Municipal Autonomous Educational Institution "Lyceum No. 21", Pervouralsk

Project on

"The Geometric Secrets of the Egyptian Pyramids"

Fulfilled

Panov Dmitry

8th grade student

Supervisor

Krotova Irina Leonidovna

2016

CONTENT

Introduction……………………………………………………………………...……3

Theoretical part

What are the Egyptian pyramids……………………………………………………6

Practical part

The presence of mathematics in the Egyptian pyramids………………………………9

Geometry in pyramids…………………………………………………..……12

Conclusion………………………………………………………………..……15

Materials used……………………………………………………..17

INTRODUCTION

Ancient Egypt is known primarily for its stone giants - pyramids that served as the burial places of Egyptian kings and pharaohs. However, not all Egyptian rulers found rest inside the pyramids, and this is not the only mystery of the Egyptian pyramids. And although scientists have been studying the pyramids for more than a century, only recently they managed to lift the veil of secrecy over how the Egyptians built them and why they abandoned construction.

Modern history is replete with white spots, and this is not surprising, because if modern people knew about the technologies and capabilities of people who lived in the distant past, they would have a different look at the "development" of modern society. There is an understanding that in ancient times people knew much more than modern science is trying to show us, and this knowledge was not limited only to the external material world, but led to an understanding of the internal, spiritual processes in a person. Ancient people possessed a perfect science of man. If we talk about the monumental buildings of the past, then many amazing architectural monuments have come down to our time. Among them are stone structures of unimaginable scale.

The oldest Egyptian mathematical texts that have come down to us date back to the beginning of the 2nd millennium BC. Mathematics was then used in astronomy, navigation, land surveying, in the construction of houses, dams, canals and military fortifications. The Egyptians wrote on papyrus, which is poorly preserved, and therefore, at present, there is much less knowledge about the mathematics of Egypt than about the mathematics of Babylon or Greece. It was probably better developed than can be imagined from the documents that have come down to us. This is indirectly confirmed by the fact that Greek mathematicians studied with the Egyptians.

The Egyptian pyramids arouse curiosity and admiration, and at the same time they are an intellectual challenge to humanity, demonstrating its impotence in unraveling the mysteries of these ancient structures. The very existence of the Egyptian pyramids, the mystery of their origin and purpose, worried the best minds of mankind for many millennia. Many scientists have devoted their lives to revealing these secrets, but despite the long history of excavations and research, despite the development of science and technology in the modern world, humanity is still not able to answer the huge number of mysteries that are hidden in the Egyptian pyramids. The main questions that have always worried the researchers of the pyramids can be reduced to four main points: who, when, how and, most importantly, why built these majestic structures. Since the time of Herodotus, who visited Egypt in the 5th century BC, and until now, scientists have practically not found answers to these questions.

There is no doubt that the main problem on the way to solving the riddle of the Great Pyramids is the complete inconsistency of the actions of various researchers and, as a result, the lack of systematic research on the issue. Specialists in the history and culture of ancient Egypt are limited to official version, not free from obvious contradictions, and refuse to acknowledge the existence of a problem, much less discuss it with "non-specialists". Non-specialists in the history and culture of Egypt, but experts in any other field of knowledge sin with one-sided approaches that do not take into account the complex nature of the problem. The provocative nature of the problem itself attracts people with an artistic mindset who are ready to put forward fantastic hypotheses and wishful thinking too often and uncritically.

Therefore, the first step is to formulate a set of key circumstances that require a satisfactory explanation in the development and consideration of any hypothesis - this will create certain restrictions on the proposed hypotheses, which will allow them to be more tolerant. It is advisable to adhere to Occam's principle and not so much to look for an initial premise from which the existence and purpose of the pyramids can follow, but to take care that what is observed cannot be explained otherwise than with the help of the proposed idea. Secondly, any hypothesis that can be not only taken into account, but discussed, must contain specific proposals for its verification with a prediction of possible results.

It is both of these circumstances that should form the methodological essence of the approach to the study of the problem of the Great Pyramids of Egypt.

The relevance of this topic is that, on the other hand, people remain people: they, as always, try to find answers, each at their own mundane level, based only on the knowledge and experience that they used to rely on. But what if something more is hidden in the mystery of the Egyptian pyramids, which scientists, due to the limited knowledge and experience and the dogmatic nature of their thinking, are simply not able to know? For example, in the drawings of the Nazca desert, UFOs and crop circles: the elementary narrowness of thinking and the conservatism of pundits do not allow them to penetrate the secrets of Being, and therefore they continue to insist on their theories in which there is no and cannot be a place for another Existence other than physical. It resembles walking in a circle, when it seems that the next circle will be the final one. Unfortunately, marking time does not move progress.

The purpose of this work: to study the secrets of the Egyptian pyramids from the point of view of mathematics.

To achieve this goal, it is necessary to solve the following tasks:

1) Find general information about the Egyptian pyramids

2) Analyze the found information and choose the one that can be consistent with the geometry

3) study this information and draw appropriate conclusions

WHAT ARE THE EGYPTIAN PYRAMIDS

Egyptian pyramids are the greatest architectural monuments Ancient Egypt, including one of the "seven wonders of the world" - the pyramid of Cheops and an honorary candidate for the "new seven wonders of the world" - the Pyramids of Giza. Pyramids are huge pyramid-shaped stone structures used as tombs for the pharaohs of ancient Egypt. The word "pyramid" - Greek, means a polyhedron. According to some researchers, a large pile of wheat became the prototype of the pyramid. According to other scientists, this word comes from the name of the funeral cake of a pyramidal shape. A total of 118 pyramids have been discovered in Egypt.

When referring to the Egyptian pyramids, as a rule, they mean the Great Pyramids located in Giza, not far from Cairo. But they are not the only pyramids in Egypt. During the period of the first dynasties, special “houses after life” appeared - mastabas - funerary buildings, consisting of an underground burial chamber and stone structure above the surface of the earth. The term itself already refers to the Arab time and is due to the fact that the shape of these tombs, similar in section to a trapezoid, reminded the Arabs of large benches called “mastaba”.

The first pharaohs also built mastabas for themselves. The oldest royal mastabas, dating back to the times of the 1st dynasty, were built from adobes - unbaked bricks made of clay or river silt. They were built in Nagadei Abydos in Upper Egypt, as well as in Saqqara, where the main necropolis of Memphis, the capital of the rulers of the first dynasties, was located. In the ground part of these buildings there were chapels and rooms with grave goods, and in the underground part there were actually burial chambers.

The purpose of the pyramids was multifunctional. They served not only as the tombs of the pharaohs, but were also attributes of the greatness, power and wealth of the country, cultural monuments, repositories of the country's history and information about the life of the pharaoh and the people, a collection of household items.

It is clear that the pyramids had a deep "scientific content", embodied in their shape, size and orientation to the terrain. Every detail of the pyramid, every element of the form was chosen carefully and had to demonstrate the high level of knowledge of the pyramid makers. After all, they were built for millennia, "forever." And it is not for nothing that the Arabic proverb says: "Everything in the world is afraid of time. Time is afraid of the pyramids."

Among the grandiose pyramids of Egypt, the Great Pyramid of Pharaoh Cheops (Khufu) occupies a special place. Before proceeding to the analysis of the shape and size of the pyramid of Cheops, we should remember what system of measures the Egyptians used. The Egyptians had three units of length: "cubit" (466 mm), equal to seven "palms" (66.5 mm), which, in turn, was equal to four "fingers" (16.6 mm).

The pyramids were built about 4.5 thousand years ago. Before erecting the pyramid, the builders leveled the terrain on which the pyramid was to be erected. The central axis of the pyramid was determined, around which the rock was removed under the blocks, which were the basis for its installation.

Over 800 kilometers from the installation site, 130 granite blocks were mined, each of which weighs from 12 to 70 tons. These blocks have been delivered. Subsequently, for the construction of internal chambers, they had to be raised by 65 meters and installed.

The lower, middle and upper chambers were built, which are negligible in comparison with the entire huge mass of the monument. A passage was built 90 meters long and less than a meter wide, this passage leading to the lower chamber was cut right into the rock. Precise tools were required to keep the angle of the passage accurate and constant along its entire length. Also, in order to gouge a tunnel of this length, lighting was required, but no traces of soot were found. So what did the ancient Egyptians use to illuminate and control the angle of immersion?

The pyramid consists of more than 2 million blocks of various shapes and sizes, although, as we know from the experience of modern builders, it is easier to work with blocks of the same size. The average mass of blocks is 2.5 tons. The accuracy of the overall design of the pyramid is striking, it meets modern standards. For example, the top camera is perfectly aligned horizontally and vertically. The accuracy of the installation of blocks exceeds the standards of modern construction. The error is only half a millimeter. This is amazing accuracy for such an ancient object. This cannot be achieved by modern builders using the very modern equipment. The pyramid has survived at least three large-scale earthquakes in its history, one of which razed the city of Cairo to the ground in the 13th century. What was the level of knowledge of the builders if everything inside the pyramid remained in place?

The geographic orientation of the pyramid along the magnetic poles of the planet was also performed in a jeweler's way. It has a deviation of the western side 2'30" and the eastern side 5'30" from the true direction to the north, and the northern and southern sides by 2'28" and 1'57" respectively from the Equator line.

THE PRESENCE OF MATH IN THE EGYPTIAN PYRAMIDS

One of the interesting features of this pyramid is that it has not four, but eight faces, because. each of the four sides is slightly concave in the middle, which further complicates the construction process.

Let's analyze the dimensions of the pyramid of Cheops.

Most researchers agree that the length of the side of the base of the pyramid, for example, GF = 233.16 m. This value corresponds almost exactly to 500 "cubits". There will be full compliance with 500 "cubits" if the length of the "cub" is considered equal to 0.4663 m. The height of the pyramid (AC) is estimated by researchers differently from 146.6 to 148.2 m. elements. What is the reason for the differences in the estimate of the height of the pyramid? The fact is that, strictly speaking, the pyramid of Cheops is truncated. Its upper platform today has a size of approximately 10 * 10 m, and a century ago it was 6 * 6 m. It is obvious that the top of the pyramid was dismantled, and it does not correspond to the original one. Estimating the height of the pyramid, it is necessary to take into account such a physical factor as the "draft" of the structure. For a long time under the influence of colossal pressure (up to 500 tons per 1 m 2 lower surface) the height of the pyramid has decreased compared to the original height. What was the original height of the pyramid? This height can be recreated if you find the basic "geometric idea" of the pyramid.

In 1837, the English Colonel G. Wise measured the angle of inclination of the faces of the pyramid: it turned out to be equal to a = 51 ° 51 ". This value is still recognized by most researchers today. The indicated value of the angle corresponds to the tangent (tg a), equal to 1.27306. This value corresponds to the ratio of the height of the pyramid AC to half of the side of its base CB, i.e.AC/CB=H/(L/2)=2H/L. And here the researchers were in for a big surprise! The point is that iftake the square root of the golden ratio, then we get the following result = 1.272. Comparing this value with the value tg a = 1.27306, we see that these values ​​are very close to each other. If we take the angle a \u003d 51 ° 50 ", that is, reduce it by only one arc minute, then the value of a will become equal to 1.272, that is, it will coincide with the valueWHAT???.It should be noted that in 1840 G. Wise repeated his measurements and clarified that the value of the angle a = 51 ° 50 ". These measurements led researchers to the following very interesting hypothesis: the ratio AC / CB = 1.272 was laid at the basis of the triangle DIA of the pyramid of Cheops!

Consider now a right triangle ABC, in which the ratio of the legsAC / CB = rootZ. If now the lengths of the sidesrectangleABC denote by x, y, z, and also take into account that the ratio y / x = rootz, then in accordance with the Pythagorean theorem, the length z can be calculated by the formula:z= sum rootxsquared andyin a square. Let us now derive some other relations for the pyramid of Cheops, which follow from the "golden" hypothesis. In particular, we find the relationouter areapyramid to the area of ​​its base. To do this, we take the length of the leg CB as a unit, that is: CB = 1. But then the length of the side of the base of the pyramid GF = 2,and the base area of ​​EFGH will be equal to SEFGH = 4.

Let us now calculate the area of ​​the side face of the Cheops pyramid SD.Insofar asheight AB of triangle AEF is equal to t, then the area of ​​the side face will be equal to SD = t. Then the total area of ​​all four side faces of the pyramid will be equal to 4t, and the ratio of the total external area of ​​the pyramid to the base area will beequal to the golden ratio! This is the main geometric secret of the Cheops pyramid!

An analysis of other Egyptian pyramids shows that the Egyptians always sought to embody some important mathematical knowledge in their pyramids. In this regard, the pyramid of Khafre is very interesting. Measurements of the pyramid showed that the angle of inclination of the side faces in it is 53 ° 12 ", which corresponds to the ratio of the legs of a right triangle 4: 3. This ratio of the legs corresponds to the well-known right triangle with sides 3: 4: 5, which is called "perfect", " sacred" or "Egyptian" triangle. According to historians, the "Egyptian" triangle was given a magical meaning. Plutarch wrote that the Egyptians compared the nature of the Universe with the "sacred" triangle; they symbolically likened the vertical leg to the husband, the base to the wife, and the hypotenuse to the one that is born from both.

For a 3:4:5 triangle, the equality is true: 3 squared + 4 squared = 5 squared, which expresses the Pythagorean theorem. Is it not this theorem that the Egyptian priests wanted to perpetuate by erecting a pyramid on the basis of the triangle 3:4:5? It is difficult to find a better example to illustrate the Pythagorean theorem, which was known to the Egyptians long before its discovery by Pythagoras.

Thus, the ingenious creators of the Egyptian pyramids sought to impress distant descendants with the depth of their knowledge, and they achieved this by choosing as the "main geometric idea" for the pyramid of Cheops - the "golden" right-angled triangle, and for the pyramid of Khafre - the "sacred" or "Egyptian" triangle.

GEOMETRY DEPTH

Let's look at the pyramid of Cheops again. But we will only act not according to algebraic formulas, but from the point of view of geometry.

Many Egyptologists and researchers of the Cheops pyramid assume that the builders of ancient Egypt knew the numerical value of the golden section 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 the knowledge of these numbers is not necessary, since for the construction of the pyramids it is enough to know the proportions of the heptagon and use the ratio of the lines that exist in the geometric figure of the heptagon.

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 EKA heptagon with the apex at point K has a value of 360/7 = 51.429 degrees (51 degrees 25.71 minutes), and the actual angle of inclination of the Cheops pyramid faces has a value of 51 degrees 50 minutes.

The builders of the pyramid of Cheops compensated for the existing difference by adding to the height of the triangle AEK the value of human growth AX. That is, the builders conventionally 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 ECX with the apex at point K. Namely, if the height of the ECX triangle has a value of 318 cubits, then the height of the EKA triangle is approximately 314 cubits, and the value human height approximately 4 cubits. Egyptian builders increased the correct angle of the heptagon, as if there was a person at the top of the pyramid of Cheops, and as a result, the golden ratio was encrypted in the ratios of the EK / KX lines and the proportions of the human body were laid in the general geometry of the future pyramidal structure, which was the idea of ​​​​the architectural design of the future pyramid . In essence, the builders and creators of the architectural plan of the Great Pyramid of Cheops inscribed a double heptagonal or diheptagonal network of lines into a living circle, in which the vertical diameter differed from the horizontal diameter by the relative size of human growth.

The 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 proportions of the male and female bodies. The blue outline indicates the approximate silhouette of the side faces of the pyramid, while the white outline indicates the approximate silhouette of the diagonal edges.

The angle DLA with the apex 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 (slope of the diagonal edges) and EKA (slope of the side faces) with vertices at points L and K differ from the angular values ​​of a regular bigeptagon by the relative size of human height, since the bigeptagon 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 a size of 4 Egyptian cubits and is conventionally located at the top of the pyramid.

INTERESTING EGYPTIAN PYRAMIDS OF EGYPT

The Pyramid of Cheops

One of the most great pyramids in the world. Built by pharaoh Khufu, the second pharaoh of the fourth dynasty, whose Greek name was Cheops. Its height reached 146.6 m, and the size of the base - 230 m. The pyramid consists of blocks of limestone, granite and basalt. Inside it there are 3 burial chambers, which are designed one above the other. The entrance to the pyramid is located at a height of 15 meters on the north side, but tourists enter it through a gap made by Caliph Abu Jafar al-Ma'mun in order to search for countless treasures.

Pyramid of Khafre (or Khafre)

The second largest pyramid of Ancient Egypt, next to which is the sculpture of the world-famous Great Sphinx - a formidable lion with a human head. Its height reached 143.5 m, however, unlike the pyramid of Khufu, its inner space is more modest. There are two chambers and two crossing passages. There is also a burial chamber located under its base.

pink pyramid

One of the most large pyramids in Dahshur and the third largest in Egypt after the two pyramids of Giza. It got its name due to the color of the stone blocks, which acquire a pink tint in the rays of the setting sun. In addition, this structure is considered the first successful attempt to build an isosceles regular pyramid.

The final pyramid in the ensemble of grandiose structures of Giza. It is located 200 m from the pyramid of Khafre, however, it is much smaller in size than its predecessors - only 66.5 m in height. Inside it, two small chambers were also found, but there are no traces of burial. The pyramid has 3 companions, surrounded by a common fence.

CONCLUSION

In the work done, I learned and got acquainted with some of the secrets of the Egyptian pyramids. Coordinated them with mathematics and carried out several tasks. I also found and got acquainted with information about the greatness and features of each Egyptian pyramids.

The art of Ancient Egypt is a reflection of concrete, real reality at different stages of its historical development. The ancient Egyptians considered earthly life to be just a brief episode of eternal existence. That is why for the construction of houses, residences of nobles and royal palaces, they used not very durable materials. Things looked different with the construction of dwellings for the immortal soul of the pharaoh and the nobility, which, like the temples of the gods, were built of stone. The monuments that have survived to this day testify to the strength of these buildings. Egyptian pyramids at Giza, tombs of Egyptian pharaohs. The largest of them - the pyramids of Cheops, Khafre and Mykerin in ancient times were considered one of the Seven Wonders of the World. The construction of the pyramid, in which the Greeks and Romans already saw a monument to the unprecedented pride of the kings and cruelty, which doomed the entire people of Egypt to senseless construction, according to scientists, was the most important cult act and should have expressed, apparently, the mystical identity of the country and its ruler. The population of the country worked on the construction of the tomb in the part of the year free from agricultural work. A number of texts testify to the attention and care that the kings themselves (albeit of a later time) paid to the construction of their tomb and its builders. From ancient times to the present day, many have explored the pyramids, because the builders of the pyramids have not left us any explanation on this matter. The first among such seekers was the indefatigable Greek traveler and historian Herodotus, who, back in the middle of the 5th century. BC e. visited Egypt and suggested that the pyramids were built using wooden machines that lifted blocks from ledge to ledge. What these cars looked like was unknown, apparently, to himself. The very process of their construction remains a mystery to this day - even with modern technology, creating something similar is a difficult task. But the Egyptians did not have any cranes or powerful dump trucks. They did not have not only steel cables, but also the simplest iron tools. But they literally lifted mountains of stone and laid these monoliths with amazing precision. And yet, of greatest interest is the reason for the appearance of such structures, which no one had created before the Egyptians. Why was it necessary to build them so large and at the same time calculate all the proportions with such amazing accuracy? This remains unexplained. https://en.wikipedia.org/wiki/Ancient_Egypt

Encyclopedia "Wonders of the World" V.V. Kiselev, S.V. Andreeva. UDC 087.5 BBK 9 Ch-81

Encyclopedia "I know everything" Z.V. Nikolaevich MFR 98-B

Martin Gardner. Mathematical wonders and secrets - M.: Nauka, 1978. 128 p.

Dictionary

We have developed a research plan 1. Familiarize yourself with the theories about the construction of the pyramid, which are covered in ancient sources and literature. 2. Determine the size of the pyramid. 3. Analyze the methods of building a pyramid. 4. Draw your own conclusions based on the opinions of experts about how the pyramids were most likely built.

Version 1: Wooden machines According to Herodotus, who was the first to describe in detail the pyramids of Giza, Herodotus' slaves were simultaneously employed in the construction of the pyramid of Cheops. Construction went on for 20 years.

Having considered all the proposed versions, we made a comparison. Wooden Cars Inside Out Kites Mound Behind: Great amount people simultaneously employed in construction. Pros: "Strange" cavities under the masonry. Pros: Huge height could be easily overcome without ground lifting devices. Pros: construction of a stone "serpentine" around the outer perimeter of the Great Pyramid. Cons: Herodotus lived in the 5th century BC and was not contemporary with the construction of the pyramids. Stepwise construction Against: It would take the most accurate calculations. Con: Too gigantic block weight, against a light kite. Heaviness. Against: such a road will inevitably interfere with the calculations and measurements carried out during construction. Conclusions: The Great Pyramid of Cheops was most likely built with the help of an embankment, although this could in many ways interfere with the accuracy of the calculations by the architects. According to our assumptions, ancient architects and builders could compensate for these difficulties with their remarkable skill.

There are less and less unsolved mysteries on our planet every year. The constant improvement of technology, the cooperation of scientists from various fields of science reveals to us the secrets and mysteries of history. But the secrets of the pyramids still defy understanding - all discoveries give scientists only tentative answers to many questions. Who built the Egyptian pyramids, what was the construction technology, whether there is a curse of the pharaohs - these and many other questions still remain without an exact answer.

Description of the Egyptian pyramids

Archaeologists talk about 118 pyramids in Egypt, partially or completely preserved to our time. Their age is from 4 to 10 thousand years. One of them - Cheops - is the only surviving "miracle" from the "Seven Wonders of the World". The complex called "The Great Pyramids of Giza", which includes and, was also considered as a participant in the New Seven Wonders of the World competition, but it was withdrawn from participation, since these majestic structures are actually the "wonder of the world" in the ancient list.

These pyramids have become the most visited excursion objects in Egypt. They are perfectly preserved, which cannot be said about many other structures - time did not spare them. Yes and locals contributed to the destruction of the majestic necropolises, removing the lining and breaking out the stones from the walls to build their houses.

The Egyptian pyramids were built by pharaohs ruling from the 27th century BC. e. and later. They were intended for the repose of the rulers. The huge scale of the tombs (some up to almost 150 m high) should have testified to the greatness of the buried pharaohs, things that the ruler loved during his lifetime and which would be useful to him in the afterlife were also placed here.

For the construction, stone blocks of various sizes were used, which were hollowed out of the rocks, and later brick began to serve as the material for the walls. Stone blocks were turned and adjusted so that a knife blade could not slip between them. Blocks were stacked on top of each other with an offset of several centimeters, which formed a stepped surface of the structure. Almost all Egyptian pyramids have a square base, the sides of which are oriented strictly to the cardinal points.

Since the pyramids performed the same function, that is, they served as the burial place of the pharaohs, their structure and decoration are similar inside. The main component is the burial hall, where the ruler's sarcophagus was installed. The entrance was arranged not at ground level, but several meters higher, and was masked by facing slabs. Stairs and corridors led from the entrance to the inner hall, which sometimes narrowed so much that they could only be walked on squatting or crawling.

In most necropolises, burial chambers (chambers) are below ground level. Ventilation was carried out through narrow shaft-channels, which penetrated the walls. Rock paintings and ancient religious texts are found on the walls of many pyramids - in fact, scientists draw some of the information about the construction and owners of the burials from them.

The main mysteries of the pyramids

The list of unsolved mysteries begins with the shape of necropolises. Why was the shape of the pyramid chosen, which is translated from Greek as “polyhedron”? Why were the edges located clearly on the cardinal points? How did the huge stone blocks move from the place of development and how were they raised to a great height? Were the buildings erected by aliens or people who own a magic crystal?

Scientists even argue over the question of who built such tall monumental structures that stood for millennia. Some believe they were built by slaves who died in the hundreds of thousands building each. However, new discoveries of archaeologists and anthropologists convince us that the builders were free people who received good food and medical care. They made such conclusions based on the composition of the bones, the structure of the skeletons and the healed injuries of the buried builders.

All cases of death and death of people involved in the study of the Egyptian pyramids were attributed to mystical coincidences, which provoked rumors and talk about the curse of the pharaohs. There is no scientific evidence for this. Perhaps the rumors were spread to scare off thieves and marauders who want to find valuables and jewelry in the graves.

To the mysterious interesting facts can be attributed to the short time frame for the construction of the Egyptian pyramids. According to calculations, large necropolises with that level of technology should have been erected in at least a century. How, for example, was the pyramid of Cheops built in just 20 years?

Great Pyramids

This is the name of the burial complex near the city of Giza, consisting of three large pyramids, a huge statue of the Sphinx and small satellite pyramids, probably intended for the wives of the rulers.

The initial height of the pyramid of Cheops was 146 m, the length of the side was 230 m. It was built in 20 years in the 26th century BC. e. The largest of Egyptian landmarks has not one, but three funerary halls. One of them is below ground level, and two are above the base line. Intertwining corridors lead to the burial chambers. On them you can go to the chamber of the pharaoh (king), to the chamber of the queen and to the lower hall. The chamber of the pharaoh is a chamber made of pink granite, has dimensions of 10x5 m. A granite sarcophagus without a lid is installed in it. Not a single report of scientists contained information about the mummies found, so it is not known whether Cheops was buried here. By the way, the mummy of Cheops was not found in other tombs either.

It still remains a mystery whether the Cheops pyramid was used for its intended purpose, and if so, then apparently it was plundered by looters in the past centuries. The name of the ruler, by whose order and project this tomb was built, was learned from the drawings and hieroglyphs above the burial chamber. All other Egyptian pyramids, with the exception of Djoser, have a simpler engineering device.

Two other necropolises in Giza, built for the heirs of Cheops, are somewhat more modest in size:

Tourists travel to Giza from all over Egypt, because this city is actually a suburb of Cairo, and all transport interchanges lead to it. Travelers from Russia usually go to Giza as part of excursion groups from Sharm el-Sheikh and Hurghada. The trip is long, 6-8 hours one way, so the tour is usually designed for 2 days.

The great buildings are available for visiting only during working hours, usually until 17:00, in the month of Ramadan - until 15:00. It is not recommended to go inside for asthmatics, as well as people suffering from claustrophobia, nervous and cardiovascular diseases. Be sure to take drinking water and hats with you on the tour. The tour fee consists of several parts:

1. Entrance to the complex.
2. Entrance inside the pyramid of Cheops or Khafre.
3. Entrance to the Museum of the Solar boat, on which the body of the pharaoh was transported across the Nile.

Against the backdrop of the Egyptian pyramids, many people like to take photos while sitting on camels. You can bargain with camel owners.

Pyramid of Djoser

The first pyramid in the world is located in Saqqara, near Memphis - former capital Ancient Egypt. Today, the pyramid of Djoser is not as attractive to tourists as the Cheops necropolis, but at one time it was the largest in the country and the most complex in terms of engineering.

The burial complex included chapels, courtyards, and storage facilities. The six-step pyramid itself does not have a square base, but a rectangular one, with sides of 125x110 m. The height of the structure itself is 60 m, inside it there are 12 burial chambers, where Djoser himself and members of his family were supposedly buried. The mummy of the pharaoh was not found during the excavations. The entire territory of the complex of 15 hectares was surrounded by a stone wall 10 m high. At present, part of the wall and other buildings have been restored, and the pyramid, whose age is approaching 4700 years, has been preserved quite well.

When referring to the Egyptian pyramids, as a rule, they mean the Great Pyramids located in Giza, not far from Cairo.

The largest of them is the pyramid of Cheops, the second pharaoh of the IV dynasty. This pyramid is still the largest architectural creation of human hands. At the base, it is a square with a side of 227.5 meters. The height during construction is 146.6 meters, and now the pyramid is 9 meters lower: the upper stones fell during earthquakes.

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The Pyramid of Cheops

Even in ancient times, the pyramids of Giza were considered one of the seven "wonders of the world." But even today they are able to hit anyone. The largest of them is the pyramid of Cheops, the second pharaoh of the IV dynasty. This pyramid is still the largest architectural creation of human hands. At the base, it is a square with a side of 227.5 meters. The height during construction is 146.6 meters, and now the pyramid is 9 meters lower: the upper stones fell during earthquakes. The construction of the pyramid (and it was completed around 2590 BC) took 2.3 million stone blocks weighing two and a half tons each. The total volume of the pyramid is 2.34 million cubic meters. The faces of the pyramid are oriented to the cardinal points, and their angle of inclination to the base is 51o52". The entrance is located on the north side. Separate blocks, according to the Arab historian Abdel Latif (XII century), fit so precisely to each other that it is impossible to slip between them blade of knife.

There are no inscriptions or decorations inside the Cheops pyramid. There are three burial chambers. The burial chamber of the pharaoh is a room about 11 meters long, five meters wide and almost six meters high. The walls of the tomb are finished with granite slabs. The red granite sarcophagus is empty. Neither the pharaoh's mummy nor grave goods have been found. It is believed that the pyramid was plundered in ancient times.

On the south side of the pyramid is a structure shaped like a ship. This is the so-called Solar Boat - one of the five on which Cheops was supposed to go to the other world. In 1954, a boat 43.6 m long, disassembled into 1224 parts, was discovered during excavations. It was built of cedar without a single nail and, as evidenced by traces of silt preserved on it, before the death of Cheops, it was still floating on the Nile.

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"Horizon of Khufu" is the name of the Pyramid of Cheops.

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Pyramid of Khafre

The second largest pyramid of Giza belongs to the pharaoh Khafre. It was built 40 years later than the first one. Sometimes it seems that the pyramid of Khafre is even larger than that of Cheops. In fact, it is slightly smaller. The side of the square base of the Khafre pyramid is 215 meters. Height - 136 meters. However, in ancient times, like the pyramid of Cheops, it was 9 meters higher. The angle of inclination is sharper than that of the first pyramid: 53o8 ". Here, the entire complex of structures is more clearly visible, consisting of a temple in the valley, a road, a temple of the dead and the pyramid itself. The lower temple, in which 25 statues of pharaohs once stood, is known for that here, on the threshold of the kingdom of the dead, Khafre was mummified

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Pyramid of Menkaure

The pyramid of Menkaure completes the ensemble of the great pyramids of Giza. Its construction was completed in 2505 BC. This pyramid is much smaller than its predecessors. The side of the base is 108 meters, the original height is 66.5 meters (today - 62 m), the angle of inclination is 51o. The only burial chamber of the pyramid is carved into its rocky base, emphasizing the greatness of the pyramids of Cheops and Khafre. The latter are not difficult to distinguish from each other: at the pyramid of Khafre, near the top, a white basalt lining is partially preserved.

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Project Ancient Egypt - a country of sphinxes and pyramids. HYPOTHESIS The ancient pyramids of Egypt contain a great many secrets and mysteries. Until today, scientists have assigned the pyramids only the role of the sarcophagi of the pharaohs - the rulers of the country and the Egyptian priests. People neither in former times nor now could understand for what purposes and for whom these gigantic temples were erected. Question: Is it possible to unravel the mysteries of the Egyptian pyramids? Objective of the project:

• Explore the mysteries and mysteries of the Egyptian pyramids.

Project objectives:

• Why were the pyramids built?
• Find out how and from what the pyramids were built?
• What methods of building pyramids were used in the creation of the pyramids?
• What does the Sphinx symbolize?
• Find out what mysteries are kept in the Egyptian pyramids?

Group 1: Why were the pyramids built? PYRAMIDS - "HOUSES OF ETERNITY"

• Ancient Egypt explains this by the special meaning that they had in Ancient Egypt funeral cults closely associated with the widely developed cults of the dying and resurrecting deities of the nature of the world and Ancient Egypt. Naturally, the king and the slave-owning nobility of Ancient Egypt, who played the main role in these cults, paid special attention to securing their posthumous "eternal life", and, consequently, to the construction of solid tombs. earthly, and a dead person needed shelter and food just as much as a living one; the tomb was thought to be the home of the deceased. From this was born the desire in ancient Egypt to preserve the body of the deceased, or at least the head.
• So, the tomb in ancient Egypt - the house of the deceased - was supposed to serve as such a room where the mummy would be in complete safety, where the statue of the deceased would be placed and where his relatives could bring everything necessary for his food.

THE FIRST PYRAMIDS The Egyptian pyramids are World Heritage Sites. Now Egyptologists have 108 pyramids. But surprisingly, it was not the Egyptians who were the first to build the pyramids. The first stepped pyramids, called ziggurats, appeared in ancient Ur and Babylon, around the time (c. 2750 BC) when the Second Dynasty ruled in Egypt. But the "correct" pyramids are a purely Egyptian invention, dating back to about 2550 BC, during the reign of the Fourth Dynasty. Group 2: How were the pyramids built? HOW WERE THE PYRAMIDS BUILT? The pyramid consists of two million three hundred thousand cubic limestone blocks with smoothly polished sides. It was calculated that each block weighs an average of 2.5 tons, and the heaviest - 15 tons. The total weight of the pyramid is about 5.7 million tons. Its stones are held by their own weight - there is no binding material. Despite this, the blocks are so carefully fitted to each other that the gap between them is no more than five millimeters. Such skillful work of masons is surprising. After all, it was made mainly with stone tools. The architect of this pyramid is also known - Khemuin. Researchers were perplexed as to how the ancient builders could erect such grand building, and even not just erect, but give it a geometrically correct pyramid shape. How were the pyramids built? Now there is an opinion that the vast majority of the blocks of the great Egyptian pyramids are made of concrete. After many centuries, it becomes difficult to distinguish concrete blocks from those cut from the same rock, as they collapse, weather and take on the appearance of "natural stones". In the 80s. 20th century French chemist, Professor of the University of Bern Joseph Davidovich, analyzing the chemical composition of the "monoliths" of which the pyramids are composed, suggested that "they are made of concrete." Davidovich identified 13 components from which concrete could be prepared. The theory of making blocks for building pyramids as presented by Davidovich looks like this. Workers rubbed soft rock with primitive millstones or graters. Then it was dried, poured into baskets and transported to the construction site. Several porters were carrying baskets of powder upstairs. At the top, a wooden formwork was prepared, filled with a mixture of powder. Water was poured, the solution was stirred. After the block hardened, the formwork was removed. Moved on to the next one. This is how the pyramid grew. Moreover, in the manufacture of giant blocks, it was not at all necessary to make them entirely from a solidifying liquid solution. Why was the pyramid shape chosen?

• The shape of the pyramid has miraculous properties.
• In particular, it was found that not only the shape of the pyramid is important, but also its proportions, as well as the orientation of the pyramid to the cardinal points.
• Numerous studies show that the maximum effects are manifested in the geometric center of the pyramid and above its top.
• Note that in the geometric center of the Great Pyramid, the Grand Gallery ends - one of the most impressive and carefully executed "details" of the pyramid. Here begins a horizontal passage to the so-called "king's chamber", replete with multiple incomprehensible details: height differences, grooves in the walls, a granite lintel, etc.
• On the other hand, it was at the top of the Great Pyramid, according to Egyptian mythology, that its most important element was located - the stone Ben-Ben.

MYSTERIES OF THE GREAT PYRAMID OF CHEOPS (PI) Why did the ancient architects achieve such high accuracy, if this accuracy could not even be seen with a simple eye? One of the answers to these questions, perhaps, lies in the desire of ancient architects to encrypt some fundamental numerical values ​​in the dimensions of the Great Pyramid. And this requires high dimensional accuracy. As a result, for example, the ratio of the length of the base of the pyramid to its height, divided in half, gives the famous number "pi" (the ratio of the circumference to its diameter) to six decimal places! This number is mentioned in the ancient Egyptian papyrus Rinda (kept in the British Museum in London). Perhaps it is deliberately encrypted in the size of the Pyramid of Cheops, and with a more accurate value than the great Archimedes, who lived 2000 years later, knew it! This idea inspired enthusiasts to search for other fundamental ratios in the Pyramid of Cheops. LENS PYRAMID American engineer Raymond D. Manners, in an article published in the magazine "Fate" for November 1996, reports that in its original form the Pyramid was distinguished by two features: sparkling surfaces and ... concave in the middle part of the face! The ancient builders covered the Pyramid with a layer of polished limestone 2.5 meters thick! There were 144,000 20-ton cladding stones. They were so brilliant that they could be seen hundreds of kilometers away. In the morning and at noon, the sunlight reflected from this vast mirror surface was visible from the moon. SO WHAT IS INSIDE THE GREAT PYRAMID OF CHEOPS? At present, the main entrance to the Pyramid is the entrance pierced by the Arabs. The real entrance is higher, seventeen meters above the ground and seven meters east of the main north-south axis. The entrance tunnel has a section of 1.04m x 1.19m and is clamped by floor blocks 2.6m thick, 3.6m wide and a floor slab 0.76m thick and 10m long. From the entrance, a tunnel leads to the center of the pyramid, to the rocky foundation on which it rests, and further into the depth of 105.15 meters. In addition, there is a section of the corridor 45 meters long. Then he changes direction to horizontal and goes 8.83 meters. PYRAMIDS ARE LIKE THE STARS To be more precise, these stars are: Mizar and Kochab, in the constellations Ursa Major and Ursa Minor. Today's "northern" star - the Polaris - in those years did not point to the north at all, and could not serve as a guide for the Egyptians. It is not known whether the ancient architects really determined the direction to the north by two stars, but there is no argument against the fact that they could do this. All we know for sure is that the pyramids aligned to the north because the Egyptians believed that a dead pharaoh became a star in the northern sky. Therefore, it is quite logical to assume that when building pyramids for the dead pharaohs, they looked towards their new home. years - 75 years more than previously thought. Third group: What does the Sphinx symbolize? THE GREAT SPHINX The Great Sphinx is a mysterious creature with the body of a lion and the head of a man, carved from solid stone. The length of the Sphinx from the tip of the paws to the tail is 57.3 meters, the height is 20 m. It is believed that the Sphinx was cut down during the construction of the Khafre pyramid, and its face bears the features of this pharaoh. According to one version, the Sphinx in the last century was fired from guns by Napoleon's gunners. According to another, the Mamluks, who ruled at one time in Egypt, fired at the Sphinx from cannons. In Egypt, during the period of the Middle and New Kingdoms, sphinxes were often depicted with the head of a ram or a falcon. However, the Great Sphinx at Giza is the oldest of the Egyptian sphinxes. Apparently, sphinxes played the role of guardians of sacred places. Myths and legends of the Sphinx

• This majestic monument is fraught with many secrets and mysteries, for thousands of years it was shrouded in myths and legends, it was worshiped and feared, it saw the change of eras and civilizations, and only it, the Sphinx of Giza, remained imperishable and silent keeper of the secrets of the distant past.

LEGENDS

• 1. Once he was considered an eternal god. Then he fell into the trap of oblivion and fell into an enchanted dream. What secret does this majestic guardian keep? In the myths of the ancient Greeks, the Sphinx is a monster generated by Typhon and Echidna, with the face and chest of a woman, the body of a lion and the wings of a bird. The Sphinx was located on a mountain near the city of Thebes and asked each passerby a riddle - "Which of the living beings walks on four legs in the morning, on two in the afternoon, and on three in the evening?" childhood, maturity and old age. After that, the Sphinx threw herself off the cliff.

LEGENDS

• 2. Another legend tells that this huge predator guards the peace of the pyramids day and night, and with the help of the "third eye" monitors the circulation of the planets, Sirius and the rising of the Sun, feeding on cosmic power. In exchange for this, he had to make sacrifices. 3. Another legend says that a giant statue of a mysterious beast guards the "elixir of immortality." According to legend, the founder of esoteric knowledge, Hermes Trismegistus, owned the secrets of making a "philosopher's stone", with which metal could be turned into gold. Also, the "philosopher's stone" was the basis for creating the "elixir of immortality." According to legend, Trismegistus was the son of an Egyptian god named Thoth, who built the first pyramid on the banks of the Nile and erected the Sphinx next to the pyramid complex in Giza, designed to protect the recipe for the "elixir of immortality" that was hidden in its depths.

LEGENDS

• 4. Initially, in the myths, the Egyptian Sphinx retained the features of a lion with the head of a man. He wandered along the roads near Parnassus, devouring passers-by. In the myths of the ancient Greeks, the Sphinx is a monster spawned by Typhon and Echidna, with the body of a lion, the face and chest of a woman, and the wings of a bird. located on a mountain near the city of Thebes, the Sphinx asked each passerby a riddle - "Which of the living beings walks on four legs in the morning, two in the afternoon, and three in the evening?" Those who failed to solve the riddle, the Sphinx killed. Oedipus managed to give a guess - "A man in childhood, maturity and old age." Then the Sphinx threw herself off the cliff. 5. The Arabs living in this area called the statue Abul Hol, which means "father of horror." As philologists have established, the full name of the statue meant "the living image of Khafre." Thus, the Sphinx was the incarnation of King Khafra with the symbols of royal power and the body of the king of the desert. Therefore, in the understanding of the ancient Egyptians, the Sphinx in one person was a god and a lion guarding his pyramid.

LEGENDS

• Many mystical teachings and magicians of all times have tried to find magical explanations for the purpose of the sphinx. Here is what the classic of the occult Eliphas Levi wrote in his History of Magic: “Hermes Trismegistus formulated his symbol, called the Emerald Tablet: “What is below is like what is above, and what is above is like what is below, for actions of miracles of one essence. Light is Isis or the moon; fire is Osiris or the sun; they are the mother and father of the great Tellus, and she is the universal substance. Hermes Trismegistus states that these forces reached their absolute manifestation at the moment when the earth was created. The four manifestations of a single substance were represented by the Sphinx. Its wings corresponded to the air, the bull's body to the earth, the female breast to the water, and the lion's paws to the fire. This is the secret of the three pyramids guarded by the Sphinx with square bases and triangular faces. In erecting these monuments, Egypt tried to erect the Herculean pillars of universal science.

Sensations of the secrets of the Sphinx, discovered during its renovation

• Time has spared this great monument ancient history but the people treated him much less respectfully. One Egyptian ruler ordered to beat off the nose of the Sphinx. At the beginning of the 18th century, the giant's face was fired from a cannon, and Napoleon's soldiers fired into his eyes from guns. The British beat off the stone beard and took it to the British Museum.
• Today, the acrid smoke of Cairo factories and car exhausts destroy stones. In 1988, a huge block weighing 350 kilograms broke off from the neck of the Sphinx and fell. The disrepair of the sculpture caused concern among UNESCO. Refurbishment began, sparking renewed interest in the mysteries of the Sphinx and the opportunity to re-explore the grandiose sculpture. The discoveries were not long in coming.

• The first sensation: Japanese archaeologists led by Professor Yoshimura, using special instruments, first illuminated the array of the Cheops pyramid, and then examined the stones of the Sphinx. The conclusion was striking: the stones of the sculpture are older than the blocks of the pyramid.
• The second sensation was the discovery under the left paw of a stone lion of a narrow tunnel leading towards the pyramid of Cheops.
• The third sensation: on the Sphinx, traces of erosion of a large flow of water that moved from north to south were found. It was not a flood of the Nile, but a biblical catastrophe that occurred about eight to twelve thousand years BC.
• The fourth sensation: French archaeologists made a curious remark: the dating of the Egyptian stream coincides with the date of the death of the legendary Atlantis!
• Fifth sensation: The face of the Sphinx is not the face of Khafra.

• It is believed that the Sphinx was built by Pharaoh Khafre 4.5 thousand years ago. For more than half of its life, the sphinx was buried up to its neck in sand. Since it was badly damaged by erosion, the idea of ​​a greater antiquity of the sphinx arose: erosion from water, and not from sand and wind. Geological research has shown the same. 10 thousand years ago there were lakes in the Sahara. Schock and West presented their findings at the annual conference of the Geological Society of America. A fierce debate ensued between geologists and Egyptologists. The front and sides are more susceptible to erosion. Whereas the back is smaller, which means it was most likely made later. The front is twice as old as the back. How old is the Sphinx? At first glance, the face of the sphinx is absolutely similar to the face of Pharaoh Khafre, which seems to prove the time of its creation. But a detailed analysis of all the parameters showed that the face of the sphinx and the face of the pharaoh are not identical. Proportions and shapes do not match. And special studies were made that proved that the faces on the sculpture of Pharaoh Khafre in the Cairo Museum and the face of the Sphinx are different.

Findings:

• The Sphinx has always been considered the guardian of knowledge, the guardian of the portal leading to the world of higher intelligence, a symbol of the strength of human nature ... The personification of the unity and balance of the forces of the nature of the earth with the higher forces that live in the Universe. All connected in the Great Sphinx. The perfect symbol of dedication to eternal life. And the mystery of the origin of the Sphinx goes back to time immemorial. What do we know about those times? Practically nothing, but the legends and myths that have survived to this day raise many questions and, in practice, do not give answers to them. However, it can be assumed that in the depths of centuries a highly developed civilization existed on our Earth, and its representatives, possessing advanced science, could foresee the coming catastrophe and try to preserve their knowledge for future generations. One of the ancient legends says: "When the Sphinx speaks, life on Earth will descend from its usual circle." But while the sphinx remains silent...
• When was it built? When was it reconstructed? In honor of whom and by whom it was created ... Most likely, there will never be exact answers to these questions ... After all, the deeper science advances, the more questions arise ...

Fourth group: What mysteries do the Egyptian pyramids keep in themselves? ? MYSTERIOUS MINE

• The famous archaeologist John Kinnaman, before his death in 1961, spoke about an amazing adventure that happened to him in his youth. According to him, in 1924 he visited a previously unknown tunnel under the pyramid of Cheops. He stumbled on the entrance to it quite by accident. The scientist claims that after the tunnel he ended up in a room filled with numerous mechanisms of unknown purpose.
• In 1945, 20 years after Kinnaman's adventure, the son of the king of Egypt, Prince Farouk, wandered around the pyramids. By chance, he pressed some kind of slab at the base of the Sphinx. Unexpectedly, a hidden mechanism was activated, and the entrance to the tunnel opened, which led down to large rooms. There, according to the prince, there were ... robots.
• And in 1998, between the Sphinx and Khafre's pyramid, 250 meters from the base of Khufu's pyramid, a mysterious mine filled with water was discovered.

? CONSTRUCTION OF THE PYRAMIDS

• Archaeologist and surveyor Flinders Petrie, having examined the pyramids, made his conclusions about the technology of their construction. According to Petri, the ancient craftsmen had at their disposal tools of a class “which we have only recently reinvented,” for example, saws at least 2.5 meters long, made of bronze, and their cutting edges are equipped with diamonds.
• Even greater mystery surrounds the processing of the inner cavity of the sarcophagus. To do this, the Egyptians had to "switch from reciprocating to rotary cutting, as if turning the saw into a pipe." Naturally, none of the Egyptologists managed to find the diamond drills and saws themselves. However, the nature of the surfaces processed by drilling and sawing convinced him of the existence of such tools among the ancient Egyptians.
• What kind of tool this is, how they worked with it, how they maintained such high accuracy - remains a mystery.

? THE CURSE OF THE PYRAMIDS

• One strange feature was noticed behind the Egyptian pyramids: they are capable of destructively influencing the most modern and accurate equipment. According to some reports, up to 80% of electronic devices that have been near the pyramids fail. Old Cairoans say that during the 1967 Arab-Israeli war, three Israeli planes that tried to fly low over the pyramids of Giza, one after another, for a completely incomprehensible reason, crashed into the sand. Ordinary Arabs explain this by the "curse of the pharaohs."

?«PYRAMID EFFECT»

• The French scientist Jacques Bergier built a cardboard model of the Pyramid.
• Scientists have made sure that perishable products are stored for a long time in the Pyramid model.
• A pendulum suspended above the top of the model swings to the side or rotates slowly around the top.
• Plants first gravitate to the east, then describe a semicircle, moving from south to west.
• The Czech inventor Karel Drabal adapted a similar model for self-sharpening razor blades in 1959, and received a patent for this unusual invention. According to Drabal, he shaved with the same blade, placing it overnight in a model, more than two thousand times! It is believed that the pyramidal shape captures cosmic energy.

? PYRAMIDS - CHRONOLOGICAL LIGHTHOUSE OF THE MEMORIAL DATE

• With the help of a computer, it was possible to reconstruct the starry sky above Great Pyramid in 2500 BC. It turned out that in those days one of the southern corridors of the Pyramid of Cheops was exactly directed to the star Sirius, identified by the Egyptians with the Goddess Isis. Another southern corridor pointed to the lower of the three stars that made up Orion's Belt, a constellation believed to be the abode of the god Osiris, who brought civilization to the Nile Valley.
• The use of a computer made it possible to calculate the time of the exact coincidence of the Orion Belt and the three largest Egyptian pyramids - this moment belonged to 10642 - 10546 BC. e., although all three pyramids were completed around 2500 BC, the plan of the Giza complex was drawn up 8000 years earlier! It was passed down from generation to generation until the time when it was possible to combine the inner corridors with the direction to the desired stars!.

?PYRAMIDS - REPOSITORIES OF KNOWLEDGE

• In the pyramid complex, the language of geometry tells about the mathematical, astronomical and geographical knowledge of the ancient Egyptians - from the number "pi" to the diameter of the globe.

FINDINGS

• Based on the information studied, students came to the conclusion that the secrets of the Egyptian pyramids have been of interest to scientists since time immemorial. There are many different theories about the origin, construction of the pyramids, their mysteries.
• And at the present stage, many secrets remain unsolved.

Informational resources

• Art of the countries of the East. - M., 1986
• Encyclopedia for children.- M., 2000. Vol.1
• Chemist I.A. How to teach world artistic culture. - M., 1994
• big department world history. General history of arts. http:\\artyx.ru
• Visual arts: history, styles. ya, styles. http:\\www/arhystory.ru
• Story ancient world. Electronic supplement to the textbook for grade 5 http:\\www/ancienthistory.srb.ru