Nine Chapters of Arithmetic marks the formal formation of China's ancient mathematical system based on calculation.
In the Three Kingdoms and Jin Dynasties, ancient mathematics in China was mainly based on theoretical research, with Zhao Shuang and Liu Hui as the main representatives.
Zhao Shuang was a native of Wu during the Three Kingdoms period. In the history of China, he was one of the first mathematicians to prove mathematical theorems and formulas, and his academic achievements were reflected in his interpretation of Zhou pian Shu Jing. He also proved the Pythagorean theorem by geometric methods in Pythagorean Notes, which actually embodied the method of "cut-and-complement principle". Solving quadratic equation by geometric method is also a great contribution of Zhao Shuang to Chinese ancient mathematics. During the Three Kingdoms period, Ren Wei Liu Huize annotated Nine Chapters Arithmetic. His Notes on Nine Chapters of Arithmetic not only explains and deduces the methods, formulas and theorems of nine chapters of arithmetic in general, but also systematically expounds the theoretical system and mathematical principles of China's traditional mathematics, which is groundbreaking. His invention of secant (the area of a regular polygon inscribed with a circle is infinitely close to the area of a circle) laid the foundation for the calculation of pi, and Liu Hui also calculated the approximate value of pi-"3927/1250 (3.1416)". The geometric model of "Mouhe Square Cover" designed by him laid an important foundation for future generations to seek the formula of sphere volume. In the process of studying the volume of polyhedron, Liu Hui proved "Yang Equestrian" by the limit method. In addition, Island Calculation is also a mathematical monograph compiled by Liu Hui.
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.
The most representative works in this period are the works of Zu Chongzhi and Zuxuan. Focusing on mathematical thinking and reasoning, they took a step forward on the basis of Liu Hui's Notes on Nine Chapters of Arithmetic. According to historical records, his book seal script (Yi) has achieved the following achievements: ① Pi is accurate to the sixth place after the decimal point, which is 3. 14 15926.
The main achievement in Sui and Tang Dynasties was the establishment of China's mathematics education system, which was probably mainly related to the establishment of imperial academy Middle School Mathematics Academy and imperial examination system. At that time, the Ten Arithmetic Classics became special teaching materials for students. There are 10 mathematical works in The Ten Books of Calculation Classics, such as Calculation Classics, Nine Chapters of Arithmetic and Calculation Classics on the Island, which Zhou Pi loves. 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.
1 1 century to14th century was the heyday of ancient Chinese mathematics, which was characterized by the emergence of many outstanding mathematicians and mathematical works. The mathematics of Song and Yuan Dynasties was the highest realm of ancient mathematics in China. In the world, the mathematics of Song and Yuan is almost neck and neck with Arabic mathematics.
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 popularized the "multiplication and division method" in Shu Shu Jiu Zhang, discussed the numerical solutions of higher-order equations, and cited more than 20 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. The Great Survey edited by Deng [2 volumes], the Secant Circle and Eight-line Table [6 volumes] and giacomo Rowe's Survey [10 volumes] are all works introducing western trigonometry.