He cut a circle from a circle with a diameter of 2 feet by connecting a regular hexagon, and then he 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 generally accepted and correct judgments as the premise of proof. Most of his reasoning and proof are logically rigorous, thus establishing nine chapters of arithmetic and his own solutions and formulas on the basis of inevitability. Although Liu Hui did not write a self-contained book, he noticed that the mathematical knowledge used in Nine Chapters Arithmetic has actually formed a unique set, including concepts and judgments, and is based on mathematical proof.