Jia Xian abstracted most of the essays in "Nine Chapters Arithmetic" and didn't leave specific objects or even numerical values like general essays, which improved the theoretical level of "Nine Chapters Arithmetic".
Jia Xian's thoughts and methods had a great influence on Song and Yuan Mathematics, and he was one of the main promoters of Song and Yuan Mathematics.
Shen Kuo, a great scientist in the Northern Song Dynasty, had a unique view on mathematics. In Meng Qian Bi Tan, he pioneered the gap product technique, the high-order arithmetic progression summation problem, the rounding technique and the approximate formula for calculating the bow arc length for the first time.
About half a century between Song and Yuan Dynasties is the concentrated expression of China's mathematical climax, and it is also the period when China left the most important mathematical works, forming the middle and lower reaches of the Yangtze River under the Southern Song Dynasty and Taihang Mountain under the Jin and Yuan Dynasties. Does the South Center go to Qin? Represented by Yang Hui, numerical solution of higher-order equation? This paper mainly studies congruence solution and improved multiplication and division method and agile algorithm.
Qin wrote "Arithmetic in Nine Chapters of Counting Books" in volume 18. Divide into big swallows? Time? Tian Yu? Looking for? Forage? Money Valley? Architecture? Army? The achievement and complexity of the urban 1981problem exceeded the previous calculation. Some questions have 88 conditions, and some answers are as many as 180. The number of military questions is unprecedented, which reflects his concern for the Yuan War.
Yang Hui * * * wrote five mathematical works, namely "Detailed Explanation of Arithmetic Algorithms in Nine Chapters"? Daily algorithm? Multiply, divide and change the background? "Tian Bi Class Multiplication and Division Method" and "Continuation Gucci Algorithm". There are four handed down from generation to generation, ranking first among mathematicians before Yuan Dynasty.
The northern center at the turn of the Song and Yuan Dynasties, represented by Ye Li, focused on astrophysics and the solution of higher-order equations. Ye Li's round sea mirror (volume 12)? Yi Gu Yan Duan (3 volumes) is the earliest work handed down from generation to generation so far, and it is mainly based on celestial technique.
After Yuan unified the whole country, a mathematician in Yuan Dynasty? Zhu Shijie, an educator, is a combination of two mathematical centers in the north and the south, reaching the highest level of calculation in China.
Zhu Shijie has two important works, Arithmetic Enlightenment and Meeting with Philip Burkart, which have been handed down from generation to generation. He once traveled around the world as a famous mathematician for more than 20 years, and many people learned mathematics from him.
Besides, Yang Hui? How did Zhu Shijie and others improve the agile algorithm for calculating multiplication and division? Summary led to the emergence of abacus and abacus, and completed the transformation of computing tools and computing technology in China.
In the middle and late Yuan Dynasty, Ding Ju algorithm appeared again? Jia Heng's complete algorithm? He introduced Ping Zi's detailed algorithms and other work to improve the multiplication and division of agile algorithms.
Shen Kuo's works