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Chapter III bad points , say the distribution of goods or by grade assessed the proportion of tax issues
Chapter IV, less wide , stresses open square, the cube is calculated
Chapter V business credit , say the size of a variety of shapes is calculated
Chapter VI, are lost, according to the population how to speak, and prices are high or low, long distance and other factors to calculate tax and distributed around theissues such as the calculation method
Chapter VII of the lack of profit , that is the assumption that the method used to solve the problem of a class is as follows This year there are people to buy a total of complex, each of eight people the money a surplus of three the money, each Seven people money less than four money, Q the number of geometric price? 6 such problems, in the Nine Chapters on the number of patients have a complete solution
Chapter VIII of the equation is on the simultaneous solutiongeneral description of group
Chapter IX , mainly the application of the Pythagorean Theorem and right triangle similar to the ratio between a variety of measurement and calculation of high, deep, broad, far problem.
Jiuzhang arithmetic, not only to prepare a more complete structure, forming a style of mathematics has its own system, and the mathematical level of the advanced in the ranks of the world, some of which achievement is far ahead in the world. Such as insufficient surplus technique similar to modern determinant method , which side in Europe to the Middle Ages to the double-try to form Until the sixteenth century in Europe when the parties reached a similar simultaneous equations of the general solution equation has been introduced in Chapter negative concepts, and the generation and use of positive and negative addition and subtraction rules, and India to the seventh century, the Europe to the sixteenth century, the only have a clearer concept of the negative.
To Jiuzhang arithmetic of mathematics in China as the representative system, characterized by community based solution for the main purpose of the practical problems in order to count as the main financing tool, the value of a replica rolex decimal system of notation system operator, its content, including arithmetic, algebra, geometry, and so on. The mathematical system in its own course of development, gradually moving towards its peak, has not changed the long-sheng of the situation, and forged many of the fruit. The most outstanding achievements are
The ancient world, the most accurate pi. Wei Jing-three million four years 263 years, the famous mathematician Liu Hui in the Nine Chapters on Arithmetic as a note, the creation of a cutting circle of the new method of operation. He believes that when the next round with the edge of the infinite regular polygon increases, its perimeter that is increasingly approaching the circumference length, fine cut of indemnity, the indemnity small loss. Cutting and cutting of that can not be cut, and fit with a round having lost everything. 7 from the can see that the idea of Liu Hui has been applied to limit the calculation of pi. Liu Hui application cut-round operation, from the circle next date is hexagonal, while doubling the number of step by step, direct calculation is then to 192 yen in the area of polygon, find the circumference
Liu Hui39s work, to derive a precise figure to seven effective pi 3.1415926 lt lt3.1415927. Get this result, which is equivalent to the application of count nine the number of chips on a large number of various operations including prescribing for more than 130 times, the amount of work is not hard to imagine. In order to calculate the square
About the rate. Zu Chongzhi data obtained pi, far away in front of the world until after the millennium, the Arab mathematicianal Kashi in the year 1427, the French mathematician-dimensional special leaf Viete AD years 1540- 3, only more accurate data obtained. Obtained dense rate, until the sixteenth century in Europe is to achieve.
Other factors, such as the Sui Dynasty founded by Liu Zhuo, such as the second pitch interpolation in the Tang Dynasty and his entourage, ranging from the second pitch interpolation, Wang39s three equation method Song and Yuan Dynasties for more than three times during the equation solution method, high-order sum arithmetic progression, a simultaneous congruence, etc., are also leading in the world for hundreds of years old. And widely used in the Ming Dynasty abacus beads, it is one of hundreds of years the most advanced computing tools, there are still some vitality.
As proof of the ancient Greek emphasis on the neglect of the geometric calculation, the figures of ancient China in a very developed area, in real life issues faced by the geometric and arithmetic, or algebra are the methods to answer, thereby limiting the relative geometric proof. However, this does not mean that there is no geometry in ancient China. Mozi them in the Mojing made by a round, straight, point, line, face, body, parallel to a variety of propositions and concepts, can be associated with Euclidean geometry, theorems and propositions comparable. Pythagorean Theorem and its applications, graphics tools for regulation, the commonly used moments are also reflected in the geometry of ancient China has a considerable achievement. Of course, in practical under the guise of mathematical calculation, the geometry of ancient China there is no rational argument in regard to the full development computational mathematics itself Jiuzhang arithmetic style under the influence of exercise have long been used by way of questions and answers do not make a a good abstract and improved to make it more rational extent, this can not but say a major flaw.
Section II of the compass and other achievements in physics