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What are the original ideas of Liu Hui's Nine Chapters Arithmetic Notes?
After "Nine Chapters Arithmetic", China's mathematical writings took two forms, one was to annotate "Nine Chapters Arithmetic", and the other was to compile new works based on "Nine Chapters Arithmetic". However, Nine Chapters of Arithmetic only contains short essays, examples and answers, without any proof. During the Han and Wei Dynasties, many scholars, such as Ma Xu, Zhang Heng, Zheng Xuan, Liu Hong, Xu Yue and Kan Ze, studied Nine Chapters Arithmetic, and all their works have been lost. However, those who "what you see is what you receive" in Liu Hui's Notes on Nine Chapters Arithmetic can understand its general situation.

Mathematicians tried to improve the value of pi, but the result was not ideal. For example, Zhang Heng finds π= 10, which means that the correct solution of pi has not been found. Complementary methods are widely used to prove geometric problems. For plane graphics, it was later called map lookup method. In straight line shape, it is reliable, but in curve shape, it can't really complete the proof. For three-dimensional graphics, later generations called it food inspection method. Liu Hui said: "The person who talks about calculation is the product of three dishes and has far-reaching influence." The three products are a cube with a length, a width and a height of 65,438+0 feet, a cutting block (two cutting blocks are obtained by tilting the cube) and a straight horse (that is, a right-angled quadrangle, a straight horse and a turtle nest are obtained by tilting the cutting block, that is, a tetrahedron with twisted sides). Generally speaking, the test method can only be used to verify the volume formula of a standard solid (that is, the one that can be decomposed or combined into three products), and it is powerless to the general situation. When people demonstrate the volume formulas of cones, circular pavilions and spheres, they use the method of comparing their bottom areas. This is the primary stage of the Zutai principle. The principle of uniformity is used in mathematical calculation. In a word, although people have made valuable efforts to prove the correctness of the formula of Nine Chapters Arithmetic and prepared rich materials for Liu Hui to adopt what he saw, most of these methods are inductive argumentation, and most of the difficult algorithms of Nine Chapters Arithmetic have not been strictly proved, and some of them have not been pointed out. Liu Hui's previous mathematics level did not make much progress on the basis of Nine Chapters Arithmetic, which gave Liu Hui "an opportunity to explore leisure time and understand meaning" and left a galloping world.