Liu Hui was the most outstanding mathematician in the world in the 3rd century A.D. His Nine Chapters Arithmetic Notes written in A.D. 263 and his later calculations on the island were China's most precious mathematical heritage, thus establishing his immortal position in the history of Chinese mathematics.
Liu Hui's mathematical works are rarely passed down to later generations, and they are all copied for a long time.
His main works are: Nine Chapters of Arithmetic Notes (volume 10); The weight difference (1) was renamed as island calculation in the Tang Dynasty. Chapter 9 gravity difference Map Volume L. Unfortunately, the latter two were lost in the Song Dynasty.
Liu Hui's Nine Chapters Arithmetic was written in the early Eastern Han Dynasty, with 246 solutions. In many aspects, such as solving simultaneous equations, calculating four fractions, calculating positive and negative numbers, calculating the volume and area of geometric figures, etc. , all belong to the advanced ranks in the world.
However, due to the primitive solution and the lack of necessary proof, Liu Hui made supplementary proof. In these proofs, his creative contributions in many aspects are shown. He was the first person in the world to put forward the concept of decimal, and used decimal to represent the cube root of irrational numbers. In algebra, he correctly put forward the concept of positive and negative numbers and the principle of addition and subtraction, and improved the solution of linear equations. In geometry, "secant" is put forward, that is, the method of finding the area and perimeter of a circle by using inscribed or circumscribed regular polygons to exhaust the circumference. He scientifically obtained the result that pi = 3. 14 16 by using secant technology. He cut a circle from a circle with a diameter of 2 feet by using the circle cutting method, and then got a regular hexagon 12 and a regular hexagon 24 ... The thinner he cut, the smaller the difference between the area of a regular polygon and the area of a circle. In his original words, it is "cut carefully, and the loss is not big. If you cut again, there will be no loss." He calculated the area of 3072 polygons and verified this value. The scientific method of calculating pi put forward by Liu Hui has established China's leading position in the world for more than 1000 years.
Liu Hui has made great contributions to mathematics, and put forward the idea of "seeking the number of emblems" among endless problems. This method is consistent with the later method of finding the approximate value of irrational roots. It is not only a necessary condition for accurate calculation of pi, but also promotes the generation of decimals. In the solution of linear equations, he created a simpler method of mutual multiplication and elimination than direct division, which is basically consistent with the current solution; And put forward the problem of indefinite equation for the first time in the history of Chinese mathematics; He also established the summation formula of arithmetic progression's first n terms; Many mathematical concepts are put forward and defined, such as power (area); Equation (linear equation); Positive and negative numbers and so on. Liu Hui also put forward many recognized correct judgments as the premise of proof. Most of his reasoning and proof are logical and rigorous, so he bases the nine-chapter arithmetic and his own solutions and formulas on inevitability. Although Liu Hui didn't write his own works, the mathematical knowledge he used in Nine Chapters Arithmetic has actually formed a unique theoretical system, including concepts and judgments, with mathematical proof as the link.
Liu Hui's theory "carefully cut the circle and lose little;" Cut hard, can't cut, just into the circle, don't lose anything "can be regarded as the representative work of China's ancient limit concept. In the book Island Calculation, Liu Hui carefully selected nine survey questions. The creativity, complexity and representativeness of these topics attracted the attention of the west at that time. Liu Hui has quick thinking and flexible methods. He advocates reasoning and intuition. He was the first person in China who explicitly advocated using logical reasoning to demonstrate mathematical propositions.