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Pyramid of khufu Mathematics Examination
The direction of the Great Pyramid is extremely accurate, with four bases facing due east, due west, due south and due north respectively. Its error is less than 0.0 15%, and it is still one of the most accurate buildings on the earth.

The original height of the Great Pyramid is146.7m, and the base circumference is 9210.5m. The ratio of base circumference to height is 2π, which is twice that of the well-known pi (3. 14 16). In history textbooks, pi is Greece more than 200 BC.

Mathematicians first discovered it. However, this formula was embodied in the construction of the Great Pyramid as early as 4000 years ago.

It's not surprising that only π is used. A more thought-provoking question is: Why did the ratio of base to height of the Great Pyramid choose 2π instead of other coefficients?

According to the reliable data obtained by satellite surveying the earth, the radius of the northern hemisphere (from the equator to the North Pole) is 6356 kilometers, which is 43200 times the height of the Great Pyramid 146.72 meters. The equatorial circumference of the earth is 40075.5 kilometers, which is reduced by 43200 times to 927.67 meters, which is only 6. 17 meters away from the base circumference of the Great Pyramid of 92 1.5 meters, that is, the error is only 0.3%. According to this, some scholars believe that the ratio of the height of the Great Pyramid to the perimeter of its base is actually 43,200 times that of the northern hemisphere of the earth. As for the error of 0.3%, it may be the result of not counting the irregular protruding part of the equator.

Moreover, it must be pointed out that the number 43200 is not arbitrarily set, but related to the precession of the earth. The so-called precession movement refers to the position movement of vernal equinox on the ecliptic caused by the periodic change of the earth's rotation axis. This kind of movement speed is very slow. It only moves 1 degree every 72 years. Every 2 160 30 degrees is a constellation, and every 4,320 60 degrees is two constellations. Therefore, astronomers often refer to numbers such as 72,2160,4320 as precession. According to historical records, precession was first discovered by the Greek astronomer Hippocrates in 129 BC, but it has already appeared in the proportional relationship between the Great Pyramid and the earth.

The internal structure of the Great Pyramid is also full of mathematical mysteries. For example, the King's Hall, the most important room in the tower, is located in the center of the tower, both vertically and horizontally. Viewed vertically, it is only half the height of the tower. Seen from the cross section, the building area of Wangdian is just half of the whole cross section area. The Wangdian Building is 1 1.38m long and 5.69m wide, and the length unit of ancient Egypt is 20x 10 elbow. And its wall height is 5.82 meters, which is 1 1. 18 cubits. If calculated from the ground center, it is exactly equal to1.618m, which is the so-called golden ratio. This ratio has been proved to be the most harmonious ratio seen by human eyes. It is well known that it was discovered by the Pythagorean school in ancient Greece, and the Greeks proudly used it when building the Parthenon. But as early as two thousand years ago, it already existed in the palace of the Great Pyramid.

Marx once said that a science can only be perfect if it can be expressed by mathematics. Because mathematical language is a language that transcends specific words and cultural forms, and it is a language that any wisdom can feel. The frequent appearance of mathematical language in the Great Pyramid makes us feel that this is the information left by a highly developed civilization. It tells us that the designers of the Great Pyramid not only have profound mathematical attainments, but also seem to have measured the earth, mastered the basic structure of the earth and the solar system, and have a deep understanding of precession.

But in this distant prehistoric times, humans have not invented Arabic numerals, nor do they know the purpose of "0". At that time, who could have such profound knowledge of mathematics and astronomy?

The mystery of mathematics has not yet been solved, and another bigger question has surfaced in people's minds: how did the ancient Egyptians build this huge building?

The Great Pyramid consists of 2.6 million huge stones, each weighing several tons to dozens of tons. There is no cement or mortar between the stones. According to records, the surface of the Great Pyramid was originally covered with a layer of polished facing stone, about * * * 1 15000 pieces, each weighing about 10 ton. However, after the 130 1 earthquake, these stones were removed by the then rulers and used as stones for the reconstruction of Cairo. At present, only the bottom of the Great Pyramid and the top of the Kafra Pyramid have a few decorative stones. But even after the decorative stones disappeared, the cooperation between the stones inside the Great Pyramid was still very close, and even sharp blades could not be inserted. At that time, people had no metal tools. How did the builders process these huge stones?

The Great Pyramid is not a simple pile of stones, but a complex tunnel and atrium. In order to maintain the 2π relationship between the base perimeter and the tower height, the inclination angle of the Great Pyramid is set at 52 degrees. Correspondingly, all the tunnel angles in the tower are 26 degrees, which is exactly half of 52 degrees. This is obviously based on the careful design of surface dynamics, and it is also in line with architectural principles. However, in construction, if such an angle is encountered everywhere, it must be calculated according to trigonometric function. Especially the big tunnel leading to the royal family, the ground is 47 meters long and 2. 1 meter wide, which is a cantilever building with an angle of 26 degrees from top to bottom. This is an almost impossible miracle in construction engineering.

Although the Great Pyramid is huge, its precision in construction technology is extremely subtle. The average length of its base is 230.35 meters, and the error between the longest side and the shortest side is less than 0.2 meters, that is, the error rate is less than 0. 1%. However, the error between its four angles and the theoretical absolute 90-degree right angle is only 2 seconds. Even in modern buildings that use all kinds of the most advanced instruments, this is almost impossible.

Also, there is no trace of the torch being used in the corridors and cloisters of the Great Pyramid, or in rooms such as the royal family and the back room. How did the builders at that time illuminate the inside of the pyramid? You know, there is almost no natural light in the depths of the pyramids, and unless the lighting problem is solved, construction will be empty talk.

In the construction of the Great Pyramid, there are too many incredible precisions, too many "impossible" and impossible answers.

Pyramid, a miracle of the world, is also a problem of the world.

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