The social development from the Warring States to the Qin and Han Dynasties raised many calculation and measurement problems for mathematics, such as the government's taxation according to the amount of land, proportional labor sharing, and large-scale earthwork construction. The reform of calendar also involves the calculation of various day data. All these have promoted the development of mathematics. In the six lessons of aristocratic children recorded by Zhou Li, there is a "nine numbers", which means that mathematics is divided into nine details. "Nine Chapters Arithmetic" is probably written on the basis of "Nine Numbers", absorbing the achievements of Xu Shang Arithmetic and Du Zhong Arithmetic that appeared before it.
There are different views on its completion time: some people think it was completed in the early years of the Eastern Han Dynasty; Some people think that the book was written in the middle of the Western Han Dynasty; Some people think that this book was written in the era of Wang Mang.
The author of "Nine Chapters Arithmetic" has always been difficult to verify, only knowing that it was the result of gradual improvement by many people, and inherited the origin of pre-Qin mathematics development. After entering the Han Dynasty, it was compiled and revised by many scholars and was written in the early years of the Eastern Han Dynasty (A.D. 1 century), which was the crystallization of the joint efforts of several generations. Mathematicians Zhang Cang and Geng Shouchang did supplementary work in the early years of the Western Han Dynasty. Because Hanshu Yiwenzhi contains 26 volumes of Xu Shang arithmetic and 16 volumes of Du Zhong arithmetic, there are no nine chapters of arithmetic. "Nine Chapters Arithmetic" may be written after Xu Du's works, so it may contain the contents of Xu Du's two books.
Most of the later ancient mathematicians began to study and study mathematics from Nine Chapters Arithmetic, and many people commented on it, among which Liu Hui (263) and Li (656) were the most famous. 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. Nine Chapters Arithmetic was introduced to Korea and Japan in Sui and Tang Dynasties.
Nine chapters arithmetic is the development and summary of mathematics founded and consolidated in feudal society of Warring States, Qin and Han Dynasties. As far as its mathematical achievements are concerned, it is a world-famous mathematical work. For example, the operation of quartering, the present skills (called the three-rate method in the west), square roots and square roots (including the numerical solution of quadratic equations), the skills of surplus and deficiency (called the double solution in the west), various formulas of area and volume, the solution of linear equations, the principle of addition and subtraction of positive and negative numbers, the Pythagorean solution (especially the Pythagorean theorem and the method of finding Pythagorean numbers) and so on are all very high levels. Among them, the solution of equations and the addition and subtraction of positive and negative numbers are far ahead in the development of mathematics in the world. As far as its characteristics are concerned, it forms an independent system centered on calculation, which is completely different from ancient Greek mathematics.
The content of "Nine Chapters Arithmetic" is divided into nine chapters: the first chapter is Tian Fang, with 38 questions in total, including plane area and fractional algorithm;
The second chapter Xiaomi, 46 questions, talks about various proportions;
Chapter three, the problem of diminishing distribution, materials are distributed in proportion according to grades, and taxes are shared according to grades;
The fourth chapter consists of 24 questions, which are about the square root of area and volume and the issuer;
The fifth chapter is business work, with a total of 28 questions, which is about the calculation of solid area and the manual calculation of earthwork;
The sixth chapter, with 28 topics in total, is about distributing taxes and dispatching workers according to the equal loss method.
The seventh chapter, surplus and deficiency, includes 20 problems, and talks about the solution to the arithmetic gain and loss problem, and there are also several proportional problems;
Chapter 8, Equation, 18, is about the solution of the application problem of multivariate linear equation, which contains 2-6 unknowns, which is basically the same as the "addition, subtraction and elimination method" in the current middle school textbooks;
Chapter 9 Pythagorean Theorem, with a total of 24 questions, uses Pythagorean Theorem to calculate various problems of "height, depth, width and distance", which are directly related to measurement and drawing.
"Nine Chapters Arithmetic" includes arithmetic, algebra and geometry in elementary mathematics. Its characteristic is to attach importance to theory, but not divorced from reality. It recorded the most advanced fractional arithmetic and proportional arithmetic in the world at that time. Profit and loss problem's solution in the book is a kind of creation, which occupies an important position in the history of world mathematics. In the third and fourth centuries, India had an algorithm that was completely consistent with China's surplus and deficit. In Arabia, Central Asia and medieval Europe, the "double law" prevailed (there are two hypotheses), which probably developed under the influence of China and profit and loss problem. The concept of positive and negative numbers and the rules of addition and subtraction in the book are also the first in the world. The Indian mathematician Brahman Gupta was the first to know negative numbers abroad in the 7th century, and it was not until Europe16th century that he realized negative numbers. China's Pythagorean Theorem Pythagorean chapter is the same as the famous "Lotus Problem" in Indian mathematics, but the data are different, and the rest are exactly the same, but India is later than China 1000.
Comparing Nine Chapters Arithmetic with Geometry Elements, the earliest mathematical monograph in the West, it is found that Geometry Elements runs through the whole book with the method of formal logic, while Nine Chapters Arithmetic is arranged according to the nature of the problem. The Elements of Geometry mainly talks about geometry with a little arithmetic, while Nine Chapters of Arithmetic contains a wide range of contents such as arithmetic, algebra and geometry. Geometry Elements pays more attention to theory than practical application, while Nine Chapters Arithmetic pays more attention to theory and connects with practical application. The two books have their own advantages and disadvantages, forming different styles of mathematics in the East and the West.
After the birth of Nine Chapters Arithmetic, it has been used as the main teaching material for teaching mathematical knowledge. /kloc-China's mathematical works before the 6th century all followed the style of Nine Chapters Arithmetic. Famous mathematicians in past dynasties annotated it, and new mathematical concepts and algorithms were constantly introduced in the annotation, which promoted the development of ancient mathematics in China.
"Nine Chapters Arithmetic" spread to Korea and Japan and became a textbook. It was introduced to Europe through India and Islamic countries. Profit and loss problem's introduction of Arab countries is called "Khitan Algorithm" (China Algorithm). This book has been translated into Japanese, English, Russian and German. It has attracted the attention of all countries in the world.