Nine Chapters Arithmetic is the first mathematical monograph in ancient China, and it is the most important one among the ten computational classics. The book is very rich in content and systematically summarizes the mathematical achievements in the Warring States, Qin and Han Dynasties. At the same time, Nine Chapters Arithmetic has its unique achievements in mathematics. It not only mentioned the problem of score at the earliest, but also recorded the problem of surplus and deficiency at the earliest. The chapter "Equation" also expounds the negative number and its addition and subtraction algorithm for the first time in the history of world mathematics. The book has been supplemented many times, and the completion time is no longer available. However, it is estimated that the current version will be available at the latest in the first century AD. Zhang Cang corrected it in the Western Han Dynasty. Many people have commented on it, including many famous mathematicians in history, the most famous of which are Liu Hui (AD 263) and Li (AD 656) ... It should be noted that Nine Chapters Arithmetic has no author, is a comprehensive historical work, and is the most advanced applied mathematics in the world at that time, and its appearance marks the formation of a complete system of ancient mathematics in China. [Edit this paragraph] The main content of the nine chapters of arithmetic: The content of the nine chapters of arithmetic is very rich. The book takes the form of problem sets, including 246 applied problems related to production and life practice. Each problem has a problem (question), an answer (answer) and a technique (problem solving steps, but there is no proof), some are one problem and one technique, and some are multiple problems and one technique or one technique. According to their nature and solutions, these problems belong to the following nine chapters: millet, decline (Cui), Shaoguang, work, equal loss, profit and loss, equation and Pythagorean. The original edition has illustrations, and this edition only leaves the text.

The main contents of "Nine Chapters Arithmetic" are:

Chapter 1 "Square field": calculation of field area;

Chapter two "millet": conversion of grain proportion;

Chapter 3 "Decline": the problem of proportional distribution;

Chapter 4 "Less but Wide": Given the area and volume, find its side length, diameter length, etc.

Chapter 5 "commercial engineering": geotechnical engineering and volume calculation;

Chapter VI "lose-lose": reasonable allocation of tax revenue;

Chapter seven "surplus and deficiency": the problem of dual management;

Chapter 8 "Equation": the problem of linear equations;

Chapter 9 "Pythagorean Theorem": Various problems solved by Pythagorean Theorem. [Edit this paragraph] Chapter IX Mathematical Achievements of Arithmetic Chapter IX Mathematical achievements of Arithmetic are various:

(1), the main achievements in arithmetic are fractional operation, proportional problem and "surplus and deficiency" algorithm. Nine Chapters Arithmetic is the earliest book in the world that systematically describes fractional operation. The second, third and sixth chapters have many problems of proportion, which are also relatively early in the world. The "residual" algorithm needs to give two assumptions, and it is a creation. In medieval Europe, it was called "double solution". Some people think it came from China through the Arab countries in the Middle Ages.

(2) In geometry, it is mainly the calculation of area and volume.

(3) In algebra, there are mainly linear equations, square, cubic and general quadratic equations. The chapter "Equation" also introduces negative numbers and their addition and subtraction algorithms for the first time in the history of world mathematics. As a world-famous scientific work, Nine Chapters Arithmetic was introduced to Korea and Japan during the Sui and Tang Dynasties. Now it has been translated into Japanese, Russian, German, English, French and other languages. [Edit this paragraph] Historical textual research on Nine Chapters Arithmetic: At present, there are different opinions about when the current version of Nine Chapters Arithmetic was written. Most people think that the author of Nine Chapters Arithmetic was at the end of the Western Han Dynasty and the beginning of the Eastern Han Dynasty, around the first century A.D. ... it was probably the crystallization of collective creation by many people in a historical period before the book was written. After two thousand years of manual copying, mistakes and omissions will inevitably occur, and some contents of Nine Chapters Arithmetic are not easy to understand, so there have been many corrections and annotations in history.

The collation of Nine Chapters Arithmetic mainly includes the addition and deletion of Zhang Cang in the Western Han Dynasty, the collation of Liu Hui in the Three Kingdoms Period and the collation of Li in the Tang Dynasty. In the Southern Song Dynasty, Yang Hui selected 80 typical problems in Nine Chapters Arithmetic for detailed explanation and classification. ~ 18 1 1 year) Revision, sketch, illustration, explanation, especially illustrations of the fine draft of Nine Chapters Arithmetic. In modern times, Qian Baocong (1892 ~ 1974) collated ten computational classics, including Nine Chapters Arithmetic, and made detailed comments on Nine Chapters Arithmetic and Liu and Li's notes in popular language and modern mathematical terms. Since 1980s, proofreading books by Bai Shangshu, Guo Shuchun and Min have appeared successively. [Edit this paragraph] Evaluate Nine Chapters Arithmetic and its influence on later generations: Nine Chapters Arithmetic is the earliest work in the world that systematically describes fractional operation; Among them, the residual algorithm is an amazing creation; The chapter "Equation" also expounds the negative number and its addition and subtraction algorithm for the first time in the history of world mathematics. In algebra, Nine Chapters Arithmetic put forward the concept of negative number and the law of addition and subtraction of positive and negative numbers for the first time in the history of world mathematics. The solution of linear equations taught in middle school is basically the same as that introduced in Chapter 9 Arithmetic. Paying attention to practical application is a remarkable feature of nine chapters arithmetic. Some knowledge of the book has also spread to India and Arabia, and even to Europe through these areas.

Nine Chapters Arithmetic is the crystallization of several generations, and its appearance marks the formation of the ancient mathematical system in China. Most mathematicians in later generations began to learn and study mathematical knowledge from Nine Chapters of Arithmetic. Both Tang and Song Dynasties were clearly defined as textbooks by the state. 1084 was published by the Northern Song Dynasty, and it was the earliest printed mathematics book in the world.

It can be said that Nine Chapters Arithmetic is China's outstanding contribution to the development of mathematics.