The Nile often overflows and inundates fertile fields, and the rulers need to requisition and re-measure the land. In fact, Egyptian geometry originated here. Herodotus, a Greek historian (about 484-424 BC) clearly pointed out in his book History that "Strids, Soteras" (1) distributed the land of Egypt to all Egyptians and residents. He distributed square land of the same size to all people and asked the landlord to pay him rent every year as his main tax. If the river overflows, the king sends someone to measure the area of the lost area. So his rent will be collected according to the reduced land area. I think it is because of this practice that Egypt has geometry for the first time. "That's where the Greeks learned it. The Greek mathematician Democritus (about 460-357 BC) once 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. "

The so-called harpedonaptai probably refers to the surveyor who takes the drawstring as the main tool.

In order to promote the development of agricultural production, Egyptians must pay attention to the flood cycle of the Nile and accumulate a lot of astronomical knowledge in practice. For example, when they noticed that Sirius and the sun appeared at the same time, it was a sign that the Nile flood was coming. The interval between Sirius's two early morning rises is regarded as a year, including 365 days. Divide a year into 12 months, and each month has 30 days and nights. And gradually explore the use of sundials to measure time. About 1500 BC, the water clock-clepsydra is a kind of container with holes in the bottom. Fill this container with water, and the time when the water flows out of the hole below is the unit for calculating time.

It can be inferred that the famous pyramids were built four or five thousand years ago BC. According to the study of its structure and shape, it can be seen that the Egyptians mastered a lot of geometric knowledge at that time, resulting in the length error of the base only 1.6 cm, which is the whole length, and the right angle error of the base only 12 "or right angle. The four sides of the pyramid face southeast and northwest respectively, and the deviation between the two sides of the bottom square and true north is only 2'30 "and 5'30". This practical building promoted the development of mathematical calculation in Egypt.

To sum up, the needs of actual production and life prompted the emergence of Egyptian mathematics.

Second, the basis of learning Egyptian mathematics

The ancient Egyptians created their own character set. One set is hieroglyphics, and the word "hieroglyphics" comes from Greek, which means: sacred writing. Since about 2500 BC, hieroglyphic abbreviations have been used, called hieratic Writing.

1, rand papyrus

The first mathematical classics in Egypt were written in hieroglyphics. Among them, "Rand papyrus" is of great value to the study of ancient Egyptian mathematics. It was found in the ruins of Thebes, the capital of ancient Egypt. 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. The copy was published in 1898.

This paper cursive script was written according to the time when Thebes ruled Egypt (after 1800 BC). This is written by a monk named Ames. As he said, it was written according to the materials of the Middle Kingdom of Egypt (2000- 1800 BC).

The appearance of this cursive script had a great influence on Egyptian culture. The author claims that it is a classic of "observing the existence of all things, thoroughly studying the changes of all things, and revealing all secrets …". In fact, the secret of "number" is only the calculation of "score". This book is divided into three parts, one is arithmetic; The second is geometry; The third is miscellaneous questions. * * * 85 questions, recording the practical problems of working people. For example, the distribution of workers' remuneration; Calculation of area and volume; Conversion of different grain quantities and so on. Among them, there are also purely theoretical problems, such as the difficulty in calculating scores.

2. Moscow papyrus

Moscow papyrus was acquired by Ross collectors in 1893. It was transferred to Moscow Museum on 19 12. This papyrus is 550 cm long and 8 cm wide, and * * * records 25 questions. Due to the loss of preface, the title of the book cannot be verified. Historian 6. Tula Wu Ye (Jiypaer 1868- 1920) is in1917 b.b. strouwe (ctpybe1891-/kloc-.

Thirdly, the application of Egyptian mathematics and its contribution to the development of mathematics.

1, Egyptian application of mathematics

Mathematics in Egypt comes from actual production and life, and they apply what they have learned to practice.

Egyptians applied mathematics to the management of state and church affairs. For example, if we really want to pay workers, we should make clear the volume of grain and the area of land, collect local taxes estimated according to the area of land, and calculate the number of bricks for building houses and defense projects.

Apply mathematics to the calculation of brewing and so on. The term "pesu" is the amount of wine or bread produced by a unit grain. The calculation is as follows:

Number of grains × ratio = number of alcohol (or number of bread)

In these simple calculations, units need to be converted.

Apply mathematics to astronomical calculation. Since the first dynasty, the Nile has been the source of life for the Egyptians. It takes a lot of calculation to accurately predict the date of flood. They combined geometry knowledge and used it to build temples, so that the sun can shine into temples in certain ways on certain days of the year.

2. Egyptians' contribution to the development of mathematics.

When we review the emergence and development of Egyptian mathematics, it is not difficult to see that they have made certain contributions to the development of mathematics in later generations. Among them, Greek mathematics, which has a great influence on the development of mathematics, also draws lessons from Egyptian mathematics. For example, the Greeks studied Egypt's specific multiplication methods and the calculation of unit fractions.

The Egyptians did not systematize the scattered knowledge of mathematics, 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. The main contributions of the Egyptians to mathematics can be summarized as follows:

(1) basically completes the four operations in a specific way, and extends them to fractions, and there has been a method to find approximate square roots.

⑵ Some types of quadratic equations with one variable can be solved by arithmetic.

They have mastered the knowledge of arithmetic progression and geometric numbers.

⑷ In geometry, some quadrature methods of plane and solid figures are obtained.

5] Take the value of pi (at that time) and correctly understand the problem of dividing a circle into several equal parts.

[6] They are already familiar with the basic principle of proportion, and some mathematical historians also believe that Egyptian mathematics has sprouted trigonometric functions.