During the Renaissance, geometry in Europe was widely developed, and analytic geometry theory was formed to solve geometric problems by algebra.
After 16, western geometry was introduced to China one after another, and it was combined with ancient arithmetic in China, which made the mathematical research in China a combination of Chinese and western. After the Opium War, modern mathematics began to be introduced into China, and China's mathematics turned into a period of studying ancient arithmetic, geometry and modern western mathematics.
1582, Italian missionary Matteo Ricci went to China. 1607, he translated the first six volumes of Geometry Elements and one volume of Measuring the Meaning of Law with Xu Guangqi, and compiled Yi Rong's Pen Meaning with Li Zhizao. 1629, Xu Guangqi was appointed by the Ministry of Rites to supervise the revision of the calendar. Under his auspices, he compiled the almanac of Chongzhen (137). The almanac of Chongzhen mainly introduces the geocentric theory of European astronomer Tycho. As the mathematical basis of this theory, it also introduces Greek geometry, some trigonometry of Yushan in Europe, Napier's calculation, Galileo's scale specification and other calculation tools.
Among the western mathematics introduced to China, The Elements of Geometry has the greatest influence. The Elements of Geometry is China's first mathematical translation. Most mathematical terms are the first, and many are still in use today. Xu Guangqi thinks there is no need to doubt it and change it, and thinks that "there is no one in the world who can't learn well". The Elements of Geometry is a must-read for mathematicians in Ming and Qing Dynasties, which has a great influence on their research work.
There are many books handed down from generation to generation by beginners in the Qing Dynasty by studying Chinese and Western mathematics. Among them, Wang Xichan's Illustration, Mei's Collected Works (including 13 kinds of mathematical works ***40 volumes) and Visual Research have great influence. Mei Wending is a master of western mathematics. He sorted out and studied the solution of linear equations, Pythagorean solution and the method of finding positive roots of higher powers in traditional mathematics, which brought vitality to the dying mathematics of Ming Dynasty. Xirao Nian's Vision is the first book in China to introduce the western perspective.
Emperor Kangxi of Qing Dynasty attached great importance to western science. Besides studying astronomy and mathematics by himself, he also trained some talents and translated some works. After Yongzheng acceded to the throne, he closed his door to the outside world, which led to the cessation of importing western science into China and the implementation of a high-handed policy at home. As a result, ordinary scholars can't get in touch with western mathematics and dare not ask themselves what they have learned, so they bury themselves in studying ancient books. During the reign of Ganjia, the Ganjia school, which mainly focused on textual research, gradually formed.
With the collection and annotation of Ten Books of Calculating Classics and mathematics works in Song and Yuan Dynasties, there appeared a climax of learning traditional mathematics. Among them, Wang Lai, Li Rui and Li. Can break the old rules and have inventions. Compared with Song and Yuan Algebra, their work is better than Chen Wenzhao's. Compared with western algebra, it is a little late, but these achievements were obtained independently without being influenced by modern western mathematics.
1840 after the opium war, modern western mathematics began to be introduced into China. First of all, the British set up the Mohai Library in Shanghai and introduced western mathematics. After the Second Opium War, Zeng Guofan, Li Hongzhang and other bureaucratic groups launched the "Westernization Movement", also advocated the introduction and study of western mathematics, and organized the translation of a number of modern mathematics works. In these translations, many mathematical terms and terms have been created, which are still used today, but the mathematical symbols used have generally been eliminated. After the Reform Movement of 1898, new law schools were established in various places, and these works became the main textbooks.
While translating western mathematical works, Chinese scholars have also done some research and written some works, the most important of which are Li's "Solution to the Transformation of a Sharp Cone" and "Solution to Several Roots". Xia Wanxiang's illustration hole method, illustration song, illustration song, etc. They are all research results that will connect Chinese and western academic thoughts.
Because the imported modern mathematics needs a process of digestion and absorption, and the rulers in the late Qing Dynasty are very corrupt, overwhelmed by the impact of the Taiping Heavenly Kingdom Movement and plundered by imperialist powers, they have no time to take care of mathematical research. It was not until the May 4th Movement of 19 19 that the study of modern mathematics in China really began.
Contents of Mathematical Manuscripts: Learning Methods of Mathematics in Senior High School
1. the thinking method of combining numbers and shapes
The combination of number and shape is to fully investigate the internal relationship between the conditions and conclusions of mathematical problems, not only analyze its algebraic significance but also reveal its geometric significance, skillfully combine the quantitative relationship with the spatial form, and find and solve the problem. Make the problem difficult and simple, so as to be solved. For example, in some algebraic expressions whose numerator and denominator are trigonometric functions or linear functions, it is required to convert the range of values into the linear distance between two points to solve them; Or in some algebraic problems with radical signs, the structure has no obvious geometric significance, and the distance formula between two points may not be used at this time. If we can use method of substitution and the thinking method of combining numbers and shapes, the problem can be solved quickly. Therefore, the combination of mathematics and thinking method is a very important method to solve mathematical problems.
2. Discuss ways of thinking by category
The thinking method of classified discussion means that when solving some mathematical problems, according to certain principles or standards, on the basis of comparison, the mathematical objects are divided into several parts that are both related and different, and then discussed one by one, and then the conclusions of these categories are summarized to get the answers to the questions. For example, solving inequality ax >；; 2. We divide it into & gt0, a=0 and a.
3. Thought method of function and equation
The idea of functional equation refers to the idea of constructing suitable functions and equations when solving some mathematical problems, and transforming the problems into the study of the properties of auxiliary functions and auxiliary equations. For example, when solving the distribution problem of equation roots, of course, it can be solved step by step, but it is very complicated. If we solve it from the viewpoint of function, the process of reasoning and proving inequality will be much simpler and clearer. Students who don't believe can work out this problem below:
4. Equivalent transformation of thinking methods
Equivalence transformation is an important thinking method to transform the problem of unknown solution into a problem that can be solved within the scope of existing knowledge. When students encounter problems that are difficult to make directly, they can deal with them by turning them into familiar problems, or turning more complicated problems into simpler ones, such as from transcendence to algebra, from unreasonable to rational, from fractions to algebraic expressions. For example, when it is difficult to directly construct an inequality with parameters as elements in the problem of exploring the range of parameters, we can often introduce a correlation coefficient A and transform the problem equivalently with the help of A.