Egyptian Pyramid and Mathematics Abstract: Mathematics, as an important part of human civilization, has a very long history. So, when was the subject of mathematics born? As one of the four cradles of human civilization, the superior geographical position of ancient Egypt prompted them to develop agriculture. Due to the needs of agricultural production, we have accumulated rich experience from long-term practical activities such as irrigation, measuring field area, calculating warehouse volume, calculating calendars suitable for agricultural production, and related wealth calculation and product exchange, and gradually formed corresponding technical knowledge and related mathematical knowledge. Objectively speaking, as far as the source of foreign mathematics development is concerned, ancient Egypt is the first. Keywords: pyramid data architectural knowledge (geometry) Egyptian mathematics 1. The historical and cultural background of ancient Egypt (ancient Egypt) generally refers to the Egyptian civilization in the lower reaches of the Nile during the period from the 32nd century BC to the 343rd BC when Persia perished. As early as 3 100 BC, Upper Egypt and Lower Egypt were unified by menes in the south, and the first slavery dynasty was established. Ancient Egypt, with one of the longest rivers in the world, is a typical hydraulic empire. Its geographical position is not much different from that of Egypt today. Hunting, fishing and animal husbandry were the most primitive ways of making a living in ancient Egypt. The annual flood of the Nile brought fertile silt to this valley, and the ancient Egyptians who lived by nomadic people settled in this land and changed from hunting to farming. With the development of agriculture, handicrafts and trade have also developed rapidly, which has led to the accumulation of knowledge in various disciplines of natural science. As one of the four ancient civilizations in the world, Egypt has a long history and ancient culture. Second, the mysterious data of the pyramid When it comes to Egypt, everyone will naturally think of the pyramid, one of the seven wonders of the world. Pyramid of khufu, located in Giza province near Egypt, is the largest pyramid in Egypt, which was built around 2500 BC. The pyramid consists of about 2.3 million stones, and the outermost stone is about 1 15000, taking the average. As big as a car, even more than 15 tons, if these stones are cut into small pieces with an average of one cubic foot and lined up along the equator, their length is equivalent to two-thirds of the circumference of the equator. The pyramid as a whole is quadrangular, with the square bottom facing the four positive directions of east, west, north and south, with a side length of 230.5 meters and an error of less than 20 cm. Tower height 146.6m (now about 137m), which is equivalent to 40 stories high. With such a low error rate, even using the most accurate base building on the earth now makes no difference; What is even more surprising is that the height of the Great Pyramid of Khufu times one billion equals the distance from the earth to the sun. 3. It is conceivable that the ancient Egyptians accumulated rich geometric knowledge in the process of building these huge buildings. How was such a mysterious and huge pyramid built? How is the geometric knowledge contained in it created? The Nile often overflows and floods fertile land. When the land boundary is destroyed, the rulers have to levy grain taxes according to different quantities, so they must re-measure the land. In fact, the geometry of Egypt comes from this. Herodotus, a Greek historian (about 484 BC-424 BC), clearly pointed out in his book Herodoti Historiae: "Sesotris distributed the land of Egypt to all Egyptian residents. He distributed square land of the same size to all people and asked the landowner to pay him rent every year as his main tax. If the river overflows, the king will send someone to investigate and measure the area of the lost area. So his rent will be collected according to the reduced land area. I think it is precisely because of this practice that the king sent people to survey and measure the area of the lost land. The Greek mathematician Democritus (about 460 BC-357 BC) also pointed out: "I have to believe that almost all Egyptians can draw figures to prove all kinds of straight lines, and everyone is a pioneer in drawing rope boundaries. "I think the so-called pioneer of drawing lines probably refers to the related measurement problems with drawing lines as the main tool. In order to develop agricultural production, Egyptians must pay attention to the flood cycle of the Nile. In practice, they have accumulated a lot of astronomical knowledge and mathematical knowledge. For example, they noticed that when Sirius and the sun appeared at the same time, it was a sign that the Nile flood was coming. They think that the interval between two mornings in Sirius is one year, including 365 days. They divide the year into 12 months, and each month has 30 days and nights. They gradually understood how to measure time with a sundial. About 1500 BC. Egyptians have used the water bell-leaky tank, which is a container with a hole in the bottom. Fill this container with water, and take the time when the water flows out of the hole below as the unit to calculate the time, which is somewhat similar to the old hourglass timing method in China that we are familiar with. I think all this implies the calculation of building a famous pyramid. Fourth, the construction of architectural knowledge (Geometry) must have a lot of preface work before the construction of the Golden Pagoda. Let's imagine what happened when the pyramids were built. First of all, we assume that a plan must be drawn before the pyramid is built. This may be the first floor plan in the world. From the analysis, the cartographer must know that the pattern and the completed building are different in size, but the shape is the same. It can be judged that the Egyptians at that time had mastered the knowledge of proportion and similarity. The knowledge of similar triangles that we learned in middle school may be created here! After drawing the floor plan, a large clearing should be leveled out, and the actual size should be set out on the ground to prepare for construction. Building materials are large stones weighing several tons, and a pyramid needs many such stones. At that time, transportation had not been invented, and there was no such road. Only stones can be transported as close as possible along the Nile by boat, and then transported to the construction site by rolling logs. It can be seen from here that they have already known and applied the principle that the friction force is smaller when rolling friction is used instead of sliding friction in the physical knowledge we have learned. Every stone must be chiseled and ground according to a certain shape in advance. Every corner of the stone should be repeatedly corrected to a right angle with a triangular plate. Then, lay a huge stone as the foundation. The second floor should be smaller according to a certain proportion, and each floor should be placed in the middle of the next floor. In this way, add one layer at a time, reduce equally on all sides, and finally meet accurately at the top of the tower. How to draw a right angle accurately is probably the biggest problem that the ancient Egyptians have to solve. Because the foundation of the pyramid must be strictly square, and the four corners must be strictly right angles; No matter which angle is slightly deviated, the whole building will be deformed. At that time, measuring instruments had not been invented, and it was not easy to make a square as big as one kilometer in circumference! Then, to check whether one side of the wall or boulder is upright, how to make a right angle in the air? I think it is very common to see those craftsmen using hammer lines in rural areas now, that is, one end of a rope is tied with a hammer, and the other end is fixed on the wall to let the hammer line swing freely, and when it stops, it is at right angles to the ground. If the wall can be parallel to the hammer line, it is perpendicular to the ground. This method is simple and practical, and the hammer line is very simple to make. I think the ancient Egyptians may have skillfully used the hammer line. In Egypt, the main unit of length is the wrist ruler, that is, the length from the elbow to the tip of the middle finger. In rural areas, when farmers build their own huts, they usually use steps, such as "This house is six steps long and four steps wide". But when the pyramid was built, there were thousands of people, and everyone had different steps. So, they stipulated the length of someone-it is said that this person was a certain part of the king's body at that time, as a standard unit; Then, according to this standard unit, a certain length of wooden strips or metal strips are made as general measuring tools. This is the earliest ancestor of the ruler we are familiar with today. It took hundreds of thousands of people and millions of boulders to build a pyramid, and it took decades to make no mistakes. You see how brilliant the ancient Egyptians were in design, calculation, measurement and construction! Later, the mathematician measured the height of the pyramid. There are many mysteries about the measurement of pyramids, which have been puzzling scientists all over the world. There was once an Englishman named John who carefully calculated the dimensions of various parts of pyramid of khufu. The bottom of the pyramid is square. He added two adjacent sides of a square and divided it by the height, that is, (230.5+230.5)/146.6 = 461.0146.6, and the number was about 3. 14, which was actually pi. Why does PI appear in pyramid of khufu? John couldn't figure it out and finally went crazy. Another Englishman, Petrie, made another survey of pyramid of khufu. He found that the error of the lines and angles of the Great Pyramid is almost zero, and the error is less than 65,438+0 inches over the length of 350 feet. Thales, a Greek scientist, also used a similar right triangle to calculate the height of the pyramid through the shadow length of the cane and pyramid. Many mysteries of the Great Pyramid remain unsolved, attracting countless scientists to explore. In recent years, scientists have measured this pyramid with precision instruments. Surprisingly, it is found that the relative error of the base side length is less than 1: 14000, that is, less than 2 cm. The relative errors of the four base angles are not more than 1:27 000, that is, not more than 12', and the errors of the four directions are only between 2' and 5'. Until now, the mystery of the pyramids still attracts countless scientists to explore and explore. Sixth, the characteristics of Egyptian mathematics The ancient Egyptians created quite developed mathematics while building magical pyramids and other buildings. 1, rand papyrus Egypt's original mathematical code was written in hieroglyphics. Among them, "Rand papyrus" is of great value to the study of ancient Egyptian mathematics. 1858 was purchased by A H Rhind and then bequeathed to the British Museum in London. Therefore, it is called rand papyrus. This paper cursive script is 550 cm long and 33 cm wide. It contains 85 questions, and the time is about 1700 BC.

2. Moscow papyrus

Moscow papyrus was acquired by Ross collectors in 1893. It was transferred to Moscow Museum on 19 12. This papyrus is 544 cm long and 8 cm wide, and * * * records 25 questions. The age is about 1850 BC. People's knowledge and understanding of ancient Egyptian mathematics mainly comes from these papyrus and other precious historical documents that have been preserved so far. Mathematics in Egypt comes from actual production and life, and they apply their acquired mathematical knowledge to practice. They didn't systematize the scattered mathematical knowledge, making it an independent subject, but only as a tool. Simple rules with no connection in form are used to solve problems in people's daily life. This verifies the natural law that everything comes from life and is used in life. The Great Pyramid of Khufu is one of the seven wonders of the world. John tyler, an amateur of astronomy and mathematics, studied the Great Pyramid according to the data provided by literature, and found many incredible mathematical principles hidden in it. The pyramids are composed of about 2.3 million stones, the outermost stone is about 1 15000, and each stone weighs 2.5 tons on average. If these stones are cut into small pieces with an average of one cubic foot, their length is equivalent to two-thirds of the circumference of the equator. In the Middle Ages, when the production tools were backward more than 4,000 years ago, it was a very difficult mystery how the Egyptians collected and transported so many huge stones and built such a magnificent pyramid. He also found that the base angle of the pyramid is not 60, but 5 1 5 1', thus finding that the area of each triangle is equal to the square of its height. The ratio of tower height to tower foundation perimeter is the ratio of radius of the earth to perimeter. So pi can be obtained by dividing the tower height by twice the bottom edge. Taylor believes that this ratio is by no means accidental. Prove that the ancient Egyptians already knew that the earth was round and the ratio of the radius to the circumference of the earth. The tower height multiplied by 109 is equal to the distance from the earth to the sun. The Great Pyramid contains not only the unit of length, but also the unit of calculating time: the circumference of the tower foundation is exactly the number of days in a year calculated according to a certain unit. Taylor's field trip was praised by the Royal Society and awarded a gold medal by the Society. The mystery of the pyramids constantly attracts thousands of enthusiastic people to explore. Students, are you ready?