The development of arithmetic

The calculation of pi is a nerve-racking problem in ancient mathematics. In Zhou Kuai Shu Jing and Nine Chapters Arithmetic, China obtained the approximate values of pi with a diameter of one week and three weeks. Liu Hui created the secant circle. The approximate value of pi is obtained systematically and strictly by using inscribed regular polygons. He thinks this result can continue. When the number of polygons increases indefinitely, the sum of the areas of polygons is equal to the area of a circle. "If you cut carefully, you will lose a little. If you cut it again, you can't cut it, and there is nothing to lose with the circle. " Liu Hui's "Secant" laid a theoretical foundation for the study of pi. Zu Chongzhi, a great scientist in ancient times, made outstanding achievements in mathematics, astronomical calendar and mechanical manufacturing. Mathematically, he found that pi was between 3. 14 15926 and 3. 14 15927. Zu Chongzhi also uses two fractions to express pi, one is 355/ 1 13, which is called density ratio, and the other is 22/7, which is called approximate ratio. German Otto reached this level in 1573, more than 1000 years later than Zu Chongzhi, so western experts in the history of mathematics proposed to name this precise value of pi as "ancestral rate".

At the end of the Tang Dynasty, the traditional calculation was replaced by abacus, which was greatly improved in the Song and Yuan Dynasties. Abacus and abacus formulas played an important role in the popularization of practical mathematics, and were the most advanced calculation tools and methods in the world at that time. During the Song and Yuan Dynasties, a number of high-level mathematical works and famous mathematicians emerged in China, among which Qin, Yang Hui and Zhu Shijie were regarded as the four great mathematicians in the Song and Yuan Dynasties. Their main achievements include the solution of higher-order equations and higher-order equations, the study of binomial expansion coefficient triangles, and how to find the area of triangles with known three sides, which reached the most advanced mathematical level in China and the world at that time.

China's mathematical works

Most of the mathematical works written by many outstanding mathematicians in ancient times have been lost for a long time, and only a few can be passed down to today. Among them, ten mathematical works, Zhou Pi Ai Jing, Nine Chapters Arithmetic, Island Arithmetic Classic, My Cao Arithmetic Classic, Sun Zi Arithmetic Classic, Xiahou Yang Arithmetic Classic, Zhang Qiu Arithmetic Classic and Five Classics Arithmetic and Composition, are collectively called the ten classic books of arithmetic. These ten books are the most important mathematical works from Han Dynasty to Tang Dynasty 1000. They not only occupy an important position in the history of Chinese mathematics, but also have a long-standing reputation in the history of world mathematics.