# The basis of the development of ancient Chinese mathematics

Liu Hui s main works are: Nine Chapters of Arithmetic 10 volumes; Heavy Difference is the Islands of Arithmetic 1 volume; Nine Chapters of Heavy Difference Illustration 1 volume. Unfortunately, both of the latter two books are missing. Liu Hui s mathematical achievements are roughly two aspects: one is to clarify the ancient Chinese mathematical system and lay its theoretical foundation; the other is to put forward his own ideas on the basis of inheriting the achievements of predecessors. Nine Chapters of Arithmetic has formed its own relatively complete theoretical system in the aspects of number system theory, chip calculus theory, Pythagorean theory, area and volume theory, and circle cutting and pie ratio.

Nine Chapters of Arithmetic is one of the most important classic mathematical works in China. The current nine chapters of Arithmetic collects a total of 246 applied problems and solutions to various problems, which belong to Fangtian, Corn, Decay, and Shao respectively. Nine chapters on broadcasting, commercial power, loss, profit and loss, equations, and go-go. The various algorithms included in Nine Chapters of Arithmetic were supplemented and revised by Han mathematicians on the basis of mathematics handed down before the Qin Dynasty to meet the needs of the time.

Nine Chapters of Arithmetic not only has an important position in the history of Chinese mathematics, but also has made outstanding contributions to the development of world mathematics. Fraction theory and its complete algorithms, ratio and proportion allocation algorithms, area and volume algorithms, and solutions to various types of application problems have been compared in chapters such as Fangtian, Corn, Attenuation, Quotient, and Loss of Equity. Detailed narrative. The contents of the opening methods in the chapters such as Shaoguang, Insufficient, Equation, Pythagorean, Insufficient (Double Hypothesis), Concepts of Positive and Negative Numbers, Solutions of Linear Simultaneous Equations, General Formulas of Integer Pitch String Leading position in the history of world mathematics.

Liu Hui used the same and different types of numbers to explain the algorithms of general division, reduction, four operations, and simplification of complex fractions. In the commentary of the formula, he discussed the unreasonable formula from the endless meaning of the formula. The existence of roots, and the introduction of new numbers, created a method of approximating irrational roots infinitely with decimal fractions.

Liu Hui gave a more explicit definition of the rate of precedence, and based on the three basic operations of multiplication, contract, and homogeneity. He established a unified theoretical basis for number and formula operations. He also used rate to define China. The equation in ancient mathematics is the augmented matrix of linear equations in modern mathematics.

Liu Hui demonstrated the calculation principles of the Pythagorean theorem and the solution of Pythagoreans one by one, established a similar theory of Pythagoreans, and developed the Pythagorean measurement technique. The analysis of the typical figures has formed a similar theory with Chinese characteristics.

HuiLiu Hui in the Nine Chapters of Arithmetic \\ u0026 Middot; Martian note, proved the exact formula of the area of ​​the circle by cutting the circle, and gave a scientific method to calculate the pi. He first cuts a circle starting from a hexagon inside the circle. Each time the number of sides is multiplied, the area of ​​the 192 polygons is calculated, and we get \\ u0026 pi; = 157/50 = 3.14, and the area of ​​the 3072 polygons is calculated, and we get \\ u0026 pi; = 3927/1250 = 3.1416, which is called the Hui rate.