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How is the mathematical theoretical system established?
After the publication of Nine Chapters Arithmetic, there are basically two ways to write mathematics in China: one is to annotate Nine Chapters Arithmetic; The second is to compile new works according to Nine Chapters of Arithmetic. Among them, Liu Hui's Notes on Nine Chapters of Arithmetic is regarded as the beginning of the theoretical system of ancient mathematics in China. Zu Chongzhi's mathematical research was the most representative in the Southern and Northern Dynasties. On the basis of Liu Hui's Notes on Nine Chapters of Arithmetic, he greatly promoted traditional mathematics and became a model of attaching importance to mathematical thinking and reasoning, and the theoretical system of China's classical mathematics was established.

Sun Tzu's Calculations is a three-volume book, which is often mistaken for Sun Wu, a strategist in the Spring and Autumn Period. Actually, it was written around Wei, Jin, Southern and Northern Dynasties, and the author is unknown. This is an introduction to mathematics. Through many interesting topics, I will give you some preparatory knowledge such as notation, multiplication and division.

There are many interesting problems in the calculation of Sun Tzu's Art of War, such as "things are unknown", which are widely circulated among the people and popularize mathematical knowledge to people.

In fact, the special historical background in Wei and Jin Dynasties not only stimulated people's interest in learning mathematics and popularized mathematical knowledge, but also enriched the theoretical construction at that time, which made the ancient mathematics in China develop greatly in theory. At that time, the wind of "speaking plainly" began to rise in the ideological circle, and an unprecedented vivid situation appeared since the Warring States Period. In line with this, mathematicians attach importance to theoretical research and try to build the mathematical knowledge accumulated from pre-Qin to Han Dynasty on an inevitable and reliable basis. Liu Hui and his Nine Chapters Arithmetic Notes are the greatest mathematicians and the most outstanding mathematical works produced in this era.

Liu Hui lived at the turn of Wei and Jin Dynasties when the wind of "talking clearly" rose, but it did not flow into "talking clearly". Influenced by ideological disjunction, Liu Hui summarized and analyzed various algorithms in Nine Chapters Arithmetic, and thought that mathematics was like a big tree, with branches but the same root, which originated from one end and formed a complete theoretical system.

What problems were solved in Liu Hui's Nine Chapters Arithmetic Notes in 1977?

Liu Hui's Notes on Nine Chapters of Arithmetic was written in 263, with the original volume 10. The first nine volumes comprehensively demonstrate the formula of "nine chapters arithmetic" Solution, formulated the principle of complementary in and out? Cross-sectional area principle? The concept of homogeneity principle and rate creates a correct method to find pi, points out and corrects some inaccurate or wrong formulas in Nine Chapters Arithmetic, explores a correct method to solve the volume of a sphere, and creates a new technology to understand the reciprocal elimination and equation of linear equations. Approximate the approximate value of irrational roots with decimals, etc. , extensive use of analogy? Inductive reasoning and deductive reasoning, the latter is the main one. Volume 10 was originally named "Heavy Difference", and was annotated by Liu Hui, which developed and perfected the theory of heavy difference. This volume is a single line later, because the first question is to measure the height of the island, and it is called "island calculation".

What are the advantages of establishing China's classical mathematical theory system?

The establishment of China's classical mathematical theory system is not only due to Liu Hui's outstanding contribution to Nine Chapters Arithmetic Notes and the calculation contribution of Sun Tzu's Art of War, but also due to Zhang Qiu's calculation in Wei, Jin, Southern and Northern Dynasties. The seal script also enriched the theoretical creation in this period.

Zhang Qiujian, a mathematician in the Northern and Southern Dynasties, wrote three volumes of Zhang Qiujian Calculation, which was written in the Northern Wei Dynasty. This book supplements some arithmetic progression's formulas, and its hundred chickens problem leads to three-dimensional indefinite equations. Its important point is that it created the precedent of "asking many questions and answering many questions", which was not found in the ancient mathematics books of China in the past.

Roosters are worth 5p each, hens are worth 3p each, and three chickens are worth 1 penny. Buy 100 chickens at 100 pence. Q: Which of these 100 chickens is the rooster? How many hens and chickens are there?

This problem is widely spread and there are many solutions, but from the perspective of modern mathematics, it is actually a problem of finding integer solutions of indefinite equations.

There are many expressions about the problem of hundred chickens, such as "a hundred monks eat a hundred people" and "a hundred money buys a hundred birds". Yang Hui's Arithmetic Book in Song Dynasty also had similar problems, and in addition, similar problems were also circulated in the Middle Ages in the Near East, which was almost identical to the title of Zhang Qiu's Simple Calculation Classic, showing its influence on later generations.

Compared with the founders of the above classical mathematical theory, Zu Chongzhi attached importance to mathematical thinking and mathematical reasoning, and he greatly promoted traditional mathematics.

The book Composition written by Zu Chongzhi, as a textbook of imperial academy in Tang Dynasty, was included in the famous Ten Books of Calculating Classics. He made the true value of pi accurate to 3. 14 15926, which was the most advanced achievement in the world at that time. Together with his son Zuxuan, he successfully solved the problem of calculating the volume of the ball by using the "Mouhe Square Cover" and got the correct formula of the volume of the ball.

In 462, Zu Chongzhi also compiled the Ming Calendar, which used precession to reform the leap system. He opposed superstitious divination, deduced from the ancients, calculated related values more accurately by mathematical methods, and adhered to the scientific spirit of seeking truth from facts.

Sun Tzu's calculation of classics