Nine Chapters Arithmetic was written around A.D., which systematically summarized China's mathematical achievements from pre-Qin to mid-Western Han Dynasty. The author of this book can't be verified, except for the addition and deletion of famous mathematicians in the Western Han Dynasty, such as Zhang Cang and Geng Shouchang. This book is divided into nine chapters. A * * * has collected 246 mathematical problems, which are divided into nine categories according to the method of solving problems and the scope of application, and each category is regarded as a chapter.
The Southern and Northern Dynasties witnessed the vigorous development of ancient mathematics in China, and many books about mathematics appeared, such as Sun Tzu's Calculations, Xiahou Yang's Calculations and Zhang Qiu's Calculations.
There are 10 books on mathematics, such as island calculation. Therefore, the mathematical education system at that time was of positive significance for inheriting ancient mathematical classics.
In 600 AD, Liu Zhuo of Sui Dynasty put forward the world's first quadratic interpolation formula with equal spacing in Huang Liji. In the Tang Dynasty, monks and their entourage developed it into a quadratic interpolation formula with unequal intervals in their Dayan calendar.
Jia Xian put forward the "multiply-multiply-open method" in the Nine Chapters of the Yellow Emperor to open any higher power. The same method was not discovered by British Horner until 18 19. Jia Xian's binomial theorem coefficient table is similar to1"Basga Triangle" which appeared in Europe in the 7th century. Unfortunately, the manuscript of Jia Xian's Nine Chapters of Yellow Emperor's Fine Grass Algorithm has been lost.
Qin was an outstanding mathematician in the Southern Song Dynasty. 1247 extends the "multiplication and division method" in Shu Shu Jiu Zhang, discusses the numerical solution of higher-order equations, and cites more than 20 kinds of solutions of higher-order equations (the highest is the decagonal equation) according to practice. It was not until16th century that the Italian Philo proposed the solution of cubic equation. In addition, Qin also studied the theory of a congruence.
On 1248, Ye Li published "Circle Survey of the Sea Mirror", which is the first book to systematically discuss "Tianshu" (one-dimensional higher-order equation) and has a milestone significance in the history of mathematics. What is particularly rare is that in the preface of this book, Ye Li openly criticizes and despises scientific practice activities, and devalues mathematics as a long-standing fallacy such as "cheap skills" and "playthings".
In A.D. 126 1 year, Yang Hui (the year of birth and death is unknown) in the Southern Song Dynasty used "piling technique" to find the sum of several kinds of high-order arithmetic progression. In A.D. 1274, he also described the "Nine-fold Agile Method" in his book The Origin of Multiplication and Division Transformation, and introduced various calculation methods of multiplication and division. In A.D. 1280, Wang Xun and Guo Shoujing listed the interpolation formula of triple difference when compiling the calendar method of the Yuan Dynasty. Guo Shoujing also found two formulas equivalent to the present spherical triangle by geometric method.
In A.D. 1303, Zhu Shijie of Yuan Dynasty (date of birth and death unknown) wrote a jade mirror with four elements. He extended "Tianshu" to "Quaternary" (Quaternary high-order simultaneous equation) and put forward the elimination method. It was not until A.D. 1775 that the Frenchman Bezot proposed the same solution in Europe. Zhu Shijie also studied the summation of finite series, and on this basis, obtained the interpolation formula of higher-order difference. It was not until A.D. 1670 that Gregory from England and Newton from Europe (A.D. 1676- 1678) put forward the general formula of interpolation.
/kloc-After the establishment of the Ming Dynasty in the middle and late 4th century, the rulers carried out the imperial examination system characterized by eight-part essay, which greatly reduced the contents of mathematics in the national imperial examination, so the ancient mathematics in China began to show a general decline.
In the Ming Dynasty, abacus began to spread in China. Cheng Dawei 1592's Command Arithmetic Unified Clan is a masterpiece of abacus theory. However, some people think that the popularity of abacus is one of the main reasons for inhibiting the further development of ancient mathematics in China based on abacus.
From the end of 16, western missionaries who came to China introduced some western mathematical knowledge to China. Mathematician Xu Guangqi learned western mathematics knowledge from Italian missionary Matteo Ricci, and they also translated the first six volumes of Elements of Geometry (completed at 1607). Xu Guangqi demonstrated the Pythagorean prospecting in China with western logical reasoning methods, so he wrote two books to measure similarities and differences and Pythagorean significance. Deng's Great Survey (Volume 2), Secant Circle and Eight-line Table (Volume 6) and giacomo Rowe's Significance of Measurement (Volume 10) are works introducing western trigonometry.