Mathematical historical period:

first stage

The formative period of mathematics is the period when human beings establish the most basic mathematical concepts. Since counting, human beings have gradually established the concept of natural numbers, simple calculation methods, and recognized the most basic and simplest geometric forms. Arithmetic and geometry are not separated.

The second period

Elementary mathematics is a constant period of mathematics. The most basic and simple achievements in this period constitute the main content of middle school mathematics. This period began in the 5th century BC, maybe earlier, and lasted for about two years, until17th century. This period gradually formed the main branches of elementary mathematics: arithmetic, geometry and algebra.

tertiary

The period of variable mathematics. Variable mathematics came into being in17th century, and has gone through two decisive and significant steps: the first step is the generation of analytic geometry; The second step is calculus, that is, the branch of mathematics that studies the differential and integral of functions and related concepts and applications. It is the basic subject of mathematics. The content mainly includes limit, differential calculus, integral calculus and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change. It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols. Integral calculus, including the calculation of integral, provides a set of general methods for defining and calculating area and volume.

The fourth stage

Modern mathematics. The period of modern mathematics began in the first half of19th century. The beginning of the modern stage of mathematics development is characterized by profound changes in all foundations-algebra, geometry and analysis.

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 the cultural period in Yang Chao is engraved with the symbol representing 1234. By the end of the primitive commune, written symbols had begun to replace knotted notes. Chu Shi pottery in Anbanpo, Xi 'an has an equilateral triangle consisting of 1~8 points and a pattern in which 100 small squares are 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.

Zhou Bei Shujing in 1 century BC mentioned the method of measuring height, depth, width and distance with moments in the early Western Zhou Dynasty, and listed some examples, such as hook three, rope 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 such propositions as "a hammer of one foot, take half of it every day, and it will never be exhausted"