In 22 1 BC, Qin Shihuang ended more than five centuries of annexation and war, and established the first unified and centralized feudal country in China. From the Qin Dynasty to the early years of the Western Han Dynasty, the emerging landlord class rewarded farming and weaving, built water conservancy projects, attached importance to smelting and built the Great Wall. Driven by production, science and technology have made great progress. In the early Western Han Dynasty, from Emperor Gaozu to Emperor Wudi of the Han Dynasty, people were advised to plant agriculture and mulberry trees to further develop production and technology serving the landlord class. Nine Chapters Arithmetic was written under this historical condition.
This masterpiece is a comprehensive summary of China's ancient mathematical knowledge. The book collects 246 practical mathematical problems, which are divided into nine chapters, namely square field, millet, decreasing score, less generalization, quotient work, occasional loss, surplus and deficiency, equation and Pythagorean, so it is named "Nine Chapters Arithmetic".
Fang Zhangtian tells the calculation of four mu area. Combined with this need, this paper systematically introduces the four operations of addition, subtraction, multiplication and division of fractions, turns fractions into pseudo-fractions, and finds the least common multiple of several denominators. According to the existing historical data, Nine Chapters Arithmetic is the earliest document that records fractional arithmetic in the world. Europeans didn't master these laws until15th century. Supian studies the exchange of various grains. "Decline is divided into chapters" and "all chapters are used" to discuss the proportional distribution of tax corvee. The chapter "surplus and deficiency" calculates the answer to the question according to the surplus and deficiency obtained from two assumptions. It was another creation of China's ancient mathematics, and later Europeans called it "China algorithm".
Zhang Shaoguang introduced the square root and its calculation, which also included the contents of fractions. "Commercial seal" is specially used to solve various volume calculation problems in civil engineering such as building cities and opening canals. Pythagorean chapter discusses Pythagorean theorem and similar right triangle. And put forward the solution of quadratic equation, which is the earliest record of solving quadratic equation with some algorithm in the world.
"Equation chapter" studies the solution of linear equations in detail, and introduces the concepts of positive and negative numbers and their addition and subtraction algorithms, two outstanding achievements of ancient mathematics in China. In this chapter, * * * collects the practical problems of 18 multivariate linear equations. For example, the first title is: "Today, the upper grain (ancient capacity unit) is third-hand, the middle grain is second-hand, and the lower grain is first-hand, which is actually 39; Two catches on the grain, three catches on the grain, and one catch on the grain, with 34 fights; Twenty-six buckets, one bucket of grain, two buckets of grain, and three buckets of grain. Find the geometry of the upper, middle and lower crops? " If the current method is used and the upper, middle and lower crops are set as X barrels, Y barrels and Z barrels respectively, then the equations can be obtained. In ancient China, the method to solve this kind of problem (called "equation technique") was to arrange the unknown coefficients and constant terms of the equation into an "equation set" in turn according to a "straight line". The "equation set" of this problem is like this: then, by multiplying the number of rows and adding and subtracting between rows, the unknowns are eliminated one by one, and the solution of the "equation set" is obtained. These ideas and forms can be called the precursors of the concepts of "matrix" and "matrix solution of linear equations" in modern higher algebra.
The whole content of Nine Chapters Arithmetic shows that mathematics, like all other sciences, comes from people's needs: from measuring land and volume, from calculating time and making utensils. "Nine Chapters Arithmetic" is closely combined with the reality, which embodies the distinctive features and fine traditions of ancient mathematics in China and has a far-reaching influence on the later development of mathematics in China.