all one's life

(Born around 250 AD), wei ren was an outstanding mathematician in ancient China and one of the founders of China's classical mathematical theory in the late Three Kingdoms period. History books rarely record his birth, death and life story. According to limited historical data, he was from Zouping, Shandong Province in Wei and Jin Dynasties. Never been an official.

work

Liu Hui's mathematical works are rarely handed down to later generations, and all of them have been copied over and over again. His main works are:

Nine arithmetic notes (10);

The weight difference (1) was renamed as island calculation in the Tang Dynasty.

"Nine Chapters Heavy Difference Map" L volume, but unfortunately the last two were lost in the Song Dynasty.

achievement

Liu Hui's mathematical achievements are roughly in two aspects:

First, clarify the ancient mathematical system of China and lay its theoretical foundation. This aspect is embodied in Nine Chapters of Arithmetic Notes. It has actually formed a relatively complete theoretical system:

(1) In number system theory

This paper expounds the general division, simplification, four operations and simplification rules of complex fractions with the same sign and different sign. In the annotation of prescription, he discussed the existence of irrational roots from the infinite meaning of prescription, introduced new numbers, and created a method of infinitely approaching irrational roots with decimals.

(2) In convex calculus theory.

First of all, he gave a clear definition of rate, and based on three basic operations, such as multiplication and division, he established a unified theoretical basis for the operation of numbers and formulas. He also defined the "equation" in China's ancient mathematics by rate, that is, the augmented matrix of linear equations in modern mathematics.

③ In Pythagoras' theory.

The pythagorean theorem and the calculation principle of solving pythagorean form are demonstrated one by one, the theory of similar pythagorean form is established, and pythagorean measure is developed. Through the analysis of typical figures such as "crossing in the hook" and "straight in the stock", a similar theory with China characteristics was formed.

④ In the area and volume theory.

Liu Hui's principle is put forward by using the principle of complement, the deficiency of complement and the limit method of "cyclotomy", which solves the problem of calculating the area and volume of various geometric shapes and geometries. The theoretical value of these aspects is still shining.

Second, on the basis of inheritance, put forward your own ideas. This aspect is mainly reflected in the following representative innovations:

① Circumcision and Pi

He is in "Nine Chapters Arithmetic? 6? In the note of 1 circular field technique, the exact formula of circular area is proved by secant technique, and the scientific method for calculating pi is given. He first cuts a circle from the hexagon inscribed in the circle, and every time the number of sides is doubled, he calculates the area of 192 polygon, π= 157/50=3. 14, and then calculates the area of 3072 polygon, π = 3927/1.

② Liu Hui principle

Chapter 9 Arithmetic? 6? In 1 Yang Equestrian's notes, he put forward the principle of Liu Hui's calculation of polyhedron volume when solving cone volume by infinite division.

③ the theory of "concerted housing reform"

Chapter 9 Arithmetic? 6? In the annotation of 1 Open Circle, he pointed out the inaccuracy of the formula V=9D3/ 16(D is the diameter of the ball) and introduced the famous geometric model "Mouhe Square Cover". "Mouhe Square Cover" refers to the intersection of inscribed cylinders with two perpendicular axes.

④ New technology of equation

Chapter 9 Arithmetic? 6? 1 equation skills, he proposed a new method to understand linear equations, using the idea of ratio algorithm.

⑤ gravity difference operation.

In his white paper "Island Calculations", he put forward the complex difference technique, which used complex tables, continuous cables, cumulative moments and other methods to measure the height and distance. He also developed gravity difference technology from two observations to three observations and four observations by analogy. In the 7th century, India and Europe only began to study the problem of two observations in15 ~16th century.

Contribution and status

Liu Hui's work not only had a far-reaching impact on the development of ancient mathematics in China, but also established a lofty historical position in the world. In view of Liu Hui's great contribution, many books call him "Newton in the history of Chinese mathematics".