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, which not only mentioned the problem of fractions at the earliest, but also recorded the problems 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 writing time is unknown, but it is estimated that there is a modern version in the first century AD, which was supplemented by Zhang Cang 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 of Arithmetic has no author, and it is a comprehensive historical work, which was the most advanced in the world at that time. 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, in which each problem has problems (questions), answers (answers), techniques (steps to solve problems, but there is no proof), and some are. There are many questions, skills or skills. These problems are divided into the following nine chapters according to their nature and solutions: Tian Fang, Su, Decline (Cui), Shaoguang, Shanggong, Average Loss, Profit and Loss, Equation and Pythagorean. There are illustrations in the original work, but only words are left in this biography.
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 "remainder" algorithm. "Nine Chapters Arithmetic" is the earliest book that systematically describes fractional operation in the world. There are many proportional problems in the second, third and sixth chapters, which are also relatively early in the world. The "residual" algorithm needs to be given twice, and it is a creation, which was called in medieval Europe.
(2) In geometry, it is mainly the calculation of area and volume.
(3) In algebra, there are mainly solutions to linear equations, squares, cubes 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 of arithmetic: There are different opinions about when the book came out. Most people think that from the end of the Western Han Dynasty to the beginning of the Eastern Han Dynasty, around the first century A.D., the author of Nine Chapters Arithmetic is unknown. It is probably the result of collective creation by many people in a historical period before writing this book. Due to the manual copying and engraving for two thousand years, mistakes and omissions will inevitably occur. The text of Nine Chapters Arithmetic is brief and some contents are not easy to understand, so there have been many proofreading notes 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. Chapter 9 of Arithmetic, 18 1 1), which has been revised, sketched, illustrated, explained, especially illustrated. Modern Qian Baodi (1892 ~ 198) annotated Nine Chapters Arithmetic and Liu and Li's notes in detail with popular language and modern mathematical terms. Since 1980s, there have been proofreading books published by Bai Shangshu, Guo Shuchun and Min 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, the concept of negative number and the law of addition and subtraction of positive and negative numbers were first put forward in the history of mathematics in the world. 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 this book has also spread to India and Arabia, and even to Europe through these areas.
Nine-chapter arithmetic is the crystallization of several generations' joint efforts, and its appearance marks the formation of China's ancient mathematical system. 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. Published by the Northern Song Dynasty court at that time, 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.