What is the development level of mathematics in Song Dynasty in real history? What is the scene of engineering technology?
Although the Song Dynasty was weak in force and its territory was occupied by many people, its achievements in mathematics were widely publicized in history books, and the Song and Yuan Dynasties were even regarded as a climax of the development of mathematics in China. Looking back, the development achievements of mathematics in Song Dynasty laid the foundation of Tang Dynasty. At that time, the commercial trade of the Silk Road was booming, and people demanded more and more applications of computing. Some fast algorithms have been proposed to convert multiplication and division into addition and subtraction.
Among the mathematicians in the Northern Song Dynasty, Jia Xian was once a small military attache of the straight left class, with a low rank, but he made great achievements in mathematics. He studied with Chu Yan, a famous astronomer and mathematician at that time, summarized the specific mathematical problems in previous mathematical works, and put forward many new mathematical methods, including Jia Xian Triangle, multiplication and division, etc. Shen Kuo, a great scientist, also pioneered the use of gap product method to solve the problem of higher-order arithmetic progression summation in Meng Qian Bi Tan.
During the Southern Song Dynasty, there were two mathematical centers, North and South. South China is represented by Qin and Yang Hui, while North China is represented. Zhu Shijie, after the Yuan Dynasty unified China, was the combination of two mathematical centers, which reached the highest level of China calculation.
Qin is very talented. He is proficient in mathematics, astronomy, civil architecture, poetry, temperament, bow and horse, etc. He repeatedly called on the rulers to be benevolent, and regarded mathematical knowledge as a powerful tool to increase revenue and reduce expenditure and benefit the country and the people. However, in his official career, he was inevitably involved in the ruling clique war and the dispute between the two factions in the Southern Song Dynasty. Qin had a deep friendship with the special envoy of the Tang Dynasty, and advocated using force to resist Mongolia. He was vilified as "heartless, unjust, unfilial and dishonest" by Liu Kezhuang, an advocate and faction attached to the powerful minister Jia Sidao, and there were many attacks on him by public opinion. After his death, the history of the Song Dynasty and all local chronicles did not make a biography for him. However, this does not prevent Qin from going down in history in the world. Sutton, an American historian of science, said: "Qin is one of the greatest mathematicians in his country, his time and even all times."
However, Qin's Nine Chapters represented the highest level of mathematics development in the Middle Ages. Shu Shu Jiu Zhang is divided into nine categories and 8 1 topics, which are expansion, weather, territory, forecast, taxation, money valley, architecture, military service and market changes. Its achievements are greater than previous calculations, and the subject is more complicated. It is also because of Qin's experience as a leader of civil armed forces in Tongguan when he was young. Among them, the method of "seeking a skill by extension" is 554 years earlier than that of the western mathematician Gauss, and the method of "positive and negative square root" is 572 years earlier than that of the British mathematician Horner.
Yang Hui is also an official. He is in charge of money and food in Jiangsu and Zhejiang, and is honest for officials. Compared with Qin, his experience is much simpler. His most famous achievement is the famous Yang Hui Triangle, and he is still abusing candidates. Yang Hui triangle is the geometric arrangement of binomial coefficients in the triangle. In Europe, this watch is called Pascal Triangle. Yang Hui paid special attention to education and popularization, and summed up the agile algorithm and its formula of nine-return equal multiplication and division, which greatly popularized the people's mathematics education.
Ye Li, the leader of the North Mathematics Academic Center, also studied Tianyuan art, more than 300 years earlier than the West. Ye Li is the author of Round Sea Mirror. The publication of this book marks the maturity of Tianyuan Art.. The four-element method is an extension of the celestial body method. Quaternary refers to "heaven, earth, people and things", which is equivalent to saying four unknowns: X, Y, Z and W. Astrology is a method of solving an equation with an unknown number. Quaternion method is a method to solve equations of four unknowns. Since then, Guo Shoujing of the Yuan Dynasty has compiled calendars, used "Tiandao" to find the radian of the week, and used "Tiandao" to solve the calculation problems in water conservancy projects, all of which have achieved good results. And "celestial skills" soon developed into "binary skills" and "ternary skills", and even Zhu Shijie's "quaternary skills". Like the math problem written by Ying Gu in the legend of the condor hero, there is a topic of four-element skills.
The development of mathematics in Song Dynasty benefited from the overall development of society and science and technology at that time. In Song Dynasty, the bureaucratic system became more and more perfect, and there were many kinds of state institutions. The government participated in scientific activities to a great extent, such as the construction of water transport instrument platform led by Su Song. At the same time, the invention of printing also played a role in promoting. In the seventh year of Yuanfeng in the Northern Song Dynasty, the minister in charge of managing the national literature and archives printed ten mathematical classics, including Nine Chapters Arithmetic, which was the first printed mathematical work in the world. The works of mathematicians Jia Xian, Ye Li, Yang Hui and Zhu Shijie in Song and Yuan Dynasties were mostly published shortly after they were written. With the help of printing, mathematical works have been widely circulated, which has far-reaching significance for spreading and popularizing mathematical knowledge.
Generally speaking, during the prosperous period of mathematics, the level of engineering technology will be very high.
In astronomy, the Northern Song Dynasty was the sacrificial period of China's traditional Tianxue. There are six large troops, each weighing about 65,438+00 tons. The Northern Song Dynasty also conducted seven large-scale star surveys, which were unprecedented astronomical activities. The elephant of the water transport instrument rotates once a day and night, which not only vividly shows the change of the sky, but also is the ancestor of the rotating instrument clock, a tracking instrument of the modern observatory. Among them, the first escapement is the prototype of the key parts of the watch later.
In surveying and mapping, such as Huayi Map, Yuji Map, Geographical Map, and Nine-District Mausoleum-guarding Map were all very advanced at that time. For example, the map of concubine carved in Shaoxing in the Southern Song Dynasty in six years has a scale of1:4.5 million. It is the earliest map drawn at present, and the rivers and coastlines drawn are accurate. It is the most outstanding map in the world at that time, which is inseparable from the development of mathematics.