Egypt is one of the most culturally developed regions in the world, located on both sides of the Nile, and formed a unified country around 3200 BC. The Nile regularly floods, flooding all the valleys. When the water recedes, it is necessary to re-measure the cultivated area of residents. Because of this need, the geodesic knowledge accumulated for many years has gradually developed into geometry.
After 2900 BC, the Egyptians built many pyramids as tombs for pharaohs. From the structure of the pyramids, we can know that the Egyptians at that time knew a lot about astronomy and geometry. For example, the deviation between the right angles on both sides of the bottom and true north is very small.
Today's understanding of ancient Egyptian mathematics is mainly based on two rolls of cursive script written in Mongolian; One is hidden in London, called rhind papyrus, and the other is hidden in Moscow. The oldest writing in Egypt is hieroglyphics, which later evolved into a simpler way of writing, usually called monk's book. In addition to these two volumes of cursive script, there are some historical materials written in hieroglyphics on sheepskin or engraved on stone tablets and wooden boards, which are hidden all over the world. The two volumes of cursive script date from BC1850 to BC 10.
Egypt has used decimal notation for a long time, but it doesn't know the decimal system. Each higher unit is represented by a special symbol. Egyptian arithmetic is mainly addition, and multiplication is the repetition of addition. They can solve some problems of linear equations with one variable and have a preliminary understanding of arithmetic and geometric series. Fractional algorithm is particularly important. That is, the sum of the Huasong unit scores of all the scores (that is, the fraction whose numerator is 1). Rhind papyrus used a lot of space to record the results of decomposing the score of 2/n(n from 5 to 10 1) into unit scores. Why and how to decompose it is still a mystery. This complex fractional algorithm actually hinders the further development of arithmetic. Papyrus also gives a calculation method of circular area: subtract its diameter from 1/9, and then square it. The calculation results are equivalent to using 3. 1605 as pi, but they don't have the concept of pi. According to Moscow papyrus, it is speculated that they may know the calculation method of the volume of regular quadrangular prism.
In a word, the ancient Egyptians accumulated some practical experience, but it has not yet become a systematic theory.
Two. Mathematics in Mesopotamia
Mesopotamia in West Asia (that is, the Tigris and Euphrates river basins) is one of the cradles of early human civilization. Generally speaking, the culture in this area is Babylonian culture from the 9th century BC to the 6th century BC, and the corresponding mathematics belongs to Babylonian mathematics. The mathematical tradition in this area can be traced back to Sumerian culture around 2000 BC, and then to the founding period of Christianity in 1 century. According to the cuneiform clay tablets unearthed at the beginning of19th century, about 300 pieces are pure mathematics, of which about 200 pieces are various tables, including multiplication tables, reciprocal tables, square and cubic tables, etc. About 65438 BC +0800 ~ 65438 BC +0600 BC, the Babylonians had used the system number system based on 60.
Babylonians had rich knowledge of algebra, mainly expressed in words, and occasionally expressed unknowns with symbols.
On a clay tablet before 1600 BC, several sets of Pythagorean ternary arrays (Pythagorean arrays) were recorded. According to textual research, their solution is the same as Diophantine in Greece. The Babylonians also discussed some cubic equations and quartic equations that can be transformed into quadratic equations.
Babylonian geometry belongs to practical geometry and is often solved by algebraic method. They have knowledge of the similarity of triangles and the proportion of corresponding sides. Using the formula (с is the circumference of a circle) to find the area of a circle is equivalent to taking π=3.
Babylonians often used mathematical methods to record and study astronomical phenomena in the 3rd century BC, such as recording and calculating the movements of the moon and planets. Their practice of dividing the circumference into 360 degrees has been in use ever since.
Three. Maya mathematics
The understanding of Mayan mathematics mainly comes from some remaining Mayan stone carvings. The interpretation of the hieroglyphics on these stone carvings shows that the Maya created the counting system of the value system very early, and there are two specific counting methods: the first is called the horizontal point counting method; The second type is called the central symbol. The horizontal symbol means 1 plus a dot, 5 plus a level, and 0 plus a shell, but it is not a symbol of 0.
So far, the knowledge of Mayan mathematics is so much, and only two kinds of addition and carry are shown. We can only learn some knowledge about shapes from ancient Mayan architecture. These ancient buildings are unified in appearance, so it can be judged that the Mayans at that time had a certain understanding of geometric figures.
Four. Indian mathematics
The development of mathematics in India can be divided into three important periods. One is the Dravidian period before the Aryan invasion, which was called valley culture in history; Followed by the Vedic period; Secondly, the Sitando period, because the hieroglyphics of the valley culture can not be interpreted so far, little is known about the actual situation of Indian mathematics in this period.
The earliest written record of Indian mathematics is the Vedic era, and its mathematical materials are mixed in the classic Vedas of Brahmanism and Hinduism. The age is very uncertain, and the age determined by modern people is very different. It can be traced back to BC 10 century at the earliest and to the 3rd century BC at the latest.
Some problems in solving the first and second generation equations are caused by geometric calculation, and India gives formulas by arithmetic.
The classics of Jainism are composed of religious principles, mathematical principles, arithmetic and astronomy. Few original classics have been handed down, but some annotations from the 5th century BC to the 2nd century AD have been handed down.
In 773 AD, Indian numerals were introduced to Arab countries, and later Europeans accepted them through Arabs, becoming the so-called Arabic numerals commonly used in the world today. These Indian numbers and symbols have become the basis of scientific progress in modern Europe. These figures were also included in the Indian calendar "Nine Calendars" translated by Indian astronomer Qu Tansta in China in July18, but they were not accepted by China people.
Because India was conquered by other nations, ancient Indian astronomy and mathematics were deeply influenced by foreign cultures. Besides Greek astronomy and mathematics, the influence of China culture is not excluded. However, Indian mathematics has always maintained the practical characteristics of oriental mathematics with calculation as the center. Compared with its arithmetic and algebra, India's work in geometry is very weak, and its most distinctive and influential achievements are its indefinite analysis and its popularization of Greek trigonometry.