-A Brief History of Mathematics in China 1. Mathematics appeared in the Spring and Autumn Period and the Warring States Period before Qin Dynasty. According to the Book of Changes, there are many words for counting in Oracle Bone Inscriptions unearthed in Yin Ruins. From one to ten, as well as hundred, thousand and ten thousand, are special symbolic characters. * * * There are 13 independent symbols, including decimal.
In the numeration system, the maximum number is 30 thousand. Calculation is a calculation tool in ancient China, and this calculation method is called calculation. The age of calculation and preparation is not elegant, but it is certain that calculation and preparation have become very common in the Spring and Autumn Period. Calculation and financing establish good conditions for addition, subtraction, multiplication and division. It was not until the end of the Yuan Dynasty in the 15th century that the abacus was gradually replaced, and ancient mathematics in China made great achievements on the basis of the abacus.
Has been realized. In terms of geometry, it is said in Historical Records Xiabenji that Yu Xia has used drawing and measuring tools such as ruler, moment, mark and rope in water control, and has discovered a special case of Pythagorean theorem of "three strands, four chords and five". During the Warring States Period, the Examination Book written by Qi people summarized the technical specifications of handicraft industry at that time, including some measurement contents and some geometric knowledge, such as the concept of angle.
A hundred schools of thought contended during the Warring States period also promoted the development of mathematics, and some schools also summarized many abstract concepts related to mathematics. There are famous definitions and propositions of some geometric nouns in Mojing, and Mohist school also gives the definitions of finite and infinite. Zhuangzi records the famous theories of Hui Shi and others, emphasizing abstract mathematical thoughts. These definitions, limit ideas and other mathematical propositions of many geometric concepts are quite valuable mathematical ideas, but this new idea attaches importance to abstraction and logical rigor.
It has not been well inherited and developed. In addition, the Book of Changes, which tells the gossip of Yin and Yang and predicts good and bad luck, has sprouted from combinatorial mathematics, reflecting the idea of binary system.
Second, the early Han and Tang Dynasties, Qin and Han Dynasties, was the formation period of China's ancient mathematical system. In order to systematize and theorize the growing mathematical knowledge, mathematics
Specialized books in various fields have appeared one after another. At the end of the Western Han Dynasty (the first century BC), Zhou Pi 'ai's astronomical works made two great achievements in mathematics:
(1) puts forward the special case and general form of Pythagorean theorem; (2) Measure the height of the sun. In addition, there are more complicated root-finding problems and fractional operations. Nine Chapters Arithmetic is an ancient mathematical classic, which has been edited and edited by several generations. Written in the early Eastern Han Dynasty. The main contents include four fractional and proportional algorithms, the calculation of various areas and volumes, and the calculation of pythagorean measurement. In algebra, the concept of negative number and the law of addition and subtraction of positive and negative numbers introduced in the chapter of equation are the earliest records in the history of mathematics in the world. The solution of linear equations in the book is basically the same as that taught in middle schools now. As far as the characteristics of Nine Chapters Arithmetic are concerned, it pays attention to the application and integration of theory with practice, and forms a mathematical system centered on calculation, which has had a far-reaching impact on the ancient calculation in China. Some of its achievements, such as decimal numerical system, have also spread to India and Arabia, and through these countries to Europe, which has promoted the development of world mathematics. During the Wei and Jin Dynasties, China's mathematics developed greatly in theory. Among them, the work of Zhao Shuang and Liu Hui is regarded as the beginning of China's ancient mathematical theory system. Zhao Shuang was one of the earliest mathematicians who proved mathematical theorems and formulas in ancient China, and made detailed comments on Zhou Kuai Shu Jing. Liu Hui annotated Nine Chapters Arithmetic, which not only explained and deduced the methods, formulas and theorems of the original book as a whole, but also made many innovations in the process of discussion, and even wrote the island calculation. One of Liu Hui's important tasks is to create secant, which lays a theoretical foundation and provides a scientific basis for the study of pi.
Algorithm. The society in the Southern and Northern Dynasties was in a state of war and division for a long time, but the development of mathematics was still vigorous. Sun Tzu's Art of War, Xiahou Yang's Art of War and Zhang Qiu's Art of War are all works of this period. Sun Tzu's mathematical classics give the question of "things are unknown", which leads to the solution of a congruence group problem; The "Hundred Chickens Problem" in Zhang Qiujian suan Jing leads to three unknown indefinite equations. The most representative works in this period are the works of Zu Chongzhi and others. On the basis of Liu Hui's annotation of Nine Chapters Arithmetic, they greatly promoted traditional mathematics and became a model of attaching importance to mathematical thinking and reasoning. They also have astronomy.
Outstanding contribution. Their book seal script has been lost. According to historical records, they have made three great achievements in mathematics: (1) Calculate pi to the sixth place after the decimal point and get 3. 14 15926.
The pestle theorem and spherical volume formula are obtained. (3) The solutions of quadratic and cubic equations are developed. 3. During the heyday of Song and Yuan Dynasties, computational mathematics reached its peak, which was the heyday of unprecedented prosperity and fruitful achievements in ancient Chinese mathematics. During this period, a number of famous mathematicians and mathematical works appeared, which are listed as follows: Jia Xian's Nine Chapters Algorithm Fine Grass, His Theory of Ancient Origin, Qin's Nine Chapters Calculation Book, Round Sea Mirror and an Ancient Yan Duan, Yang Hui's Nine Chapters Algorithm Detailed Explanation, Daily Algorithm and Yang Hui's Algorithm. Mathematics in Song and Yuan Dynasties reached the peak of ancient mathematics in China in many fields, even in the world at that time. The main work includes: (1) numerical solution of higher order equation; (2) The celestial sphere method and quaternary method, that is, the legislation and solution of higher-order equations, are the first time in the history of Chinese mathematics to introduce symbols and use symbolic operations to solve the problem of establishing higher-order equations; (3) The technique of solving a large extension, that is, the solution of a group of congruences, is now called China's remainder theorem; (4) Recruitment superposition, that is, high-order interpolation and high-order arithmetic progression summation. In addition, other achievements include the new development of Pythagoras solution, the study of solving spherical right triangle, and the vertical and horizontal diagram (magic square)
The research, the specific application of decimal (decimal), the emergence of abacus and so on. During this period, folk mathematics education also developed, and the exchange of mathematics knowledge between China and Islamic countries also developed.
Fourthly, the period of importing western learning lasted more than 500 years, from the establishment of the Ming Dynasty in the middle of14th century to the end of the Qing Dynasty in the 20th century. Mathematics has a common weakness besides abacus calculation. /kloc-At the end of the 6th century, western elementary mathematics began to be introduced into China, which led to the integration of Chinese and western mathematics research in China. After the Opium War, modern advanced mathematics began to be introduced into China, and China's mathematics turned into a period of mainly studying western mathematics. Until the end of19th century, China's research on modern mathematics really began.