What is the Nine Chapters of Arithmetic divided into? What are the main chapters about?

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.

The author of Nine Chapters Arithmetic is no longer here. It is generally believed that it has gradually become the final version after several generations of supplement and modification. Zhang Cang and Geng Shouchang in the Western Han Dynasty had been supplemented and sorted out, and they were generally finalized at that time. The last book was in the early years of the Eastern Han Dynasty at the latest, and most of them were Notes to Nine Chapters written by Wei Yuan, Jing Yuan and Liu Hui in the Three Kingdoms Period (263).

It is the first mathematical monograph in ancient China, and the most important of the ten classic works of calculation, which was formed around the first century A.D.. 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. Zhang Equation also expounded the negative number and its addition and subtraction algorithm for the first time in the history of world mathematics. It is a comprehensive historical work and the most concise and effective applied mathematics in the world at that time. Its appearance marks the formation of a complete system of ancient mathematics in China.

Nine Chapters of Arithmetic is a mathematical monograph in ancient China, and it is the most important one among the "Ten Arithmetic Classics" (an ancient arithmetic book between Han and Tang Dynasties). Liu Hui commented on "Nine Chapters Arithmetic" in Wei and Jin Dynasties, saying: "The Duke of Zhou made a gift and had nine numbers, which made nine chapters complete." He also said, "Zhang Cang, Hou Peiping in Han Dynasty, and Geng Shouchang, a senior farmer, all made good use of fortune telling. Because of the remnants of the old text, Cang and others call it deletion and supplement, so the purpose of collation is different or different from the old one, and the discussion is relatively new. According to textual research, Zhang Cang and Geng Shouchang in the Western Han Dynasty supplemented Nine Chapters of Arithmetic. The final edition was written in the early Eastern Han Dynasty at the latest, but its basic content was basically finalized in the late Western Han Dynasty. There are only two kinds of mathematics books recorded in Han Shu Literature and Art Annals (written by Ban Gu according to Liu Xin's Seven Views): Xu Shang Arithmetic and Du Zhong Arithmetic, but there is no Nine Chapters Arithmetic, so it can be seen that Nine Chapters Arithmetic appeared later than Seven Views. The Biography of Ma Yuan in the Later Han Dynasty records that his grandnephew Ma Xu was "well-read, good at arithmetic in nine chapters" and was born in the last 20 or 30 years of A.D. 1 century. According to the official names and place names in Nine Chapters Arithmetic, it can be inferred that the modern version of Nine Chapters Arithmetic was written in the second half of 1 century. "Nine Chapters Arithmetic" divides all the mathematical problems in the book into nine categories, edited by Chen.

1984, Shu Shu was unearthed in Hubei. According to textual research, it is more than a century and a half earlier than Nine Chapters of Arithmetic. Some contents in the book are very similar to Nine Chapters of Arithmetic, and some contents are basically the same. Some people speculate that there is a certain inheritance relationship between the two books, but there are also different views that Nine Chapters of Arithmetic has not been directly influenced by Arithmetic Book.

Most mathematicians in later generations began to study and study mathematics from the Nine Chapters of Arithmetic, and many people commented on it. The most famous ones are Liu Hui (263) and Li (656). The notes of Liu, Li and others were circulated together with Nine Chapters of Arithmetic. During the Tang and Song Dynasties, Nine Chapters Arithmetic was clearly defined as a textbook by the state. In the Northern Song Dynasty, the government also published Nine Chapters of Arithmetic (1084), which was the earliest printed mathematics book in the world. Among the modern editions of Nine Chapters Arithmetic, the earliest edition is the Southern Song Dynasty reprint of the Northern Song Dynasty (12 13), which is now in Shanghai Library (only the first five volumes are left). In Qing Dynasty, Dai Zhen copied and collated Nine Chapters of Arithmetic from Yongle Dadian. Since then, most of the editions of Sikuquanshu, Wuyingsi Rare Book and Ten Calculations inscribed by Kong (1773) are based on Dai Pai.

As a world-famous mathematical work, Nine Chapters Arithmetic was introduced to Korea and Japan as early as the Sui and Tang Dynasties. It has been translated into Japanese, Russian, German and French.