Nine Chapters of Arithmetic is the first mathematical monograph in ancient China, and it is also the most important of the ten classic works of calculation. It was written around the first century AD. Its author can no longer be examined. 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).

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Nine Chapters Arithmetic contains 246 math problems, which are divided into nine chapters. Its main contents are as follows:

The first chapter "square field" mainly describes the calculation method of plane geometric figure area. Include rectangle, isosceles triangle, right-angled trapezoid, isosceles trapezoid, circle, sector, bow and ring. In addition, the four algorithms of fraction and the method of finding the greatest common divisor of numerator and denominator are systematically expounded.

Chapter two "millet": conversion of grain proportion; Propose a proportional algorithm, which is called the prior art; The law of proportional distribution was put forward in the chapter of decay, which is called decay class;

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

The fourth chapter is "less but wider": knowing the area and volume, the length of one side and the length of the diameter are calculated backwards; This paper introduces the method of square root and square root.

Chapter 5 "commercial engineering": geotechnical engineering and volume calculation; In addition to various solid volume formulas, there are also engineering allocation methods;

Chapter VI "lose-lose": reasonable allocation of tax revenue; Solving the problem of reasonable burden of tax service by decreasing method. The existing technology, diminishing technology and its application methods constitute a whole set of proportional theory, including today's positive and negative proportion, proportional distribution, compound proportion and chain proportion. It was not until the end of 15 that a similar method was formed in the west.

Chapter seven "surplus and deficiency": the problem of dual management; This paper puts forward three types of profit and loss problem: insufficient surplus, sufficient and insufficient surplus, two surpluses and two shortages, and the solutions to some general problems that can be transformed into insufficient surplus through two assumptions. This is also the world's leading achievement, which has a great influence after it spread to the west.

Chapter 8 "Equation": the problem of linear equations; Linear equations are expressed by separation coefficient method, which is equivalent to current matrix; The direct division used to solve linear equations is consistent with the elementary transformation of matrices.

Chapter 9 "Pythagorean Theorem": Various problems solved by Pythagorean Theorem. Most of them are closely related to the social life at that time.

Baidu Encyclopedia-Nine Chapters Arithmetic