First, mathematics in ancient Egypt
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 and floods 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. As can be seen from the structure of the pyramids, 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 in London, called rhind papyrus, and the other is in Moscow. The oldest writing in Egypt is hieroglyphics, which later evolved into a simpler way of writing, usually called monk writing. 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 BC 1850 to BC 1650, which is equivalent to the Xia Dynasty in China.
Egypt has used decimal notation for a long time, but it doesn't know the value 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. Fraction algorithm is particularly important, that is, the sum of all fractions in Huasong unit fraction (that is, fraction with numerator 1). Rhind papyrus used a lot of space to record the result that the score of 2/n(n from 5 to 10 1) was decomposed into unit scores. Why and how to decompose it is still a mystery. This complex fractional algorithm actually hinders the further development of arithmetic. The paper cursive script also gives the calculation method of circular area: subtract its diameter from 1/9 and then square it. The calculation result is equivalent to using 3. 1605 as pi, but there is no 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 from19th century BC to 6th century BC is Babylonian culture, and the corresponding mathematics belongs to Babylonian mathematics. The mathematical tradition in this field can be traced back to Sumerian culture around 2000 BC, and then back to the founding period of Christianity in 1 century. The understanding of Babylonian mathematics is based on1cuneiform clay tablets excavated in the early 9th 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. From BC 1800 to BC 1600, the Babylonians had used the system number system based on 60 (including decimal 60). This notation is not perfect because there is no symbol for zero.
Babylonians have rich knowledge of algebra, mainly expressed in words, and occasionally expressed unknowns with symbols.
Before 1600 BC, many Pythagorean ternary arrays (Pythagorean arrays) were recorded on a clay tablet. According to textual research, its 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 know that triangles are similar and the corresponding sides are proportional. Using the formula (с is the circumference of a circle) to find the area of a circle is equivalent to taking π=3.
In the 3rd century BC, Babylonians often used mathematical methods to record and study astronomical phenomena, such as recording and calculating the movements of the moon and planets. Their practice of dividing the circumference into 360 degrees has been used to this day.
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 head symbol. The horizontal dot symbol means 1 plus a dot, 5 plus a horizontal dot, and 0 plus a shell, but it is not a symbol of 0.
So far, the knowledge of Maya mathematics is so much, which only shows addition and carry. About the understanding of shape, we can only learn something from ancient Mayan architecture. The appearance of these ancient buildings is very uniform, which 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; Then came the Siddhartha period. Because the hieroglyphics of valley culture can't be read 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, which is quite different from the age determined by modern people. Its date can be traced back to the earliest 10 century BC and the latest to the 3rd century BC.
Geometric calculation leads to some problems in solving the first and second algebraic equations, and India gives formulas by arithmetic.
The classics of Jainism consist of religious principles, mathematical principles, arithmetic and astronomy. There are few original classics handed down, but some notes 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, which became the so-called Arabic numerals internationally used today. This Indian number and symbol became the basis of scientific progress in modern Europe. China Tang Indian astronomer Qutanstar translated the nine calendars of Indian calendar in 7 18, but these figures 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 their arithmetic and algebra, Indians' work in geometry is very weak, and their most distinctive and influential achievements are their indefinite analysis and the popularization of Greek trigonometry.