1, Chapter 9 Arithmetic

The author of Nine Chapters Arithmetic is no longer here. It is generally believed that it has gradually become the final version after several generations of supplement and modification. Zhang Cang and Geng Shouchang in the Western Han Dynasty had been supplemented and sorted out, and they were generally finalized at that time. The last book was in the early years of the Eastern Han Dynasty at the latest, and most of them were Notes to Nine Chapters written by Wei Yuan, Jing Yuan and Liu Hui in the Three Kingdoms Period (263).

"Nine Chapters Arithmetic" also has its unique achievements in mathematics. It not only mentioned the problem of score at the earliest, but also recorded the problem of surplus and deficiency at the earliest. The chapter "Equation" also expounds the negative number and its addition and subtraction algorithm for the first time in the history of world mathematics. It is a comprehensive historical work and the most concise and effective applied mathematics in the world at that time. Its appearance marks the formation of a complete system of ancient mathematics in China.

2. Zhou Kuai Shu Jing

Zhou You Shu Jing, formerly known as Zhou You Shu Jing, is one of the ten classic books on calculation. China's earliest works on astronomy and mathematics, written about 1 century BC, mainly expounded the theory of covering the sky and the quarter calendar at that time. In the early Tang Dynasty, it was stipulated as one of imperial academy's teaching materials, so it was renamed Zhou Kuai.

The main achievement of Zhou Kuai suan Jing in mathematics is the introduction of Pythagorean theorem. (It is said that Pythagorean theorem was not proved in the original work, but was proved by Zhao Shuang, a Wu Dongren, in Zhou Xie's Notes in the Three Kingdoms Period) and its application in measurement and how to apply it to astronomical calculation. )

3. "Island Computing"

Island Calculation is the earliest book on surveying mathematics written by China scholars, and it also provides a mathematical basis for cartography. This is the tenth volume of Nine Chapters Arithmetic Notes written by Liu Hui in the fourth year of Wei Jingyuan in the Three Kingdoms (AD 263), entitled "Heavy Difference".

At the beginning of Tang dynasty, it was a single line, and the style was also the form of application problem set. The research objects are all about the measurement of height and distance, and the tools used are all measuring rods and horizontal rods connected vertically. Some people say that it is the enlightenment of practical trigonometry, but its content does not involve the concept of sine and cosine in trigonometry. All problems are to calculate the height, depth, width and distance of unreachable targets by using the data obtained from two or more observations.

4. suan Jing, Zhang Qiujian

Zhang Qiujian Jing, China's ancient mathematical works. The outstanding achievements of 92 problems (about 5th century AD) are the calculation of the greatest common divisor and the least common multiple, the solution of various arithmetic progression problems and the solution of some indefinite equation problems.

Since Zhang Qiujian, Chinese mathematicians have been deeply studying the hundred chickens problem, which has almost become synonymous with indefinite equations. From the Song Dynasty to the Qing Dynasty, the mathematical research on hundred chickens has achieved good results.

5. Ji Gu suan Jing

Jing Ji Gu Shu Jing is one of China's ancient mathematical works, written by Wang Xiaotong. He was a mathematician in the early Tang Dynasty. According to the records in Old Tang Shu, New Tang Shu and Tang Yao Hui, Wang Xiaotong was born in a civilian family. During the Wude period (around 623 AD), he was appointed as a doctor of arithmetic, and was ordered to collate the Five-tone Calendar compiled by Fu with Langzhong Zuxiaosun of the official department, and raised more than 30 objections, and was promoted to Taishi Cheng.

Wang Xiaotong devoted his life to mathematical research. He is the greatest mathematician of this period. His greatest contribution is to write Ancient Arithmetic on the basis of summarizing previous studies.