The Germination of Ancient Mathematics in China
At the end of primitive commune, after the emergence of private ownership and commodity exchange, the concepts of number and shape developed further. The pottery unearthed during Yangshao culture period has been engraved with the symbol representing 1234. By the end of the primitive commune, written symbols had begun to replace knotted notes.
Pottery unearthed in Xi 'an Banpo has an equilateral triangle composed of 1 ~ 8 dots, and a pattern of 100 small squares divided into squares. The houses in Banpo site are all round and square. In order to draw circles and determine straightness, people have also created drawing and measuring tools such as rulers, moments, rulers and ropes. According to Records of Historical Records Xia Benji, Yu Xia used these tools in water conservancy.
In the middle of Shang Dynasty, a set of decimal numbers and notation had been produced in Oracle Bone Inscriptions, the largest of which was 30 thousand; At the same time, the Yin people recorded the date of 60 days with 60 names, including Jiazi, Yechou, Bingyin and Dingmao, which were composed of ten heavenly stems and twelve earthly branches. In the Zhou Dynasty, eight kinds of things were previously represented by eight diagrams composed of yin and yang symbols, which developed into sixty-four hexagrams, representing sixty-four kinds of things.
The book Parallel Computation in 1 century BC mentioned the methods of using moments of high, deep, wide and distance in the early Western Zhou Dynasty, and listed some examples, such as hook three, strand four, chord five and ring moments can be circles. It is mentioned in the Book of Rites that the aristocratic children of the Western Zhou Dynasty have to learn numbers and counting methods since they were nine years old, and they have to be trained in rites and music, shooting, controlling, writing and counting. As one of the "six arts", number has begun to become a special course.
During the Spring and Autumn Period and the Warring States Period, calculation has been widely used and decimal notation has been used, which is of epoch-making significance to the development of mathematics in the world. During this period, econometrics was widely used in production, and mathematics was improved accordingly.
The contention of a hundred schools of thought in the Warring States period also promoted the development of mathematics, especially the dispute of rectifying the name and some propositions were directly related to mathematics. Famous experts believe that the abstract concepts of nouns are different from their original entities. They put forward that "if the moment is not square, the rules cannot be round", and defined "freshman" (infinity) as "nothing beyond the maximum" and "junior" (infinitesimal) as "nothing within the minimum". He also put forward the idea that "one foot is worth half a day, which is inexhaustible".
Mohism believes that names come from things, and names can reflect things from different sides and depths. Mohist school gave some mathematical definitions. Such as circle, square, flat, straight, sub (tangent), end (point) and so on.
Mohism disagreed with the proposition of "one foot" and put forward the proposition of "non-half" to refute: if a line segment is divided into two halves indefinitely, there will be a non-half, which is a point.
The famous scholar's proposition discusses that a finite length can be divided into an infinite sequence, while the Mohist proposition points out the changes and results of this infinite division. The discussion on the definition and proposition of mathematics by famous scholars and Mohists is of great significance to the development of China's ancient mathematical theory.
The Formation of Ancient Mathematics System in China
Qin and Han dynasties were the rising period of feudal society, with rapid economic and cultural development. The ancient mathematical system of China was formed in this period, and its main symbol was that arithmetic became a specialized subject, and the emergence of mathematical works represented by Nine Chapters of Arithmetic.
Nine Chapters Arithmetic is a summary of the development of mathematics during the establishment and consolidation of feudal society in the Warring States, Qin and Han Dynasties. As far as its mathematical achievements are concerned, it is a world-famous mathematical work. For example, the operation of quartering, the present skills (called the three-rate method in the west), square roots and square roots (including the numerical solution of quadratic equations), the skills of surplus and deficiency (called the double solution in the west), various formulas of area and volume, the solution of linear equations, the principle of addition and subtraction of positive and negative numbers, the Pythagorean solution (especially the Pythagorean theorem and the method of finding Pythagorean numbers) and so on are all very high levels. Among them, the solution of equations and the addition and subtraction of positive and negative numbers are far ahead in the development of mathematics in the world. As far as its characteristics are concerned, it forms an independent system centered on calculation, which is completely different from ancient Greek mathematics.
"Nine Chapters Arithmetic" has several remarkable characteristics: it adopts the form of mathematical problem sets divided into chapters according to categories; Formulas are all developed from counting method; Mainly arithmetic and algebra, rarely involving graphic properties; Attach importance to application and lack of theoretical explanation.
These characteristics are closely related to the social conditions and academic thoughts at that time. In Qin and Han dynasties, all science and technology should serve the establishment and consolidation of feudal system and the development of social production at that time, emphasizing the application of mathematics. Nine Chapters of Arithmetic, which was finally written in the early years of the Eastern Han Dynasty, ruled out the discussion of famous scholars and Mohists in the Warring States period on the definition and logic of nouns, but focused on mathematical problems and their solutions closely combined with production and life at that time, which was completely consistent with the development of society at that time.
Nine Chapters Arithmetic spread to Korea and Japan in Sui and Tang Dynasties, and became the mathematics textbook of these countries at that time. Some of its achievements, such as decimal numerical system, modern skills and surplus skills, have also spread to India and Arabia, and through India and Arabia to Europe, which has promoted the development of mathematics in the world.