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,
Solving Pythagorean Theorem
Solving Pythagorean Theorem
Equivalent to the current matrix; The direct division used to solve linear equations is consistent with the elementary transformation of matrices. This is the earliest solution of completely linear equations in the world. In the west, it was not until17th century that Leibniz put forward a complete law for solving linear equations. This chapter also introduces and uses negative numbers, and puts forward the addition and subtraction rules of positive and negative numbers, which are exactly the same as those in modern algebra. When solving linear equations, the multiplication and division of positive and negative numbers are actually performed. This is a great achievement in the history of world mathematics, which broke through the range of positive numbers for the first time and expanded the number system. Foreign countries did not realize negative numbers until the Yarlung Zangbo River in India in the 7th century.
Chapter 9 "Pythagorean Theorem": Various problems solved by Pythagorean Theorem. Most of them are closely related to the social life at that time. The general solution formula of Pythagorean number problem is put forward: if A, B and C are Pythagorean, strand and chord respectively, then m >；; In the west, Pythagoras and Euclid only got a few special cases of this formula, and it was not until Diophantine in the 3rd century that similar results were obtained, which was about 3 centuries later than Nine Chapters Arithmetic. There are still some contents in the Pythagorean chapter, but it is still modern in the west. For example, a set of formulas given by the last question in the Pythagorean chapter was not obtained by American number theorist Dixon until the end of 19 abroad.