objects to create a high electric field intensity at the tip. A lightning rod is designed on this principle. In the same way, at this edge, an increased intensity of another field is created - the torsion field, which is the primary information field of the Universe and carries, in esoteric terms, divine or cosmic energies. In the pyramid, the flow of cosmic energy comes from point A - the point of connection of the faces of the pyramid. This energy fills the entire internal space of the pyramid, interacting with flows of other energies. As a result, earthly energies will be modulated by cosmic energies. And, behold, the result of such processing of earthly energy in the Cheops pyramid becomes beneficial for all living things.

From a practical point of view, pyramid zones can be useful in the following ways. If you hold water in zone “2” near the base of the pyramid, then such water will become “dead” water. It will stop inflammatory processes in the body. If you keep water in the middle of zone “1”, then such water will become “living” water. It will accelerate the growth of body cells and promote wound healing.

Pyramids, cones, domes

Earlier we talked about the fact that by using pyramids, cones and domes as the main architectural elements of a church, you can create a comfortable energetic environment in the church premises. We have already become a little familiar with the pyramids. Cones are very close to pyramids. If you cut the cone in half with a vertical plane passing through the top and the center of the base, you will get an isosceles triangle, the same as a pyramid. Therefore, everything said earlier about the angle of inclination of the faces of the pyramid is also true for the angle of inclination of a straight line forming a conical surface. Since there is a circle at the base of the cone, the cone, unlike a pyramid, does not require orientation to the cardinal points. This greatly facilitates the installation of conical structures.

Now let's move on to the dome. A dome, according to the explanatory dictionary, is the shape of the roof of a building in the form of a hemisphere. We will consider as a dome all forms that in appearance resemble part of a sphere, with the convex side facing the sky and the concave side facing the earth. The curved line describing the shape of the dome can be a circle, a parabola, an ellipse...

The flow of energy coming out of the ground enters the inside of the dome and is reflected from its surface in the opposite direction. In a parabolic dome, the outgoing rays will be parallel to the incoming ones. With a different dome shape, the reflected energy flows will be directed at different angles and can extend far beyond the dome. To collect reflected rays, a cylinder is placed under such domes. It is called a light drum, since windows are usually installed in its walls to illuminate the room located under the dome.

As in the pyramid, in the dome the reflected flows of earth's energies interact with the flows of cosmic energy. As a result, the energy field in the dome is similar to the field in the pyramid. However, the field in the dome will be weaker than that of a pyramid of similar size, since the dome does not have a sharp top where cosmic energy is “concentrated”. To increase the field strength, a pointed spire, flagpole, and cross are installed on top of the dome. On the domes of Muslim mosques there is a crescent-shaped month, with its sharp end facing up.

However, another danger appears - an excessive increase in field strength at the top of the spire, which can occur periodically. Field overvoltage in the spire zone leads to a loss of its uniformity and the emergence of zones unfavorable for life. Psychics who have studied the field of small pyramids perceive this as an alternation of “negative” and “positive” zones near the top of the pyramid. This effect is easily removed. It is enough to stick a bunch of several wires into the top of the pyramid or cut off its top a little. In reality, we see that the Egyptian pyramids have a platform at the top, and the pointed spiers of buildings in European cities end with weather vanes in the form of images of people, animals, coats of arms, and the like. In St. Petersburg, on the spire of the Peter and Paul Cathedral there is a weather vane in the form of a flying angel carrying a cross.

Interestingly, the Christian cross mounted on the dome plays a dual role. On the one hand it is a field concentrator, and on the other hand it is a surge protector. This property is apparently associated with the peculiarity of the construction of the cross. The crossbar of the cross is located at a point determined by the proportion of the golden section of its vertical part. The length of the crossbar is equal to two lengths of the smaller part of the golden ratio. Golden ratio, embodied in the cross, makes it possible to reconcile its two opposing functions.

The cross performs another function - the function of a selective antenna. Here the cross is helped by another structural element. Remember what the top of a traditional Russian Orthodox church looks like. The onion-shaped dome is crowned with a cross. And between them there is a ball. Let's see how the sizes of the ball and the cross of the Church of the Intercession on the Nerl correlate. The height of the church cross is 1.31 oblique fathoms, the diameter of the ball is 0.31 oblique fathoms. Then 1.31/0.31= 4.2258… 4.236…= Ф 3. Taking into account the precision of manufacturing in the early 12th century and the accuracy of measurement in the mid-20th century, the difference is only 0.2 percent. In the cross, waves will be predominantly excited that are multiples of the length of its elements, that is, proportional to the values ​​of Ф, Ф 2, Ф 3. The ball is a selective device. It allows you to separate part of the waves entering it, including waves with a length proportional to the golden ratio. Since the diameter of the ball is consistent with the dimensions of the cross through the golden ratio, the cross and the ball adjust the energy coming from space in such a way that waves predominantly penetrate into the dome, the ratio of their lengths is described by the numbers Ф, Ф 2, Ф 3, that is, the golden ratio .

The most characteristic dome shape for Russian Orthodox churches is the onion shape. This dome consists of two parts, smoothly transitioning into one another. The upper part is a curved funnel, the lower part is a sphere with a cut off top or a spheroid - a flattened sphere. Let's take a closer look at these parts. Let us rewrite once again the complete sequence of the golden ratio: ...1/Ф 3, 1/Ф 2, 1/Ф, 1, Ф, Ф 2, Ф 3,... or...Ф  3, Ф  2, Ф  1, Ф 0 , Ф 1 , Ф 2 , Ф 3 , ... Each member of the sequence differs from the previous member by changing the exponent by one. Let's try to depict this sequence in rectangular coordinates. On the horizontal axis we will plot the value of the exponent, and on the vertical axis we will plot the value of the terms of the sequence. We obtain a graph of the exponential function f(x)= Ф x = 1.618 x. If we now rotate the resulting curved line around the horizontal axis, we get a curved funnel. It can also be called an exponential horn. Everyone has seen such a device. It is used in the manufacture of brass musical instruments. This exponential horn is located on the top of the church dome. It, like the pyramid, repeatedly reflects the flow of energy coming from the earth from the inner surface, directing it downward. At the same time, the flow of cosmic energy emanating from the ball into the horn interacts with the energies of the earth. The sphere collects the reflected rays and directs them into a light drum, the lower edge of which rests on the church building. The light drum is a cylinder, that is, a pipeline, or more precisely a cylindrical waveguide. Through it, the flow of converted energy enters the interior of the church building. The church building usually has the shape of a rectangular parallelepiped, oriented to the cardinal points. The aspect ratio of the parallelepiped corresponds to the relationship between the numbers of the Fibonacci series or proportion based on the golden ratio.

In the steppe regions of the European part of Russia, many mounds have been discovered - earthen hills with a fairly regular conical shape. These are man-made hills. In some of the mounds, archaeologists excavated and discovered burials of representatives of the nobility of the steppe peoples. Why did people spend so much labor to move thousands of tons of earth? Practical ingenuity suggests that this is necessary in order to hide the burial from lovers of freebies. After all, nobles were buried in the mounds in rich clothes with an abundance of jewelry made of precious metals. Household belongings, also richly decorated, were also placed in the burial. Naturally, all this had to be hidden more reliably from robbers. Nomadic peoples did not stand in one place, and there was no one to guard the graves. However, wouldn’t it be simpler to dig a deeper hole, place the deceased there and cover him with the excavated earth? Now they use this method of burial, and there is no need to move such a huge amount of earth. But if people did build mounds, then we need to look for a hidden meaning in this.

Let's look at the mound in terms of shape. Of course, they don’t reach the pyramids, their slopes are too gentle. Think about playing with sand on the beach. If you pour dry sand from your palms in a heap, you get a very gentle mound. It's the same with the earth. Only the earth then cakes over time, and the angle of inclination turns out to be even smaller. But this has its advantages. Let's draw a vertical section of the mound, passing through the top. You will get an isosceles triangle. Now let's direct rays parallel to the ground to the inclined sides of the triangle. They will be reflected from these sides, rise up and intersect above its top. The angle of inclination of the reflected rays with respect to the ground will be two angles of inclination of the sides of the triangle. Therefore, if the slope angle of the mound is approximately 26 degrees, then the angle of inclination of the reflected rays will be similar to the angle of inclination of the faces of the Cheops pyramid. On a real mound, energy flows flowing parallel to the ground will be affected from four sides in the direction of the meridian and parallel. Having been reflected from the slopes, the energy rays interact with each other and create an interference pattern above the mound. It looks like two pyramids connected by their bases. The top of the lower pyramid rests on the top of the mound, and the top of the upper pyramid may be at a height of about three to four times higher than the height of the mound. This double pyramid will interact with the mound, forming an energetically saturated zone within it, into which the burial will fall. This is a kind of energy guardian of the deceased.

Of course, it is difficult to believe in the existence of such a virtual, ghostly pyramid. But stone is a different matter. You can touch it. However, the material from which the pyramid is made is just a medium for the propagation of waves. It can increase or decrease the effectiveness of the interaction of energies in a form. The principle of interaction is determined by the pyramidal shape. It seems to me that the concept of form goes back to the moment of the beginning of the universe, when there was nothing but divine peace. As soon as the first movement appears in eternal rest, boundaries arise that separate peace from movement. These boundaries create the form. Since the first movement determines the most important, fundamental principles of the construction of the world, the form can determine the conditions for the interaction of energies, starting from the most primary, most subtle level. If in the current worldview system the most primary elements are torsion fields, carrying information about the structure of the Universe, and the physical vacuum, then by choosing the appropriate form it is possible to influence the torsion fields and the physical vacuum, thereby selecting the necessary information, which through the form will be expressed in certain properties useful to humans. In this case, the properties of the energies inside the form will be different from the properties of the energies outside the form. Since in the existing world there is no longer rest, but only movement, then a form can be called a set of boundaries between movements described by different laws.

We are accustomed to the fact that solids have a form, and liquids and gases take the form of the limited volume where they are placed. However, if a flow of the same liquid flows inside a liquid, an interface will appear, which means the flow will have a shape. The same is true for gases. The shape of the flows in the atmosphere is quite difficult to discern. This is due to the large size of the flows and the vagueness of their boundaries. A cyclone has the shape of a giant funnel, sometimes covering entire regions. If a cyclone has a form, then the energies inside it will affect, for example, a person differently than outside it. A healthy body hardly notices this effect, but the body of a sick person, sensitive to changes, clearly reacts to the passage of a cyclone by deteriorating well-being.

Not only matter has a form, but also a field. Remember the school experiment with a magnet and iron filings, which are located on a sheet of paper along the magnetic field lines. People have learned to give fields different shapes. For example, in an installation for studying thermonuclear fusion, an electromagnetic field in the shape of a donut was created. Therefore, it is not surprising that the mound builders created a pyramidal field above the burial site. Another thing is that they knew the properties of this field, which we can only guess about. The boundaries of the field of this energy pyramid will not be as clear as those of a stone pyramid and the impact from its field will be less pronounced. In conclusion, I would like to mention that houses with flat gable and hipped roofs will also create pyramidal fields above them. The angle of inclination of the roof determines whether this field will be conducive for people to live in them or not. Will the house have an energy guardian or a destroyer?

What houses do we live in?

If we consider a person’s home from the point of view of the direction and quality of energy flows, then we should first turn to the experience of peoples who have a closer connection with nature. The first thing that comes to mind is the dwelling of the northern peoples. The Chukchi tent and the North American Indian wigwam have a shape close to a cone. The Mongol yurt has the shape of a cylinder, covered on top with something between a flat cone and a dome. The buildings of many peoples living near the equator have the shape of a cylinder covered with a cone on top. These dwellings have a common feature. The axis of symmetry of the building, which is the axis of the cone, is located perpendicular to the surface of the earth. That is, the natural flow of energy coming from the earth to the sky, into space, and, accordingly, from space to the center of the Earth coincides with the axis of the energy flow of the cone. Then, by changing the angle of inclination of the conical surface, you can change the energy ratio in the cone to obtain the most favorable conditions for living. An energy flow of the same quality will pass through the cylinder, since no changes are made to the energy flow entering the cylinder from the ends.

In Rus', a more typical building was in the form of a rectangular parallelepiped made of logs, covered on top with a tetrahedral pyramid of poles and straw. The axis of symmetry of the pyramid coincides with the direction of the energy flow coming from the earth. With a parallelepiped the matter is more complicated.

For simplicity, let's consider a cube. This is a parallelepiped with all sides the same. The cube has two systems of symmetry axes. The symmetry axes of the first system pass through the centers of the faces and intersect in the center of the cube. There are three of them. These axes are mutually perpendicular in space. If the cube is turned into a parallelepiped, then these axes will also pass through the centers of the faces and intersect in the center of the parallelepiped. In the direction of these axes, energy flows pass through the cube and parallelepiped without distortion.

The second system of symmetry axes in the cube passes through opposite vertices. There are also three axes. The angles between these axes are other than 90 degrees. We have already looked at these axes earlier. Along them there are flows of energy from “dead” matter. Since these axes in the cube intersect in the center, then in the central zone of the cube there will be an increase in the concentration of this energy due to the summation of the three flows. This effect is unfavorable for a living organism.

Let's place a pyramid on top of the cube. It will change the flow of energy coming from the earth in a way favorable to humans and “fill” the cube with this energy. But what about “dead” energy? It is impossible to completely get rid of it, but its influence can be reduced. To do this, we transform the cube into a parallelepiped, that is, we slightly change the dimensions of the sides of the cube. The axes of symmetry of the “dead” matter of the cube, strictly speaking, are the axes of symmetry of the trihedral angles, and not the cube itself. Therefore, in a parallelepiped, at a certain aspect ratio, these axes will not intersect and a more or less uniform distribution of “dead” energy will form inside it. If the beneficial energy from the pyramid significantly exceeds the “dead” energy, then the latter will not have a noticeable effect on a living organism. And in order to maximize the energy situation in the parallelepiped, it is necessary to orient it to the cardinal points, since the Earth’s energy flows go in the direction of the meridian (north-south), in the direction of the parallel (east-west) and from the center of the Earth into space (perpendicular to surface of the earth). It is important to note here that the magnetic compass shows the direction to the magnetic pole, which does not coincide with the geographic pole. For example, for St. Petersburg and the surrounding area, the theoretical angle between the direction of the poles is about 14 degrees towards the east. But the magnetic compass is also affected by the uneven location of magnetic rocks underground, the so-called magnetic anomalies. In the vicinity of St. Petersburg, there is also a magnetic anomaly that changes the magnetic declination of the compass. Therefore, the actual magnetic declination is 8.5 degrees towards the west. If there is no map indicating the magnetic declination, then focus on the North Star.

It remains to find out what aspect ratio the parallelepiped should have so that the distribution of “dead” energy in it would be uniform. In Rus' they acted simply. When a house was built, the length, width and height were measured in fathoms with different names. The ratio between fathoms is proportional to the golden ratio (F/2 and F 3/4). Then it is enough to measure, for example, three fathoms in each direction, and the minimum of “dead” energy in the house was obtained by itself. But what should we do? After all, we have only one meter - the meter. The following can be recommended. It is not advisable to build a house in the proportions 1:1, 1:2 and 1:3. The unevenness of the “dead” energy will be maximum. It is better to build a house in the proportions 2:3, 3:4, 3:5 and so on, choosing a ratio from two Fibonacci numbers, starting with two. If the plan of the house should be close to a square, then use the proportion 1:F 3 /4 (1:1.059). Better yet, use the books of A.F. Chernyaev, where a matrix of numbers calculated on the basis of the commensurability of Russian fathoms is given.

This means that dwellings in the shape of a parallelepiped can only be used when there is a powerful emitter of energy favorable for life nearby. It can be a pyramidal, conical or dome-shaped roof. This could be a nearby cathedral or church. This could be a large pyramid near the house. In this case, it is important to have a clear orientation of the parallelepiped dwelling to the cardinal points, that is, with its face towards the north geographic pole.

Now think about, dear citizens, what kind of houses we live in. And this is what happens. Our homes are deprived of the main element that creates a favorable energy environment for life - a pyramidal roof. And if there is one, then the angle of inclination of its edges was calculated, most likely, not from considerations of the energy harmony of the home. Orientation to the cardinal points is often arbitrary. This distorts the energy from the Earth's energy flows that penetrates the premises of the house. In addition, iron grids are walled up in the walls of our houses, since almost all housing is built from prefabricated and monolithic reinforced concrete. These grids further weaken the natural energy of the Earth entering our apartments. And almost nothing remains of the flow coming from the Earth in multi-story buildings due to the numerous reinforced concrete floors. Only the energies of “dead” matter remain in them, and even directed in a way that is unnatural for humans (do not forget that we live in a triangular double pyramid, laid on its side). In general, the picture is not very encouraging.

How to improve the energy situation in your home? In a city apartment, you can use small pyramids made of plastic or the mineral shungite. Their area of ​​action, according to psychics, is about two meters. It is better to place them near the bed where you sleep or on the table where you work. Shungite crushed stone can be scattered under the bed. All this can now be bought in St. Petersburg. You can use the energy-information matrix of A. Golod with the memory of the pyramid field.

The issue is resolved relatively easier at the dachas. It is best to immediately build a house with a pyramidal roof. If you already have a house, and it is difficult to change its design, then you can build a pyramid three to four meters high next to the house. It can be used as a greenhouse or greenhouse. The beneficial energy impact of such a pyramid is quite sufficient for an area of ​​6-10 acres. The greatest concentration of energy will, of course, be in the pyramid itself. The concentration of energy sufficient for the healing effect will be in a zone with a radius of up to two heights of the pyramid. We must remember that the pyramid radiates with its edges. Therefore, opposite the faces, energy radiation will be maximum, and opposite the corners, it will be minimum. If a high-voltage power line runs near a summer cottage, then using pyramids you can create a protective wall. To do this, you need to place an odd number of pyramids in a line, if possible, perpendicular to the power line. The number of pyramids is from three and above. The size of the pyramids decreases as they approach the power line. In this case, a radiation wall is formed parallel to the power line. But when making pyramids, one must take into account A. Golod’s advice: even a minimal amount of metal used in the construction of a pyramid reduces its impact on the surrounding space significantly.

How pyramids can help us

It is difficult and uncomfortable for a person to live in modern world. The leapfrog of events, as if on purpose, tries to unsettle a person, taking away a lot of emotional and physical strength, pushing him towards a feeling of hopelessness.

We must pay tribute to the Brezhnev era. At this time, the feeling of stability of the surrounding world for a person was, perhaps, the maximum over the past century. Upon finishing school, it was possible, almost by age, to predict your whole life, career, pension amount. Of course, it was very difficult for original creative people in the conditions of the all-encompassing regulations of life at that time, but for the overwhelming majority of the country’s population it was, nevertheless, a blessing. Especially for pensioners. So they said that when he retired, he felt like a man.

And then all this prosperity disappeared in a matter of years, along with savings in the savings bank, a decent pension, and a normally paid job. The stability of the surrounding world has collapsed and will no longer be restored to its previous understanding. Where can a person now look for a foothold? Now neither the trade union committee, nor the native plant, nor the authorities will help. There is only one thing left. Look for a point of support within yourself. And to do this, you first need to calm down a little and try to establish internal balance.

This is also not an easy task. Previously, the church helped a lot with this. The man felt uneasy and, according to tradition, went to the temple of God. And there is grace! There is gilding on the images all around, the choir is singing, the priest is reading prayers for the health of the soul. Everything is calm, orderly, no one scolds, and sins will still be forgiven. That is, the church was a place for a person to find inner balance. The impact of the church on a person can be divided into three components. The first is the impact on the mind through the speech of the priest. The second is the impact on emotions through the magnificent decoration of the room, choral singing and the emotional mood of the priest. The third is the impact on the energy level through the architecture of the church building.

However, faith, including in God, is itself very intimate. And not everyone will want to go with her to church society. In addition, long years of materialistic education undermined sincere trust in the church. But a person really needs this very place of finding balance. This is where a pyramid on your summer cottage will help. It will create the necessary energetic atmosphere of comfort for a person.

If the pyramid is made in the form of a frame covered with film, then you can plant your favorite plants in it. And in the middle, make a small pond with a stream or fountain so that the water can flow. This will help you gain emotional peace. Well, then everyone will do as they see fit. Some will just sit on a bench, some will read a prayer over a candle, some will ask God for something that hurts them. This way he will slowly establish internal balance within himself. And internal balance is almost the “golden mean”. In this state, a person will be able to calmly perceive the events happening around him and choose the most correct and balanced decisions. This same state of internal balance will have enormous benefits for human health. When a person is calm and his muscles are relaxed, the energy flows in the body flow more strongly and the maximum healing effect is obtained. And it’s even better to help the body remember that it once had everything in order. To do this, we will use the advice of Dmitry Verishchagin.

You need to find in your memory at least one moment, most likely from childhood, when everything was fine with you. That is, you were full of strength and desires, you were breathing easily and freely. Your loved ones were with you. The weather was beautiful... Every person has such a moment in their life. Now try to imagine this picture before your eyes. If it doesn't work out well, don't worry. The main thing is that you found this moment. Then you need to remember how you felt then. What sensations did you have in your body? Do you remember? A bit difficult? Try again. This is very important for you! This condition is the key to regaining health. After all, a person pays too much attention to the state of his fatigue and slowly displaces the state of health from the body’s memory. After ten years, the state of fatigue becomes normal for the body. We are slowly becoming frail old people.

So, if you, being in a pyramid, surrounded by your favorite plants, being in a state of balance, put before your eyes that happy picture of you, filled with health in every cell of the body, and feel yourself in this picture, then you will create a powerful impulse to return in health. But it is very important to hold on to this feeling for as long as possible, at least two minutes, so as not to be interrupted by other thoughts at this moment. Next time, try holding the image for three minutes. And if you can hold it for fifteen minutes, then you are already a luminary of meditation.

The body usually immediately begins to respond to this signal for recovery. There is a slight tingling sensation in the legs and arms, which gradually intensifies. A slight itching appears on the skin. These are the nerve endings waking up. A feeling of heat flow appears in the limbs. This blood begins to circulate more strongly through the capillary vessels. Perhaps the appearance of warmth and a slight burning sensation in the tailbone area and in the abdomen below the navel. This enhances the work of energy centers responsible for the survival of the body. If your body doesn’t react right away, don’t be upset. Try again later. Determination and calmness are very important here. And everything will definitely work out for you.

You can also use water kept in a pyramid for healing. Water is an excellent accumulator of the energy field of the pyramid. If you wash your face or drink it with this water, then the field of the pyramid will interact with the human body through the water, improving its health. You just have to handle the water carefully. The spatial structure of liquid crystals formed in water under the influence of the pyramid field is quite delicate. It can be destroyed by sudden shaking or hitting a container with water. Therefore, it is better to drink water as soon as it is taken out of the pyramid. And under no circumstances should it be boiled, since boiling destroys the structure of the liquid crystals formed in the water under the influence of the pyramid’s field.

Raspberry ringing

God created the world from himself and created it in harmony. That is, in the inextricable connection of everything with each other and the proportionality of all component parts. Harmony is a divine law. Compliance with it is a necessary condition for participation in the divine. Man, according to Holy Scripture, is created in the image of God. This means that everything in it should be harmonious and beautiful. However, let's face it. Are our figures really that harmonious? We always want to fix them. We tighten our bellies with belts and lengthen our legs with heels. It is better to remain silent about odors emanating from the body. We pour liters of deodorants, colognes, and perfumes on ourselves. Maybe our head and brain, which allows us to think, makes us like God. Very doubtful, because our thoughts are sometimes disgusting. What else can be found in a person that would be divine and harmonious? There is something in a person that everyone knows is there, but no one really knows where it is. I'm talking about the soul. It is the soul of a person that is connected with God. It is beautiful and harmonious for all people. And although sometimes they say about some people that they are soulless, this is not so. They have simply lost touch with their soul, temporarily or permanently. Thanks to the soul, a person can feel the beautiful and harmonious, because like strives for like. Thanks to the soul, a person rejects what is disproportionate and ugly. The soul is not in favor of this, people say.

Singing and music have always accompanied people, from the moment they appeared as people until now. Why is music so necessary for people? Because its construction is based on harmony. Singing and music appeared due to the soul's need for beauty. Perhaps the first experiences of singing were reminiscent of the efforts of the heroes of Danelia’s film “Kin Dza Dza”, and the first piece of music was beating a rhythm with a stick on a dry block. Although, if we take the words of the “song” from this film a little more seriously, translate them into primitive language, take into account that the word “ku”, expressing respect, corresponds to the word “amen”, then the “song” will sound like a complaint of a primitive man to his God mothers to a difficult financial situation and too harsh a climate.

Music is the language of the soul. Through it you can contact the soul directly, bypassing reason and consciousness. Therefore, singing and music have been used in religious rituals and services since ancient times. Christianity was not left behind either. How else. The doctrine of the immortality of the soul, which primarily shows concern for its health, cannot do without a means of direct communication with the soul. However, special music and singing are used for church services. The priest even reads the prayers in chant. This is stipulated by special rules - the canon. In any language there are sublime words, there are everyday words and there are abusive ones. Likewise, in music there are sublime hymns, there are dance rhythms and there are styles that smack of blackness. Church music addresses the highest aspirations of the soul. She helps people open their souls so that a path is formed between it and consciousness. Along this path, harmony passes into consciousness. Consciousness, especially its hidden part - the subconscious, guides our everyday actions. In this way, all our actions can become beautiful over time.

Church music is church music, to be performed in church. Those few listeners who have heard the psalms performed both in a concert hall and in church say that there is no comparison. The church has such acoustics that the music pours down on you from above, as if coming from God. They're right about the acoustics. In temples, clay pots were specially walled into the walls, which create an after-sound, like an echo. But let’s try to figure out what exactly is pouring from above.

The energy field in the church building is similar in its properties to the field of a pyramid. The energies of the earth enter the dome from below, are reflected from its surface in the opposite direction, are modulated by the divine energies of the cosmos and return to the church premises. At the same time, the sound waves of the musical work spread throughout the church. The energies of the earth, modulated by the divine energies, in turn modulate the sound waves. Thereby greatly enhancing the impact of music on the human soul. This energy concentrate pours from under the dome of the church into the souls of the parishioners. One more condition is important here. The harmony of music must correspond to the harmony of divine energies. This condition is fulfilled by strict adherence to the rules of the church canon when composing and performing music. If a discrepancy arises, the soul will recognize the falsehood and will not open. You can't deceive your soul.

Another unique musical instrument is used in the church. These are bells. In Rus' there is passion, as they loved to listen to the ringing of bells. There is even an expression - raspberry ringing. This is said when the timbre of the bells is especially pleasant and evokes feelings of tenderness and pleasure in listeners. They especially loved the sound of the largest bells. Their bass, velvety ringing could be heard for many miles around. People said that the crimson ringing of a bell could be obtained by adding silver to molten bronze when making it. Of course it is. It is impossible to obtain a pleasant bell sound timbre without adding the required amount of silver. However, bells do not sound like that on earth. They acquire their true timbre only in the bell tower. Let's see how bell towers are arranged Orthodox churches. They are located in a separate extension like a tower. The bells are installed at the very top under the roof so that their chimes can be heard as far as possible throughout the surrounding area. The roof over the belfry usually has the shape of a pyramid or dome, the shape of which is determined by the golden ratio. The sound waves emanating from the bell are harmonic vibrations. During the ringing of the bells, information about the harmony of the Universe contained in the field of the pyramid and dome is superimposed on the sound harmonic vibrations emitted by the bells. This sound is perceived not so much by the ears as by the human soul and, as people say, sinks into the soul.

About plants

Until now, when we talked about energy-transforming forms, we meant that they were created by man. That the man came up with everything so cleverly. This is a big misconception. All these forms were and are used in the plant world long before the advent of man. Of course, a plant in the form of a tetrahedral pyramid is difficult to find. Plants do not like sharp angles. Natural shapes are round. Plants prefer shapes in the form of a cone, dome, column. Let's look at the trees around us. It is better to look at trees standing alone. Their geometric shapes appear more clearly.

The old oak tree has a large dome-shaped crown. Oak was highly respected by Russian writers and poets. Alexander Pushkin, when he was a lyceum student, loved to sit on the bench under it. Perhaps the influence of the energies of this tree helped awaken the poet’s talent. Leo Tolstoy in the novel “War and Peace” associates the old oak tree with a feeling of joy of life and belonging to humanity. He probably also walked under it more than once.

The spruce tree has a conical crown. Young fir trees are more reminiscent of a cone with corners, like the pyramid of life, and older spruce trees are more like a cone with corners, like A. Golod’s pyramid. Pay attention to the spruce branches. At the very top, the branches grow in a bunch and are directed upward. The lower branches first extend almost perpendicularly from the trunk, then smoothly bend downward, and the ends of the branches are parallel to the ground or slightly raised upward. The shape is very close to an exponential curve. By the way, the outlines of a spruce tree can be seen in a multi-story Chinese pagoda.

When Peter the Great introduced the New Year holiday in Rus', he chose spruce as a symbol. Why spruce and not pine is unclear. It can be assumed that the energy of spruce is better suited for this holiday. Remember that joyful and slightly solemn atmosphere that appears when a Christmas tree is brought into the house. How nice it is to decorate it. However, this is a completely different feeling of joy. It is very different from the feeling of joy that gripped Prince Bolkonsky at the sight of a green oak tree.

Since we're talking about decorating the Christmas tree, let's remember about Christmas tree decorations. We will consider them from the point of view of form. A peak is put on the very top. It has a sharp and long conical spire, and underneath it is a round or slightly flattened sphere. This is an antenna tuned to the golden ratio. A five-pointed star is also placed on the top of the tree. This is a symbol of life. The relationship between its rays corresponds to the proportion of the golden ratio. The most popular Christmas tree decorations are balls of various sizes and colors. The sphere is a selective filter. With its help, you can separate the waves that are reflected inside it even number once. The ratio of the diameter of the sphere to the wavelength that will be reflected inside the sphere along the trajectory of a regular decagon will be the golden ratio. That's how much harmony is hidden in Christmas tree decorations.

Probably each of us has been in the forest. It is especially pleasant to wander through the forest on a fine autumn day, when the trees pamper us with the amazing colors of their outfits. You walk through the forest - your soul is light, calm, a little sad, a little joyful. Breathing is free, step is light. Good!.. The forest attracts you. Although, most likely, it’s the other way around. We are the ones reaching for the forest. The forest has a special life-giving energy. Earlier we talked about tree crowns, now let's talk about trunks.

When you walk on a frequent path pine forest, tree branches are no longer conspicuous. Somewhere high above your head they intertwine with each other, forming an almost continuous canopy. Only smooth, round columns of trunks are visible, rising from the ground and going into the sky. A cylindrical column is also an energy-converting form. Only it interacts not with vertical energy flows, but with horizontal ones directed along the surface of the earth. The tree trunk is like a translucent cylindrical mirror. Part of the energy flow passes through it, part of the flow is retained inside the barrel, repeatedly reflected from the inner surface. Waves of different lengths inside the trunk will be reflected along different trajectories and, leaving the trunk, form quite clearly defined zones around it, in which the energy ratio is determined by the golden ratio. The fields of neighboring trees interact with each other, creating a life-giving field between the trunks that carries harmony. So animals and people are drawn to this field.

If two nearby trees of approximately equal thickness are located on a line running in the direction of the meridian or parallel, then the maximum field strengths are located on the line passing in the middle between the trunks and perpendicular to the straight line connecting the centers of the trunks. If you approach the trees along this line, then at first the field strength will slowly increase to a maximum. Then the field strength will quickly decrease and reach zero at the point between the trunks. After which the field strength will continue to decrease to a minimum and then slowly increase to its original value. There is a kind of “magnetization reversal” of the human energy field. If we take into account that in the sensations of psychics, a person’s lower energy centers are “negatively charged” and the upper centers are “positively charged,” then when a person passes between trees, first the lower energy centers will be stimulated, then the upper ones, or vice versa. It's good for your health. If the trees stand in two rows with approximately equal intervals, then on the line running in the middle between the rows of trees, a whole chain of zones will appear that harmonize the human field. Lay a path along this line and walk along this alley back and forth for your health.

Now it becomes clearer why colonnades and double colonnades become architectural elements of temples. Think of the Parthenon in the Acropolis of Athens or the Kazan Cathedral in St. Petersburg. Moreover, a pair or two pairs of columns must stand at the entrance to the cathedral. Passing between them, the human energy field is strongly influenced by oppositely directed flows of harmonizing energies. At the same time, in the human energy field, the ratio of energies is brought, if possible, into accordance with harmony. Translated into ordinary language this means that a person throws off the burden of everyday worries and anxieties and, freed from the bustle of the world, can begin to communicate with God.

Now let's turn to the bulb, that is, to the plant called onion. Let's take a look at its shape. At the bottom of the plant there is a spheroid energy storage device; an exponential funnel is attached to it - an energy converter. The leaves grow higher - antennas, which have a conical shape and an acute angle at the apex. That is, they are energy concentrators and intermediate converters. Arranging the leaves in a bunch protects the plant from energy overload. A similar picture emerges if we look at garlic. These plants are turned towards the Cosmos and are ideally suited for collecting, transforming and accumulating divine energy. When I asked my youngest son, “Why do people eat garlic and onions?” He replied: “So as not to get sick?” It turns out that we eat onions and garlic for the sake of the divine energy accumulated by these plants. Information about this energy is primarily concentrated in the liquid crystals of onion and garlic juice water. The impact of this information on the body will occur through thin bodies person. And, phytoncides are already a product of processing divine energy into matter.

Are there energy antipodes of garlic and onion in nature? Of course there is, and everyone is familiar with these plants. These are, first of all, beets, radishes, turnips, radishes. The narrow end of the exponential funnel turns these plants towards the center of the Earth. In the water of the juice of these plants, the energies of the Earth are concentrated, aimed at strengthening the human physical body. By the way, radishes and garlic have been eaten by people for a very long time. There is a mention of the Egyptians eating these plants in huge quantities in the records of scribes dating back to the time of the construction of the Cheops pyramid. The attentive reader will exclaim: “Oh, a carrot?” The carrot is also turned towards the center of the Earth and contains the energies of the Earth. The shape of its root crop is conical. From a physics point of view, the range of waves transmitted through a conical horn is narrower than that of an exponential horn. That is, the cone is more selective in the energies passed through it. Therefore, cone-shaped root vegetables will have narrower, but more pronounced properties. For example, carrots, as everyone knows, contain vitamin A and are good for vision. Root vegetables in the form of an exponential mouthpiece will have a wider range of effects on the body, that is, they carry general strengthening properties.

Now a little about apples. If you cut a ripe apple with a knife in the middle, so that the stem of the fruit is on the side, you will see that the seeds are arranged in a five-rayed star. Now look carefully again at the cut-off part of the apple from the stem side. You can see that a pentagon with strongly rounded vertices is visible. The apple contains the energies of life. They help accelerate life processes occurring in the human body.

Cucumbers are interesting because so far nothing particularly useful for the human body has been found in them. However, these vegetables have been used by humans as food for centuries, and with great pleasure. What's the secret? Anyone who has held a real ground cucumber in their hands knows that it has a triangular shape. It looks like an equilateral triangle with strongly rounded vertices. This shape allows you to select waves in the flow of energy that are reflected inside the cucumber along the trajectory of a regular triangle. Moreover, four such triangles are formed. An equilateral triangle is a symbol of the Holy Trinity. The energies concentrated in the cucumber are holy, divine energies. It is not surprising that nothing useful was found in the cucumber on a material level. It can't be there. All the information necessary for human health is contained in the liquid crystals of cucumber juice water. It is necessary to nourish the subtle energy shells of a person. Truly holy water. And there is more of it in cucumber than in other vegetables. So eat cucumbers and increase your spirituality at the same time.

In connection with the above, I would like to talk about juices. It turns out that the basic information necessary for human health is found in the water contained in the sap of plants. Therefore, freshly squeezed juices are an order of magnitude healthier for the body than canned juices, although with added vitamins. It is very necessary for normal physical development to consume vegetable juices: beetroot, carrot, radish juice. We, northerners, simply have nothing to replace these plants that carry the energies of the Earth. However, we must immediately warn the hasty reader. Our city-tormented bodies need to consume freshly squeezed juices little by little and in diluted form. Remember how you gave vegetable juices to your little children when they didn’t really know how to drink? Be even more careful with radish juice. In Rus' they ate radishes, diluting them with kvass. And, just in case, read books about juice treatment. In conclusion, I can offer a recipe for a radish dish that my wife’s late grandmother prepared.

Take a couple of boiled potatoes and mash them in a bowl. Rub the peeled small raw radish into thin strips on a fine grater. Finely chop some raw onions. Place all this in a bowl, add a little salt, pour in bread kvass, preferably not sweet, and mix. Before eating, add half a spoon of sour cream to the plate. The food is ready, bon appetit.

Geometry in the life of cucumbers

Those readers who have reached this point are probably wondering how they can use the knowledge gained from the brochure. I'll try to help. Since I am a big fan of the country lifestyle, we will choose the topic of greenhouses for growing cucumbers.

In the last chapter, we talked about how plants use the energies of the Earth for their life activities. If plants are fed by the energies of the Earth, then they must contain a mechanism that allows them to adjust the energy flows so that they are directed in a manner favorable to the plants. Such a mechanism is the shape of the roots, stems, leaves, flowers and fruits of plants. The shape of each plant organ is selected in such a way that the energies of the Earth help fulfill its tasks.

Let's look at this in more detail using the example of a cucumber. First of all, gardeners are interested in fruits. This means that our main emphasis will be on determining the conditions that help to form greens. In the last chapter it was said that a cucumber is triangular in cross section. To be more precise, the cross-section of green grass is a figure formed by three circles, the centers of which are located at the vertices of an equilateral triangle. This figure is called a trefoil. If you now close the depressions between the leaves of the trefoil with straight lines, you will get the shape of a cross section of a green leaf. Let us now direct parallel rays of energy to our figure. They will pass inside the figure, be reflected from its inner surface and form four regular triangles. The shape of the greenery is chosen in such a way that the reflected rays of energy are directed inside it at an angle of 60 degrees to each other. This is the “favorite” corner of the greenery. The seeds in the greens are located in the direction of the heights of small triangles and form an angle of 120 degrees with each other.

In a greenhouse, cucumber stems are usually tied with vertically stretched twine. Therefore, the greens do not lie on the ground, as happens when the plant is placed freely in an open garden bed, but hang on stems, oriented with the longitudinal axis of the greens almost perpendicular to the surface of the earth. Under these conditions, the green plant will form its “favorite” corner due to energy flows directed parallel to the surface of the earth. At the same time, the green man, due to the peculiarities of the reflection of energies in him, can use only one of the horizontal flows. Another thread will not be able to create “favorite” corners in it. Our task is to build a greenhouse of a certain shape, which will allow us to redirect the energy flows so that they correspond to the direction of the rays in the greenery. To do this, you can build a hexagonal pyramid of life, which we talked about in the first chapters of the brochure, but we will try to modify the usual rectangular greenhouse with a gable roof. Compared to a pyramid, a conventional greenhouse makes better use of the internal space.

We believe that the sides of our greenhouse are oriented exactly to the cardinal points. You can work with horizontal energy flows by changing the angle between the walls of the greenhouse. We only need to change one wall. Let's remove the northern wall of the greenhouse and replace it with two smaller walls, forming an angle of 120 degrees with each other. Then the flow of energies entering the greenhouse through the southern wall will be reflected inside from the northern wall. In this case, the reflected beam will be rotated at an angle of 60 degrees relative to the input one. Subsequently, reflecting from other walls, these rays will fill the entire space of the greenhouse. This direction of energies in the greenhouse will allow the greenery to be energized from six directions favorable to it, instead of two.

There are two issues to consider here. The first question relates to the material from which the greenhouse walls are made. This is usually polyethylene film. Despite its many advantages for gardeners, this material has a drawback. It does not transmit energies well through itself, so to speak, in the “biological” range. This is the range of energies that are emitted by living organisms and plants. This has been repeatedly confirmed by psychics. Therefore, it is better to make the southern wall of the greenhouse glass. Glass, compared to polyethylene, transmits a wider range of energies in this range. You can make the film on the south wall removable and roll it up during the daytime.

The second question is related to the exact orientation of the greenhouse to the cardinal points. This is done using a compass. But you definitely need to know the magnetic declination in your area. For the area surrounding St. Petersburg, the magnetic declination will be 8.5 degrees towards the west. Therefore, the axis of the greenhouse, parallel to the meridian, must be rotated clockwise at an angle of 8.5 degrees from the north-south line on the compass. Then the axis of the greenhouse will be directed exactly to the geographic poles of the Earth.

However, greens are green, but you still need to take care of the whole plant. Let's take a closer look at the flowers and leaves. Cucumber flowers are shaped like a five-rayed star, and the well-developed leaves have five lobes. This means their “favorite” angle will be connected in a certain way with the pentagon. We will not open America. Let's borrow this angle from the Pyramid of Khafre. It is equal to 53.13 degrees. This angle is notable for the fact that it is formed between the rays reflected inside the pentagondodecahedron - a three-dimensional figure made up of 12 regular pentagons. Since energy flows parallel to the surface of the earth are already involved in our greenhouse, we will work with energy flows coming out of the earth. We will maintain the direction of the primary flow, and the flows reflected from the roof will have to return to the surface of the earth at an angle of 53.13 degrees. To do this, you need to rotate the roof surface so that its slope angle is 18.435 degrees. The roof ridge can be directed either along the meridian or along the parallel. If the reader is confused by such a high accuracy of constructing an angle, then this angle is constructed in an elementary way. The tangent of this angle is 1/3. This means that half the length of the roof span will be three times the height of the ridge. If, for example, the scope of the greenhouse slopes is 200 centimeters, then the height of the ridge above the walls will be 33.3 centimeters. Just make sure that the edges of the roof slopes are at the same horizontal level.

It is also better to adjust the height of the greenhouse walls so that the rays reflected from the roof cover the entire area of ​​the greenhouse. You can choose the height of the walls such that the rays will fall mainly on the beds, which are usually located near the walls of the greenhouse. In this case, the amount of energy falling on the beds will double due to partial reflection from the walls. The height of the greenhouse walls is calculated from the surface of the beds. Therefore, the actual height of the walls will be greater than the height of the beds. To better imagine how the reflected rays will pass through the greenhouse, you can assemble their slats into a right triangle with an angle of 53.13 degrees. The aspect ratio of such a triangle is 3:4:5. The angle of 53.13 degrees is located opposite the side equal to 4. Attach the triangle to the wall of the greenhouse with this side, and the direction of the rays will coincide with the hypotenuse of the triangle, that is, with the side opposite the right angle. As for the 120 degree angle, it is constructed using a right triangle with angles of 30 and 60 degrees. The aspect ratio of such a triangle is 1:1.732:2.

Dear gardeners and gardeners, this brochure is the result of my long thoughts about the living conditions of humans, animals and plants on Earth. All life on our planet bathes in the ocean of energies that bring life, which the Earth generously gives to us - its children. Our task is to use this gift correctly. The Egyptians and Greeks knew how to control these energies. Until now, the secrets of these energies are kept secret by representatives of the clergy. They build churches and temples to solve their problems with the help of these energies.

Now it’s our turn to all learn how to use them. People who work on the land, who have held tender shoots in their hands, who know how fragile life is, will be able to use this knowledge for good. Try, try to control these energies of the Earth. If you have brilliant results, write to us and we will rejoice together. If it doesn’t work, write, we’ll think together about how to fix it. My address: St. Petersburg, 197372, PO Box 105.

Goodbye.

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Preface 1

Number one 2

Number two 3

Number three 4

Number four 7

Number five 10

Number six 17

Number seven 18

Egyptian pyramids 20

Life range 23

About scaling issues 25

Why do we need pyramids 26

How pyramids “work” 28

Pyramids, cones, domes 30

Kurgany 33

What houses do we live in 35

How pyramids can help us 37

Raspberry ringing 39 Gold is defined as follows: H = 4xS (2l), where H is the height, and S is the side of the base. 5 Golden section determined...

A closed pyramid can function even with minimal density, but its potential is also determined by density. The rest of the space of the pyramids is energetically minimal, and, accordingly, the return is minimal. At a height of 1/3 in the center of the pyramid there is a place corresponding to the Chamber of the King of the Great Pyramid of Cheops, which is the point of greatest concentration of energy.

The pyramid will help you achieve dizzying success

Before planting, the seeds are scattered in a pyramid in rows directed from North to South and left inside the pyramid for at least two weeks.

How to design and build a PYRAMID ACCORDING to the GOLDEN RATIO.

What is it? PYRAMID built in proportions of the golden ratio? This is a pyramid in which spheres are inscribed, standing on top of each other, the ratio of the diameters of which (larger to smaller) is equal to 1.61, that is, related to each other in the proportions of the GOLDEN SECTION, you can read what this is in more detail. In order for the pyramid to look proportional to its size on the site, it had to be about 5-6 meters high. Having calculated the base at an approximate given height, it turned out that the side of the base of the pyramid turned out to be equal to 2 meters 60 cm, and the height of the pyramid was equal to 5 meters 24 centimeters, under Such a foundation was poured with a concrete foundation. The frame of the pyramid was assembled from planed bars 6x6 cm and 6 meters long, since the length of the pyramid’s edge was 5 meters 40 centimeters. The bars were glued together with Titebond glue with corners and grooves cut. The stiffening lintels were designed so that the door could be cut in and also so that the joints would not overlap one another; you can see the lintel calculations and drawings in the appendices below.

How to make a pyramid? — Forum

When the frame was ready and installed, sheets of cellular polycarbonate cut out according to a template were glued to it with silicone, which can be seen below.

The pyramid should be oriented from NORTH to SOUTH and not contain metal, which significantly complicated the task. I had to glue the frame of the pyramid on wooden pins, and glue the transparent cellular polycarbonate with colorless silicone, as well as the guides for the sliding door. In the foundation for the pyramid, cast from concrete, it was necessary to use metal, but I hope this did not greatly affect its properties; I considered that the crystalline form of the pyramid itself, accumulating and distributing energy, is located on top within its shape. It’s already the third year since the pyramid was built, and besides the fact that there is always a wonderful harvest of sweet peppers and melons and everything is growing wonderfully around, not only our life, but also the life of our gardening community has become much better, because they say that the radius of action of a pyramid of this size is approximately one and a half kilometers.

Pyramid was oriented in the direction from NORTH to SOUTH, it must be taken into account that the compass in a populated area can greatly lie, so the POLAR STAR was taken as the NORTH point and now if you stand in front of the pyramid facing the NORTH, looking perpendicular to its edge, the polar star hangs exactly above its top is VERY BEAUTIFUL! A door was made from the EAST to enter the pyramid, because it was intended not only as a spiritual center for meditation, but also as a greenhouse for experiments and growing exotic plants. The door was made of polycarbonate, sliding on runners from guides, it turned out to be a very elegant solution. A circle was drawn around the pyramid, with a diameter of 4 meters 60 cm, so that there was 1 meter to the edge, all this can be seen in the diagram, and along this circle, which became the ZODIACAL, we planted garden plants corresponding to each zodiac sign, now each lives in its place and grows in accordance with its purpose. And inside the pyramid we grow sweet melons and wonderful sweet peppers of various colors.

How to construct the development of a pyramid in the proportions of the Golden Section? Figure 1 shows a cross-section of such a pyramid and S1/S2=0.62. In this case, it is better to build a pyramid on your summer cottage and use it to restore health. His observations showed that by deviating from this golden proportion, the pyramid did not produce the expected results. This will be the length of the side of the base of the pyramid.

It should be noted that some researchers believe that the trihedral pyramid is superior in efficiency to the tetrahedral one. A pyramid is a polyhedron, the base of which is a polygon, and the side faces are triangles that have a common size. In addition to the height, the characteristics of the pyramid are the length of the base and the height of the side face (apothem) of the pyramid. This ratio corresponds to the proportion of the golden section, or harmonious division.

The pyramid should be located away from various metal objects - heating radiators, water supply, sewerage, various designs, containers, etc., – and electric motors.

And then there will be a square at the base and the pyramid will stand, touching all the corners of the flat surface

According to Gabriel Silva, the small pyramid may not function if it is located in a geopathogenic zone, even the smallest one. In addition, it is necessary to fix the above-mentioned area so that the pyramid does not re-install on it. In addition, to achieve a good effect, a plastic pyramid requires a large amount of material due to its lightness.

The pyramid must be built without a single nail and without the use of other metals, which, with their field, introduce distortions into the field of the pyramidal space

But such a pyramid loses its dielectric properties, not to mention where to get aluminum that meets the requirements. The energy of this space must be pure, without any distortion, then healing properties the pyramids will be maximal.

Thus, multiplying the given height of the pyramid by 1.6 or 1.618, we get the length of its base

Ferromagnetic or diamagnetic materials should NEVER be used to make pyramids. When choosing material for building a pyramid, it is very important to take into account that such an important characteristic as the density of the pyramid depends on the mass of the pyramid. The density of a pyramid is its mass (weight) per unit volume.

A closed pyramid can function even with minimal density, but its potential is also determined by density. The rest of the space of the pyramids is energetically minimal, and accordingly the return is minimal.

How to build a pyramid in the country

At a height of 1/3 in the center of the pyramid there is a place corresponding to the Chamber of the King of the Great Pyramid of Cheops, which is the point of greatest concentration of energy. Before planting, the seeds are scattered in a pyramid in rows directed from North to South and left inside the pyramid for at least two weeks.

Plant essences and extracts, homeopathic medicines are processed with pyramid energy for a maximum of 4 hours, as they must preserve the so-called “subtle energy”. The treatment of these substances can be carried out every other day for 4 hours (if on the previous day the load on the pyramid was minimal).

The pyramid can be closed or framed. If you deviate from these proportions, the pyramid effect worsens. In homes built with reinforced concrete structures, pyramids may not be as effective. I would want such an amulet, even if it is made in the shape of a pyramid, especially since there are many other stones and minerals with less controversial properties.

Institute of the Golden Section - Discussions

Based on the proposed method of constructing the Cheops pyramid, the true values ​​of its characteristic dimensions were obtained through integer values ​​of ancient units of measurement.

In recent years, interest in the theory of Fibonacci numbers and the golden ratio has increased significantly in mathematics, computer science and cybernetics. Work is currently underway in this direction basic research. Scientists from Russia, Ukraine and Belarus made a significant contribution to the development of the theory of Fibonacci numbers: they introduced the concept of the golden wurf and the wurf sequence as fundamentally new invariants of biological objects with a three-member structure (shoulder-forearm-hand, thigh-shin-foot, etc.) , a generalization of the problem of the golden section was carried out and on this basis the law of structural harmony of systems was formulated, an algorithmic theory of measurement and Fibonacci number systems was created as new information foundations of computing and measuring technology, a theory of hyperbolic functions of Fibonacci and Lucas was developed, which made it possible to create a geometric theory of phyllotaxis on this basis and formulate the botanical law of transformation of spiral biosymmetries. IN Lately the golden ratio was discovered in the cardiac structures of mammals, in the structure of chloroplasts higher plants, in the rhythms of the brain. Discovered chemical compounds, organized by Fibonacci. Based on the golden section, the principles of age-related dentistry have been developed. The golden ratio is present in the structure of DNA, the Earth, the Universe...

This series of examples can be continued. The golden ratio begins to play a significant role in modern physics: the Israeli scientist Shekhtman discovered quasicrystals with 5-fold (pentagonal) symmetry, which contradicts the laws of classical crystallography; The work of the Polish scientist Jan Grzedzielski, working in the field of the theory of self-organizing systems, allowed us to take a fresh look at golden ratio as a proportion of thermodynamic equilibrium in self-organizing systems.

This indicates that all harmoniously constructed objects obey the principle of the Golden Proportion and the human eye immediately, without in-depth analysis of the structure of the object, sees its beauty. Analysis shows that as soon as we see an object as beautiful and harmonious, this means that its structure obeys the principle of the Golden Proportion.

The golden ratio is the so-called division of a segment in extreme and average ratios, in which the segments obtained after division satisfy the equality:

It has been established that the value of this ratio is equal to Ф = . The Greek letter F (PHI number), which denotes the value of the Golden Ratio, is the first letter in the name of the famous Greek sculptor Phidias, who widely used the Golden Ratio in his sculptural works.

The following method of constructing the Golden Ratio using a compass and ruler is also known from Euclid’s Elements. Let us have a double square - a rectangle with an aspect ratio of 2: 1 (see Fig. 1). I. Shmelev gave it the name two-adjacent square.

The indicated square is already built on the principles of the Golden Proportion, since the ratio of the sum of the values ​​of the diagonal and the smaller side of a right triangle to the value of the larger side of this triangle is exactly equal to the indicated value of 1.618:

Let's consider whether the Golden Ratio is present in one of the wonders of the world - the Cheops pyramid. It is known that proportions based on the golden section are distinguished by exceptionally high aesthetic qualities and determine the highest proportionality between the whole and its parts. This means that all ancient buildings (palaces, temples, pyramids) contain elements of the harmony of the golden ratio.

A number of works are devoted to this topic, which claim that the proportions of the golden section were laid down in the Cheops pyramid. The hypothesis that the proportions of the pyramid are related to the ratio of the golden section was put forward by G. Reber back in 1855, especially since this hypothesis is confirmed by the well-known testimony of Herodotus.

The dimensions of the pyramid are estimated differently by different researchers. Thus, the height of the pyramid, depending on the sources, ranges from 146.6 to 148.2 m. The reason for these discrepancies is that the pyramid is truncated. The upper part of the pyramid has a platform of 10x10 m, and a century ago it was 6x6 m in size. Obviously, the top was dismantled, and it does not correspond to the original one. Now its height from base to top is 137.3 m, and the sides of the base are 230.4 m. It is believed that before the loss of the cladding, the size of the side was 232.4 m.

The pyramid has three chambers inside: the first chamber is carved into the rock at a depth of 30 m below the base and not exactly in the middle; the second is located in the core of the pyramid exactly below the apex at a height of approximately 20 m above the base, and the third chamber is located at a height of 42.3 m above the base, slightly south of the axis of the pyramid (see Fig. 2).

At the base of the Great Pyramid of Cheops is a rock approximately 8.2 meters high. The perimeter of the Pyramid, located on a granite surface, is perfectly aligned and is a perfect square.

The original entrance is located on the north side at a height of 25 meters above the base. A narrow tunnel leads down at an angle of 26031′ to the lower chamber. At some distance from the entrance, another tunnel begins, leading to the upper chamber at the same angle as the first. Next, the tunnel goes into the Grand Gallery, 47 meters long (see Fig. 2).

The pyramids of Egypt, built almost 3000 BC, remain mysterious today both in terms of the technology of their construction and in the knowledge possessed by the builders of the pyramids. One of the biggest mysteries in the construction of pyramids is the methods of calculation of structures by the ancient architects, according to which the design and construction of objects in Ancient Egypt were carried out. Finding these dimensions is complicated by the fact that the results of measuring the parameters of ancient objects with a standard meter always turn out to be fractional. And this is despite the general belief that the ancient Egyptians were not familiar with fractions. And until the harmony of the proportional relationships of its characteristic dimensions is found, it is impossible to even come close to unraveling the secrets of the pyramids.

Let's consider how the Cheops pyramid agrees with the Golden Ratio. The golden irrational number F was known back in Ancient Egypt. Studying the geometry of the figures carved on the panels, architect I.Sh. Shevelev drew attention to the fact that on one of the panels the architect holds in his hands wands that correlate with each other as 1:, and expressed an intuitive assumption that this relationship testifies to the knowledge of the ancient Egyptian architect Hesi-Ra of the laws of the golden ratio. Architect I.P. Shmelev conducted a thorough study of the geometric proportionality of figures and the compositional structure of panels and, using interconnected numerical material, showed that the priests of Ancient Egypt, long before the school of Pythagoras, owned the theory of harmony associated with golden proportions.

The angle of inclination of the diagonal of a double square is equal to

(3)

The obtained value practically coincides with the inclination angle of the Bolshoi Gallery tunnel of 26031′. It would be easy to align the diagonal of the double square with the Great Gallery, but it does not fit well into the interior of the pyramid if placed on the base of the Pyramid.

The picture changes dramatically if we take not the level of the base, but the level of the lower chamber as the base of the pyramid (see Fig. 3). The double square ABCD, combined with the level of the lower chamber, seems to harmonize the pyramid: the lower chamber becomes connected to the main pyramid; The Grand Gallery and the tunnel leading to it run exactly along the diagonal of the double square; the tunnel running from the entrance to the pyramid to the lower chamber coincides with the diagonal of the small double square DEFG, equal to a quarter of the initial double square ABCD; the upper chamber is located at the intersection of the diagonals of the double square.

Figure 3 – Sectional diagram of the combination of a double square and the Cheops pyramid

Only the middle chamber remains unconnected. To do this, we split the small double square DEFG in half and draw a circle from point J, the diameter of which is equal to the smaller side of the small double square DEFG. The intersection of this circle with the diagonal of the original double square gives us the point of origin of the Great Gallery, and the intersection of a horizontal line drawn from this point with the vertical axis of the pyramid exactly coincides with the middle chamber (see Fig. 4).

It remains unclear from what constructions we obtain the top K of the pyramid. The angle of inclination of the faces of the Cheops pyramid varies from 51050′ to 51052′ by various authors. There are various approaches to calculating the true angle of inclination of the faces of the pyramid.

It is believed that the angle of inclination of the faces of the pyramid is estimated through an integer ratio of 14: 11, which is formed with good accuracy by the height and half of the base. However, as the author rightly believes, during construction the dimensions were specified in whole numbers, and not in irrational ratios of fractions.

Nowadays, it is discovered that all processes associated with the life of living organisms are, to one degree or another, connected with the same golden numbers, which leads to an increasingly intensive study of these connections, but, oddly enough, not the properties and geometry of the numbers themselves . One of the elements of these properties is the formation of a golden right triangle. Siliotti A. also suggests taking the most perfect, golden triangle as a basis (see Fig. 5). It is constructed as follows. Let there be a right triangle GDK. From the vertex of the right angle G we lower a perpendicular to the hypotenuse DK. It divides the triangle into two - upper and lower. In the upper triangle, we again lower the perpendicular from the vertex of the right angle R to the hypotenuse GK. She will again divide this triangle into two parts. All resulting triangles are similar to each other, and triangles FRK and GDR are equal to each other.

Point R divides the hypotenuse DK in the mean and extreme ratio, that is, in the Golden Ratio. The major leg GK of the Golden Triangle is the mean proportional between its hypotenuse and the minor leg. The presence of such a proportion between the sides can serve as another definition of the Golden Triangle, called in the pyramidological literature Kepler's triangle or Price's triangle, i.e.

When this relationship is satisfied, the area of ​​the pyramid's face is equal to the square of its height. It was this equality of areas that Herodotus determined the proportions of the Cheops pyramid.

In the commentary that D.D. Mordukhai-Boltovsky accompanies the discussion of the above testimony of Herodotus, it is said: if we consider a triangle, the hypotenuse of which is the apothem of the side face, the vertical leg is the height of the pyramid, and the horizontal leg is half the side of the base, then it is easy to see that the apothem the same is related to height as height is to half the base; here lies the germ of the principle of the golden section, or the division of a segment in extreme and mean ratios, which must have been known to the Egyptians around 450 BC.

Professor A.P. Stakhov in his work also substantiated the calculation of the height of the pyramid through the golden triangle, in which the ratio of the sides corresponds to the proportion F::1, i.e. the ratio of the sides of a right triangle GDK is = 1.272. In this case, the angle of inclination of the face is 51050′, which is in good agreement with the results of numerous measurements.

If we have decided on the angle of inclination of the faces, then what should we take as the starting point: the height of the pyramid or the length of the base? When measuring a pyramid, the side of its base was first measured, and then the angle of inclination of the face was determined using a theodolite. Using these data, the height of the pyramid was calculated. Therefore, the accuracy of measuring the side of the base could be on the order of 1 cm, and the accuracy of determining its height is much lower. Based on this, it is logical to take the side of the base of the pyramid as a basis.

Naturally, we should be interested in the true size of the length of the base, which existed before the cladding of the walls of the pyramid was removed. It is believed that the length of the side of the base of the pyramid is 232.4 m. Knowing this size, as well as the angle of inclination of the faces, it is not difficult to calculate all the other dimensions of the pyramid. However, we get fractional numbers, which were unlikely to be laid as the basis of the Great Pyramid. According to Chernyav A.F. during the construction of ancient monuments of Rus' and Egypt, each size contained a whole number of fathoms or their elements. In this case, the parameters of objects measured in whole numbers always turn out to be fractional when measured with a standard meter.

To determine the integer values ​​of the characteristic dimensions of the Cheops pyramid, it is necessary to know what system of measures the Egyptians used when building the pyramid. Most researchers refer to the book by N.A. Vasyutinsky, in which he considers the dimensions of the pyramid through the system of measures adopted in Ancient Egypt, namely through the royal cubit, equal to 0.466 m. In this case, the length of the base of the pyramid approximately corresponds to 500 cubits. But the above reasoning shows that the base of the pyramid is an intermediate value, and its true size is at the level of the lower chamber. In this case, it is necessary to look for another system of measures.

The founder of the new Russian mechanics, academician of the International Academy of Informatization at the UN A. Chernyaev believes that in church construction the ancient system of measures was preserved, which was also used in the construction of the pyramids. He, based on the works of A.A. Piletsky, introduces the concept of All-Dimensions, using the system of ancient fathoms. The author justifies the multiple of all fathoms to the golden number Ф, and shows that all the parameters of the pyramids (height, lateral side, diagonal of the base, lateral edge, apothem) are multiples of an integer number of different fathoms, remaining fractional in the meter measurement.

However, in the same work he himself says that fathoms do not have real lengths. Fathoms are not a measuring instrument and therefore do not themselves have a length. That is, fathoms do not have metricity, but are only a tool of measurement, a tool of proportionation.

Many researchers believe that there are ancient measures of length, the values ​​of which should be correlated with the size of the Earth. The English researcher Professor Tom put forward the idea of ​​​​the existence of a standard unit of measurement adopted in the ancient world. He called it the megalithic yard, equal to 2.72 feet or 0.829 m. He obtained this value based on numerous measurements of the characteristic dimensions of ancient structures that date back to 4700 - 3700 BC. on the Iberian Peninsula and the British Isles. According to the author, somewhere between 3200 – 3100 BC. Dramatic climate change has occurred everywhere, with serious consequences for Europe and the entire world. It has been established that around 3000 BC. there was a sudden climate change. Before this date, Egypt and North Africa in general had a much wetter climate than today.

That is, there was a clear violation of the world climate regime. It marked the end of the most persistent warm climate since the Ice Age, called the Atlantic Climate Period. This same period is considered the beginning of dynastic Egypt, marked by the sudden flowering of complex cosmogony, writing, and exquisite visual arts. Those. The builders of ancient megaliths moved to different parts of the Earth, including Ancient Egypt. In this case, it can be assumed that the megalithic yard remained the characteristic unit of measurement of the ancient Egyptians used in the construction of the pyramids.

Therefore, given the known dimensions of the Cheops pyramid, we will reduce them to integer values ​​of dimensions, taken in megalithic yards (m.i.). Then the size of the true base of the pyramid will be 336 m., which corresponds to 278.544 m. From here we can obtain the characteristic dimensions of the Cheops pyramid (see Fig. 6).

In Fig. Figure 6 shows the main dimensions of the Cheops pyramid in megalithic yards, and the diagram according to which the ancient Egyptians built this pyramid is presented in Fig. 4.

Figure 6 – Dimensions of the Cheops pyramid

(dimensions are given in megalithic yards)

As a result, we obtained the main dimensions of the Cheops pyramid through the Golden Ratio using ancient measures of length - megalithic yards (m.i.). At the same time, the height of the pyramid is 212 meters, which corresponds to 175.748 m, and the height of the ground part is 177 meters. or 146.733 m, which is in good agreement with known data. Then the length of the base of the ground part of the pyramid is 280 meters. or 232.12 m, which also agrees with the known dimensions of the pyramid.

Thus, the height of the Cheops pyramid increased by 30 m and became equal to 175.7 m. Based on the approach proposed by the author, the heights of all known pyramids (Egyptian and South American) must be calculated not from the surface of the earth, but from the base of the lower chambers.

Literature

Stakhov A., Sluchenkova A., Shcherbakov I. Da Vinci code and Fibonacci series. – St. Petersburg: Peter, 2005. – 320 p.

Stakhov A.P. Under the sign of the Golden Ratio: Confession of the son of a student battalion. Chapter 7. Mathematics of Harmony. 7.2. International seminar Golden section and problems of harmony of systems // Academy of Trinitarianism, M., El. No. 77-6567, publ. 14169, 2007.

Handbook of Elementary Mathematics.

How to make a healing pyramid

Geometry, trigonometry, vector algebra. P/r P.F. Filchikova. – K.: Naukova Dumka, 1967 – 442 p.

Babanin V. The mystery of the geometry of pyramids in the Egyptian triangle and in the golden ratio. URL=http://www.shaping.ru/mku/babanin03.asp

Pyramid of Cheops - characteristic dimensions. URL=http://www.board74.ru/articles/geometry/heops. html

Another hypothesis about the size and proportions of the Cheops pyramid. URL=http://www.egyptportal.ru/content/view/131/26/

Siliotti A. Egypt. Pyramids. Atlas of wonders of the world. – M., BMM JSC, 1999.

Zamarovsky V. The greatness of the pyramid. – K.: Veselka, 1988. – 373 p.

Vasyutinsky N.A. Golden ratio. – M., St. Petersburg: DILYA, 2006 – 367 p.

Furlong D. Stonehenge and the pyramids of Egypt. Keys to the Temple of Life. – M.:VECHE, 1999. – 400 p.

Shmelev I.P. Architect of the Pharaoh. Art of Russia. - St. Petersburg, 1993.

Shchetnikov A.I. Golden ratio, square roots and the proportions of the pyramids at Giza. URL= http://www.nsu.ru/dassics/Pythagoras/Pyramis.pdf

Gold of heavenly account (conversation with Chernyaev A.F.) – Science and Religion. No. 7-8. – URL=http://kladina.narod.ru/chernjaev2/chernjaev2.htm.

Chernyaev A.F. Gold Ancient Rus'. – M. 1998. URL=http://kladina.narod.ru /chernjaev/chernjaev.htm.

S.Yakushko. The determination of volume of pyramid of Kheops through a gold section.

On the grounds of the offered way of the building of the pyramid of Kheops are received true importances its typical sizes through integer of the value of the ancient units of the measurement.

Published: Scientific vision: A modern picture of the world: nature, marriage, people: a collection of scientific works / Sovereign Great Initial Mortgage of the Ukrainian Academy of Banking Certificate of the National Bank of Ukraine. – Sumi: DVNZ UABS NBU, 2008. – 320 p.

Yakushko S I, Determination of the characteristic dimensions of the Cheops pyramid through the golden ratio // Academy of Trinitarianism, M., pub. 14858, 07.22.2008

How to make a pyramid?

Geometric dimensions of the Egyptian pyramids.
Golden ratio and proportions of the human body.

The heptagonal geometric network of lines is a universal spatial figure, which during the development of human civilization was used to measure proportional relationships and create objects in which people sought to fix the principles of world harmony. Or we can say that people sought to record or encrypt knowledge about the surrounding world in the created objects of human culture, for which they used the proportional relationships of the heptagon, which, among other regular polygons, is the most significant figure expressing the proportions of the human body.
Among the many objects of world culture, the most significant monument of human knowledge are the Egyptian pyramids, and in particular the pyramid of Pharaoh Cheops or Khufu.
I cannot give a detailed analysis of all the Egyptian pyramids, and therefore I give a description only of the Cheops pyramid, which is the most significant. But the analysis of the geometric dimensions and proportions of the remaining pyramids of ancient Egypt can be done similarly with the Cheops pyramid.
And also I cannot claim that the Great Pyramids of Egypt were built according to the geometric proportions of the human body and the geometry of the heptagon, that is, I cannot claim that the builders encrypted the ideal human figure and the shape of the heptagon in the architecture of the Egyptian pyramidal structures, but such proportions are obvious.
According to various sources of information in the research of Egyptologists, different measurements of the Cheops pyramid are known, but the most reliable and obvious can be considered the studies according to which the main dimensions of the Cheops pyramid are: the length of the side of the base is 500 cubits, the height is 318 cubits, the angle of inclination of the side faces is 51 degrees 50 minutes.
An Egyptian cubit is approximately 466 millimeters, which is approximately equal to the length from the elbow to the base of the fingers, if a person’s height is 176 centimeters and corresponds to the “Russian fathom”.
According to the listed dimensions, the main proportions in the Cheops pyramid lie in the ratio of the lines of the triangle, which is formed by the height of OR, half the length of the base PR and the apothem (length of the side face) OR, as shown in the figure.

Many Egyptologists and researchers of the Cheops pyramid suggest that the builders of ancient Egypt knew the numerical value of the golden ratio and the number “pi”. And also Egyptologists suggest that these golden numbers were key in the architectural design of the Egyptian pyramids, but in reality knowledge of these numbers is not necessary, since to build the pyramids it is enough to know the proportions of the heptagon and use the ratios of lines that exist in the geometric figure of the heptagon, as shown in the following figure.

The AEK triangle in the figure is an approximate silhouette of the side faces of the Cheops pyramid. The shown silhouette of the side faces is approximate, since the angle of the ESA heptagon with the vertex at point K has a value of 360/7 = 51.429 degrees (51 degrees 25.71 minutes), and the real angle of inclination of the faces of the Cheops pyramid has a value of 51 degrees 50 minutes. The existing difference the builders of the Cheops pyramid compensated by adding the height of the human height AH to the height of the triangle AEK. That is, the builders conditionally placed a human figure on the top of the pyramid, and as a result they received 51 degrees 50 minutes as the value of the angle EKX with the vertex at point K. Namely, if the height of the triangle EKH is 318 cubits, then the height of the triangle EKA is approximately 314 cubits, and the height of a person is approximately 4 cubits.

Egyptian builders increased the correct angle of the heptagon, as if there was a person at the top of the Cheops pyramid, and as a result, the number of the golden section was encrypted in the ratios of the EK/KH lines and the proportions of the human body were laid down in the general geometry of the future pyramidal structure, which was the idea of ​​​​the architectural design of the future pyramid .
Essentially, the builders and creators of the architectural plan of the Great Pyramid of Cheops inscribed a double heptagonal or, in other words, biheptagonal network of lines into a living circle, in which the magnitude of the vertical diameter differed from the horizontal diameter by the relative magnitude of human height, as shown in the following figure.

In the figure, a diheptagonal network of lines is inscribed in the space of a living circle, which has a ratio of vertical and horizontal diameters of approximately 15/14, which corresponds to the ratio of the proportions of the male and female body. I cannot indicate the exact ratios of the diameters of a living circle in a geometric drawing, or in other words, in the architectural design of the Cheops pyramid, since this requires precise mathematical calculations. But it can be assumed that the ratios of the diameters of the living circle in the geometric drawing of the Cheops pyramid are obtained as a result of transformation, namely as a result of the transformation of a regular circle into a living circle, when the value of the segment TA is exactly equal to the value of the lines CE or DF. The blue outline in the figure indicates the approximate silhouette of the side faces of the pyramid, and the white outline indicates the approximate silhouette of the diagonal edges. The angle DLA with the vertex at point L has a value of 40 degrees 59 minutes and corresponds to the inclination of the diagonal edges of the Cheops pyramid. The values ​​of the angles DLA (the inclination of the diagonal edges) and EKA (the inclination of the side faces) with vertices at points L and K differ from the angular values ​​of the regular diheptagon in the relative magnitude of human height, since the diheptagon in the design of the Egyptian pyramid of Cheops is inscribed in the space of a living circle, which is transformed in accordance with with human growth. Namely, it is transformed in accordance with the height of the human body, which has the size of 4 Egyptian cubits and is conventionally located at the top of the pyramid.

The geometric drawings shown are approximate, since accurate calculations require a lot of numbers and mathematical formulas, which is impractical in the context of an art gallery of phantom images, but according to the shown drawings, accurate geometric calculations can be made if necessary from the point of view of scientific research into the esoteric principles of world harmony, or from the point of view of mathematical solutions to other problems in science or architecture, or in fine arts, or in fashion design, or in the context of physical culture of the body.
The above drawings allow us to understand the basic proportions of the pyramids, but in addition, many other mathematical relationships are encrypted in the geometric measures of the pyramidal structures of ancient Egypt that correspond to the principles of world harmony and the geometry of the surrounding world.
We can say that the dimensions of the Great Egyptian Pyramids contain measurements that allow us to understand the structure of the surrounding world, and knowledge of these “great Egyptian measures” allows us to design and create objects of human civilization in accordance with the universal laws of space.
The main measurement unit in ancient Egypt was the cubit, which consisted of seven palms, and each palm was divided into four fingers. In total, the elbow consisted of 28 fingers, which corresponded to 28 days of the lunar month.
Note that the diheptagonal line network has 14 vertices, and the quadheptagonal line network has 28 vertices, which is also equal to the number of days in the lunar month.
In modern Egyptology, different parameters of the Egyptian cubit are known:
- simple Egyptian cubit = 6 palms = 24 fingers = 450 millimeters;
— royal Egyptian cubit = 7 palms = 28 fingers = 525 millimeters.
But still, the value of 466 millimeters is the most reliable, since it is an anthropometric value, or in other words, the measure of the human body from the elbow to the base of the fingers.

The photograph on the left shows a wooden panel depicting a surveyor with a cane in his hand, and it is one of eleven carved wooden panels that were found in the tomb of Hesi-Ra, who is considered the architect of the Great Pyramids of ancient Egypt. The boards found have images on both sides, which in total are comparable to the 22 major arcana in a deck of tarot cards. The photo was scanned from the book by I.P. Shmelev. The “Third Signal System”, as well as the hypothesis about the relationship of the 22 arcana of the Tarot with wooden boards from the tomb of Hesi-Ra, belongs to Shmelev. The cane in the surveyor's hand is equal to the length from the middle of the body to the line of the eyebrows, which is two cubits. If we project this reed onto a biheptagonal network of lines, then its size equal to the segment AT, and is also approximately equal to the length of the side of the heptagon, as shown in the previous figure. Namely, the cane in the surveyor’s hand is equal to the segments CE, DF, LJ, MK. Consequently, the ancient Egyptian cubit with a size of 466 millimeters is equal to the length of the side of the diheptagon, that is, equal to the distance between two nearby vertices, and any other measures of measurement and mathematical parameters of the Egyptian pyramids are derived from proportional relationships, according to which the figure of the human body is inscribed in the diheptagonal geometric network, which allows us to make a statement about the correspondence of the measurements and sizes of the Egyptian pyramids with the proportions of the human body. But provided that the diheptagonal network of lines is located in the space of a living circle, which forms “an ellipse with a focal length proportional to human height compared to the height of the pyramid.” Namely, the difference in the diameters of the major and minor axes of the ellipse corresponds to the mathematical ratio of human height to the height of the Cheops pyramid.

Using a cane, the builders calculated the sides of the pyramidal structures, and in the architectural design of the Cheops pyramid the proportions of the human body were recorded, and in the Khafre pyramid the “sacred Egyptian triangle” with an aspect ratio of 3:4:5, which is otherwise called the “sacred Pythagorean triangle,” was recorded. That is, the pyramids of Khafre and Cheops have different sizes, but both are calculated according to the same cane. Apparently, different pyramids were calculated by the builders as a result of different transformations and transformations of the lines of the diheptagonal geometric network in the space of the ellipse of a living circle.
More information about sacred Egyptian or Pythagorean triangle with an aspect ratio of 3:4:5, see the pages of another site: www.emotions.64g.ru.

At the end of this page, it must be said that in ancient Egyptian sources of information there is no information about the relationship between the shapes of the human body and the lines of the heptagon and the dimensions of the pyramids, but still the heptagon is fundamental geometric figure, which correlates with pyramids and the shapes of human bodies.
It is also necessary to say that the different sizes of the pyramidal structures of ancient Egypt, and the corresponding ratios of the lines of a double heptagon or diheptagon in the space of living circles with different ratios of vertical and horizontal diameters can symbolize the mathematical values ​​of physical resonances, according to which it is possible to overcome the gravity of the Earth and the resistance of time, or it is possible to extract energy from the relationships between space and matter. What might be of interest to the inventors of a time machine or aircraft, which are similar to the flying saucers of extraterrestrial civilizations, and may also be of interest to creators of alternative sources of electrical energy that arises from the resonances of space.
But these are just hypotheses.

The next page talks about measuring instruments that can be derived from the lines of a diheptagonal geometric network.

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Pyramids are one of the most mysterious phenomena on Earth, the solution to which scientists have been struggling for hundreds of years. In fact, why and by whom were they built? In addition to the most famous pyramids in Egypt, they are at the bottom Atlantic Ocean, in the distant Amazon basin, in the taiga forests of Siberia, in Taimyr, in Australia, in China - almost all over the world! And today, trying to penetrate the secrets of the pyramids, people build pyramids of various proportions and from different materials. One thing is clear that this form has a certain energy that enthusiasts and scientists are trying to unravel and use for the benefit of humanity.

The facts are widely known that products placed in a pyramid are stored longer, milk does not sour longer, meat dries out, but does not rot. Milk produced by Soviet industry, which was packaged in triangular cardboard pyramids, was stored longer than bottled milk. If you stay in the pyramid for a short time every day, you will notice a beneficial effect on human health.

And right now it is necessary to pay attention to this fact, because... poor ecology, poor nutrition, dead tap water, stress at work, negativity from TV screens, increased levels of EMR, day after day, imperceptibly destroy human health. The immune system gradually breaks down, and after some time it is no longer able to withstand the onslaught of pathogenic cells, which results in chronic diseases.

Pyramid energy - How to build a healing pyramid at your dacha with your own hands

And in this situation, pyramids can come to the rescue, giving the body additional energy to put itself in order.

This is precisely the fact that took place in the 90s, when the first pyramid was made for friends to stand in it at full height. That pyramid allowed a person to get rid of cancer. The second pyramid “went” to Nalchik, the third - …….

All our pyramids are frame, made of wood. After all, wood is a living material. It is more comfortable to live in wooden log houses than in brick houses. It has long been noted that as long as the owners live in the house, the house also lives. If the owners leave a 70-80 year old log house, then literally after a couple of months it crumbles.

Try taking a dry spruce branch and nailing it to the window on the street side. This way you can get a good weather indicator. The branch will predict the approach of rain, drought, hurricane better than any weather forecaster. After all, she “remembers” her behavior when she was still part of the tree and reproduces it after being cut down. Due to the “memory effect” of the tree, the energy of the pyramid is enhanced. A felled tree “remembers” how energy flowed through it and generously shares it with a person. By properly directing this energy, you can “program” the energy of the pyramid, depending on its purpose.

Our pyramids are made in the following proportions:

pyramid height/base side length = 0.64

For clarity, below is a diagram of the pyramid.

By examining our prototype using dowsing, we found out that the pyramid has two energy centers, we saw the direction of the flow of energies.
We were surprised to note that the pyramid is, in fact, a three-dimensional representation of the runic symbol “Fiery (solar) Kolovrat” when viewed from above!
Do the pyramids really receive the energy of the Sun itself? There are still many interesting tests ahead, but for now you can build the same pyramid yourself and use it for medicinal and health purposes.

Checking the movement of energy in the pyramid - with the bioframe "RAD OF THE PHARAOH".

Having studied the movement of energy in a pyramid, you will be able to apply the knowledge gained to make a pyramid to suit your needs.

It is almost impossible to determine the energy of the pyramids with conventional instruments, but it is possible to determine the movement of energy in the pyramids using the dowsing frame "RAD OF THE PHARAOH"

How to make a bioframe “RAD OF THE PHARAOH” - READ HERE...

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Even the ancients noticed some amazing properties the so-called “golden ratio”. For example, the pyramid complex at Giza was built on this principle. Also in the facade of the ancient Greek temple of the Parthenon there are “golden” proportions. How is the golden ratio constructed?

You will need

• Ruler, pencil.

Instructions

1. Proportion (from the Latin word proportio) is the following equality a:b = c:d. The golden ratio is a division of a segment into parts in which the length of the entire segment is related to the length of the larger part in the same way as the length of the larger part is related to the length of the smaller part. The concept itself gold sections introduced by Leonardo da Vinci. He considered the human body to be the most perfect creation of nature. If a human figure is tied with a belt, it will turn out that the height of the entire person refers to the distance from the belt to the heels, just as the distance from the belt to the heels refers to the distance from the waist to the top of the head.
2. If we take, for example, a straight line segment AB and divide it with a point C, so that AB:AC = AC:BC, we obtain the following equality AB:AC = AC:(AB-AC) or AB(AB-AC) = AC2 or AB2-AB*AC-AC2 = 0. Next, you should take AC2 out of brackets AC2(AB2:AC2 – AB:AC – 1) = 0.
3. If we denote the expression AB:AC by the letter K, we get the quadratic equation K2-K-1=0. One of the roots of this quadratic equation will be the number 1.618. In other words, the “golden ratio” is an irrational number approximately equal to 1.618.
4. According to principle gold sections Egyptian pyramids were built. At the base of the pyramids lie a square. For example, at the base of the Cheops pyramid lies a square with a side length of 230.35 meters. The height of this pyramid is 146.71 m. Side edge The Cheops pyramid is an isosceles triangle with a right angle at the apex and angles at the base equal to 45 degrees.
5. There are four such lateral faces of isosceles triangles, since the base is a square. The triangle highlighted in red in the picture is called the “Egyptian” sacred triangle. An Egyptian triangle is a triangle with sides 3,4,5, or k3,k4,k5, where k belongs to the set of real numbers. In such a pyramid, the side of the base is related to the height as 1.618 - this is the golden ratio.
6. So to build pyramid in proportions gold sections, you need to: 1. Draw a square (the side of the square should be equal to k*3, where k is a natural number).2. Construct the diagonals of this square.3. To the point sections diagonals, lower the height equal to the side of the square divided by 1.618.4. Connect the top point of the pyramid with the four vertices of the base.

Using the properties and secrets of the manufactured pyramid, it is easy to obtain the so-called charged water, which is useful for washing with problem skin, and drinking for diseases of the gastrointestinal tract (you can simply use it for prevention). By making a pyramid, you can charge creams and foods (for example, oil). There is an opinion that vodka left overnight in the pyramid does not give a hangover, and brine, which has been in the same place, removes all traces of yesterday's intemperance in a few minutes.

A pyramid with the correct dimensions of the golden ratio is useful not only in everyday life. The onset of otitis (inflammation of the middle ear) can be cured in ONE session (about thirty minutes), the emerging rotation of the nails in two sessions (in total about three hours). All signs food poisoning, using the properties of the pyramids and their secrets, disappear ten minutes after you place the pyramid on your stomach, etc. The properties and secrets of the pyramids are best revealed if it is possible to capture the very beginning of the disease. Then one or two sessions are enough for it to stop progressing and leave you alone.

It is more difficult with chronic ailments, however, many of them can also be cured with the help of the pyramid. You just need to treat them not so much during attacks (by the way, the pain during attacks is well extinguished by the pyramid), but to be patient and do this every day, for example, while watching TV.

Using the properties and secrets of the pyramids of golden ratio proportions, you can get rid of osteochondrosis in a month and a half. With congenital heart disease and angina pectoris, you can stop the attack at the very beginning, without waiting until the pain becomes severe.

The more often you use the healing pyramid, the more convinced you are that it saves money and time, since treating even the smallest ailment with the help of our healthcare system is a complex, troublesome and, often, expensive and ineffective task. Therefore, before running to the clinic, you can try to use the properties of the pyramids - in the vast majority of cases, it is possible to do without doctors and pharmacies with the help of a healing pyramid.

Do you want to have such a pyramid at home? Do you want to have all the properties of the healing pyramids, all the secrets of the pyramids at your fingertips? But the question arises, how to make a pyramid?

Making pyramids is not very difficult - it’s simple, you need to follow all the dimensions of the Golden Ratio healing pyramid and instructions. And the detailed technology for making the pyramid is in the collection. You will be given all the dimensions of the pyramid. Making it yourself according to a drawing, knowing the dimensions, is not at all difficult.

What to make a pyramid from? You can use any thin sheet material, except metals (plastic, plywood, hardboard, plexiglass, thick cardboard, etc.). You can get by with ordinary drawing paper, but then the pyramid will turn out to be extremely short-lived, but will still have all the wonderful and healing properties of the pyramids, and will reveal its secrets to you.

And now a few screenshots from the instructions for making a pyramid

All detailed explanations, the dimensions of the healing pyramid of the golden section, and a much larger number of diagrams and drawings that make the manufacture of pyramids simple and without problems, revealing to you the secrets of the pyramids, are in the collection itself. Moreover, you do not need to be a mathematician or have a construction profession. Everything is shown and told, as they say, “on the fingers.”

In addition to the manufacturing method, you will be given practical advice on using the pyramid (its properties), and how to correctly position it in space.

Well? Did I manage to convince you?
I think yes.

How to make a pyramid at home?

First, let’s decide for what purpose the pyramid is being created. In most cases, the pyramid is installed above the bed; in this case, the base of the pyramid is desirable (but not critical) to be placed a couple of centimeters below the level of the bed legs. It can be made from any dielectric material (this is a substance that does not conduct current) - ordinary cardboard or plywood, wood, glass, plastic.

Any model should be made according to formulas based on the proportions of the Cheops pyramid: the length of the side of the base of the pyramid is 230.35 meters, the height is 146.59 meters. The ratio between these values ​​is 1.571. In this case, the angles between the sides and the base are 58 degrees, and the angle at the top is 64 degrees. In order not to suffer with these degrees, the length of the edge of the pyramid is calculated - it is 1.4945 times the height.
Side rib length - hx1.4945
Base side length - hx1.57057
The height of the pedestal in the pyramid is hx 0.3333
h is the height of the pyramid. This is the relationship of the ancient Egyptian pyramids.

Here you can download a ready-made gluing with the same proportions, cut it out, glue it and voila! Done. Download

As mentioned above, to make a pyramid you can use almost any material (boards, plywood, plexiglass, slate) that has insulating properties. But it should be built without nails, since metal distorts the field of pyramidal space.

It should be remembered that as the height of the pyramid doubles, its activity increases by 50-100 times. Therefore, if possible, take advantage of it. (This will turn out to be a high pyramid, where the edge is longer than the base).

“The passage of time slows down in the pyramids, which means the aging process can be stopped.”

How to choose a place for a pyramid?

In houses, pyramids should be installed away from sewerage pipes, water supply pipes and the like, metal and water-containing objects; a healthy aquarium is also not good. An excellent option is to build a pyramid on a summer cottage. One of the faces should be oriented north (not an edge, but a face).
As with any business, you need to start work in a good mood, without any distractions, like: “They’re all freaks, they’re annoying.”
If the pyramid is built in violation of the proportions of the “golden section” and is not oriented to the cardinal points, there may be no benefit from it, but harm is possible.

The interior space of all models should not be loaded more than 10 percent.

Cone pyramid

It was not for nothing that medieval magicians wore cone-shaped caps. Judging by the research, the conical pyramid is slightly inferior to the traditional tetrahedral one, but it is easier to manufacture. It is done simply: draw a circle on a sheet of material with a compass and cut it in half. Then you need to take one semicircle and roll it so that the extreme points of the diameter coincide. The edges are connected with adhesive tape, and a conical pyramid is obtained. By the way, it does not need to be oriented towards the cardinal directions.
Some practical tips for those who want to build a pyramid on their summer cottage.

When installing a structure in which a person can fit, the height of the structure should be 3 meters. Using the search indicator, you need to find a favorable place for its center. Let's say you have the opportunity to build a structure with a 4x4 meter base. According to the “golden ratio” proportion, the height of this pyramid will be 2.5 meters (4x1.6). According to these calculations, we make four equal triangles. The foundation of the pyramid should be oriented strictly north. The trench is filled with concrete (there should be no metal). The walls of the building rest on the waterproofing of the finished foundation. It is best to use round timber or beams that are fastened together with tongues or wedges. Brick structures will be more practical to use.

How to be treated with pyramids? Orientation to the cardinal points.

Methods of treatment with pyramids are a modified meditation with a pyramid, which does not lie on folded palms, but stands on a table at eye level.
Pain can be relieved by simply placing the pyramid on the sore spot. But at the same time, you yourself must take a position according to the geomagnetic field of the Earth: head to the north, legs to the south, in a lying position. The edges of the pyramid must also be accurately oriented to the cardinal points.
You can also use a set of tiny pyramids. You must place each such pyramid on a bioactive point recommended for treatment for a specific disease (this comes from acupuncture). Place pyramids on bioactive points for a period of 20 minutes to 2 hours once a day.

And, apparently, a pyramid can also be made, following the example of scammers who sell all sorts of healing pyramids like with gold wires. We make it for ourselves from aluminum or copper wire, twist it (no need for special precision). You can try, I think it won't hurt.

P.S. The effect of the pyramids has not been scientifically proven; no one knows what is happening there.

http://ocheretniy.blogspot.com/2012/01/blog-post_4330.html

Geometry is an exact and quite complex science, which at the same time is a kind of art. Lines, planes, proportions - all this helps to create many truly beautiful things. And oddly enough, this is based on geometry in its most varied forms. In this article we will look at one very unusual thing that is directly related to this. The golden ratio is exactly the geometric approach that will be discussed.

The shape of an object and its perception

People most often rely on the shape of an object in order to recognize it among millions of others. It is by its shape that we determine what kind of thing lies in front of us or stands in the distance. We first recognize people by the shape of their body and face. Therefore, we can confidently say that the shape itself, its size and appearance is one of the most important things in human perception.

For people, the form of anything is of interest for two main reasons: either it is dictated by vital necessity, or it is caused by aesthetic pleasure from beauty. The best visual perception and feeling of harmony and beauty most often comes when a person observes a form in the construction of which symmetry and a special ratio were used, which is called the golden ratio.

The concept of the golden ratio

So, the golden ratio is the golden ratio, which is also a harmonic division. To explain this more clearly, let's look at some features of the form. Namely: a form is something whole, and the whole, in turn, always consists of some parts. These parts most likely have different characteristics, at least different sizes. Well, such dimensions are always in a certain relationship, both among themselves and in relation to the whole.

This means, in other words, we can say that the golden ratio is a ratio of two quantities, which has its own formula. Using this ratio when creating a form helps to make it as beautiful and harmonious as possible for the human eye.

From the ancient history of the golden ratio

The golden ratio is often used in many different areas of life today. But the history of this concept goes back to ancient times, when sciences such as mathematics and philosophy were just emerging. As a scientific concept, the golden ratio came into use during the time of Pythagoras, namely in the 6th century BC. But even before that, knowledge about such a ratio was used in practice in Ancient Egypt and Babylon. A clear indication of this are the pyramids, for the construction of which exactly this golden proportion was used.

New period

The Renaissance brought new breath to harmonic division, especially thanks to Leonardo da Vinci. This ratio has increasingly begun to be used both in geometry and in art. Scientists and artists began to study the golden ratio more deeply and create books that examine this issue.

One of the most important historical works related to the golden ratio is a book by Luca Pancholi called The Divine Proportion. Historians suspect that the illustrations of this book were done by Leonardo himself before Vinci.

golden ratio

Mathematics gives a very clear definition of proportion, which says that it is the equality of two ratios. Mathematically, this can be expressed by the following equality: a: b = c: d, where a, b, c, d are some specific values.

If we consider the proportion of a segment divided into two parts, we can encounter only a few situations:

• The segment is divided into two absolutely even parts, which means AB:AC = AB:BC, if AB is the exact beginning and end of the segment, and C is the point that divides the segment into two equal parts.
• The segment is divided into two unequal parts, which can be in very different proportions to each other, which means that here they are completely disproportionate.
• The segment is divided so that AB:AC = AC:BC.

As for the golden ratio, this is a proportional division of a segment into unequal parts, when the entire segment relates to the larger part, just as the larger part itself relates to the smaller one. There is another formulation: the smaller segment is related to the larger one, just as the larger one is to the entire segment. In mathematical terms, it looks like this: a:b = b:c or c:b = b:a. This is exactly what the golden ratio formula looks like.

Golden ratio in nature

The golden ratio, examples of which we will now consider, refers to incredible phenomena in nature. This is very beautiful examples the fact that mathematics is not just numbers and formulas, but a science that has more than a real reflection in nature and our life in general.

For living organisms, one of the main tasks in life is growth. This desire to take one’s place in space, in fact, occurs in several forms - growing upward, almost horizontally spreading on the ground, or twisting in a spiral on some kind of support. And as incredible as it may be, many plants grow according to the golden ratio.

Another almost incredible fact is the relationships in the body of lizards. Their body looks quite pleasing to the human eye and this is possible due to the same golden ratio. To be more precise, the length of their tail relates to the length of the entire body as 62:38.

Interesting facts about the rules of the golden ratio

The golden ratio is a truly incredible concept, which means that throughout history we can come across many truly interesting facts about this proportion. We present you some of them:

Golden ratio in the human body

In this section it is necessary to mention a very significant person, namely S. Zeizinga. This is a German researcher who has done a tremendous amount of work in the field of studying the golden ratio. He published a work entitled Aesthetic Studies. In his work, he presented the golden ratio as an absolute concept that is universal for all phenomena both in nature and in art. Here we can recall the golden ratio of the pyramid along with the harmonious proportion of the human body and so on.

It was Zeising who was able to prove that the golden ratio, in fact, is the average statistical law for the human body. This was shown in practice, because during his work he had to measure a lot of human bodies. Historians believe that more than two thousand people took part in this experiment. According to Zeising's research, the main indicator of the golden ratio is the division of the body by the navel point. So, male body with an average ratio of 13:8, it is slightly closer to the golden ratio than the female ratio, where the golden ratio is 8:5. The golden ratio can also be observed in other parts of the body, such as the hand.

About the construction of the golden ratio

In fact, constructing the golden ratio is a simple matter. As we see, even ancient people coped with this quite easily. What can we say about modern knowledge and technologies of mankind. In this article we will not show how this can be done simply on a piece of paper and with a pencil in hand, but we will confidently declare that it is, in fact, possible. Moreover, this can be done in more than one way.

Since this is a fairly simple geometry, the golden ratio is quite simple to construct even at school. Therefore, information about this can be easily found in specialized books. By studying the golden ratio, 6th graders are fully able to understand the principles of its construction, which means that even children are smart enough to master such a task.

Golden ratio in mathematics

The first acquaintance with the golden ratio in practice begins with a simple division of a straight line segment in the same proportions. Most often this is done using a ruler, compass and, of course, a pencil.

Segments of the golden proportion are expressed as an infinite irrational fraction AE = 0.618..., if AB is taken as one, BE = 0.382... In order to make these calculations more practical, very often they use not exact, but approximate values, namely - 0 .62 and .38. If the segment AB is taken as 100 parts, then its larger part will be equal to 62, and the smaller part will be equal to 38 parts, respectively.

The main property of the golden ratio can be expressed by the equation: x 2 -x-1=0. When solving, we get the following roots: x 1.2 =. Although mathematics is an exact and rigorous science, like its section - geometry, it is properties such as the laws of the golden section that cast mystery on this topic.

Harmony in art through the golden ratio

In order to summarize, let’s briefly consider what has already been discussed.

Basically, many pieces of art fall under the rule of the golden ratio, where a ratio close to 3/8 and 5/8 is observed. This is the rough formula of the golden ratio. The article has already mentioned a lot about examples of using the section, but we will look at it again through the prism of ancient and modern art. So, the most striking examples from ancient times:

As for the probably conscious use of proportion, starting from the time of Leonardo da Vinci, it came into use in almost all areas of life - from science to art. Even biology and medicine have proven that the golden ratio works even in living systems and organisms.