1. Zhao Shuang was a mathematician in Wu Dong during the Three Kingdoms period. He once wrote Pythagoras Arithmetic Classics, and wrote Pythagoras Square Notes with more than 500 words and several figures. This annotation concisely summarizes the important achievements of Pythagoras' arithmetic in the Eastern Han Dynasty, and gives and proves more than 20 propositions about the three sides of Pythagoras' string and the relationship between sum and difference for the first time.
Zhao Shuang also derived the quadratic equation x2+ax=A (where A >；; 0，A & gt0).
The proof of "gravity difference technology" is given by using the area relation of geometric figures in sunrise photos. The method used by astronomers in the Han Dynasty to measure the height and distance of the sun is called gravity difference technique.
2. Zhu Shijie (about AD 1300) was born in Songting, Han Qing, and lived in Yanshan (now near Beijing). He "traveled around the lake and sea with famous mathematicians for more than 20 years" and "gathered scholars by following the door" (Moruo and Zuyi: Preface to Four Mirrors). Zhu Shijie's representative works in mathematics include "Arithmetic Enlightenment" (1299) and "Meeting with the Source" (1303).
"Arithmetic Enlightenment" is a well-known mathematical masterpiece, which spread overseas and influenced the development of mathematics in Korea and Japan.
"Meeting with the source of thinking" is another symbol of the peak of China's mathematics in the Song and Yuan Dynasties, among which the most outstanding mathematical creations are "thinking of the source" (formulation and elimination of multivariate higher-order equations), "superposition" (higher-order arithmetic progression summation) and "inviting difference" (higher-order interpolation).
3. Together with his father Zu Chongzhi, Zu Chongzhi's son Zuxuan successfully solved the problem of calculating the sphere area and got the correct volume formula. The well-known "principle of forming ancestors" in current textbooks can be described as the outstanding contribution of Zuxuan to the world in the 5th century.
4. Zu Chongzhi (429-500) was a mathematician, astronomer and physicist in the Southern Dynasties of China. Zu Chongzhi's grandfather, Zuchang, was an official in charge of royal architecture in the Song Dynasty. Zu Chongzhi grew up in such a family and learned a lot from childhood. People all praise him as a knowledgeable young man. He especially likes studying mathematics, and he also likes studying astronomical calendars. He often observes the movements of the sun and planets and makes detailed records.
When Emperor Xiaowu of Song heard of his fame, he sent him to work in a government office specializing in academic research in Hualin Province. He is not interested in being an official, but he can concentrate more on mathematics and astronomy there.
There have been officials who studied astronomy in all previous dynasties in our country. They made calendars according to the results of astronomical research. By the Song Dynasty, the calendar had made great progress, but Zu Chongzhi thought it was not accurate enough. Based on his long-term observation, he created a new calendar called "Daming Calendar" ("Daming" is the title of Emperor Xiaowu of Song Dynasty). The number of days in each tropical year measured by this calendar (that is, the time between winter and sun in two years) is only 50 seconds different from that measured by modern science; It takes less than one second to measure the number of days for the moon to make one revolution, which shows its accuracy.
In 462 AD, Zu Chongzhi requested Emperor Xiaowu of Song Dynasty to issue a new calendar, and Emperor Xiaowu called ministers to discuss it. At that time, Dai Faxing, one of the emperor's minions, stood out against it and thought that it was deviant for Zu Chongzhi to change the ancient calendar without authorization. Zu Chongzhi refuted Defarge on the spot with his own research data. Relying on the emperor's favor, Dai Faxing said arrogantly: "The calendar was formulated by the ancients and cannot be changed by future generations." Zu Chongzhi is not afraid at all. He said very seriously, "If you have a solid basis, argue it out. Don't scare people with empty talk. " Emperor Xiaowu of Song wanted to help Dai Faxing, and found some people who knew the calendar to argue with Zu Chongzhi, but Zu Chongzhi refuted them one by one. However, Emperor Xiaowu of Song still refused to issue a new calendar. It was not until ten years after Zu Chongzhi's death that his Da Ming Li was put into practice.
Although the society was very turbulent at that time, Zu Chongzhi studied science tirelessly. His greater achievement is in mathematics. He once annotated the ancient mathematics book Nine Chapters Arithmetic and wrote a book Composition. His most outstanding contribution is to get quite accurate pi. After a long and arduous study, he calculated pi between 3. 14 15926 and 3. 14 15927, becoming the first scientist in the world to calculate pi to more than seven digits.
Zu Chongzhi is a generalist in scientific inventions. He built a kind of compass, and the copper man in the car always pointed south. He also built a "Thousand-Li Ship" and tried it in Xinting River (now southwest of Nanjing). It can sail 100 Li a day. He also used hydraulic power to rotate the stone mill, pounding rice and grinding millet, which was called "water hammer mill".
In Zu Chongzhi's later years, Xiao Daocheng, who mastered the Song Guards, wiped out the Song Dynasty.
5. Yang Hui, Qian Guangren, Qiantang (now Hangzhou), an ancient mathematician and math educator in China, has an unknown life experience. It can be inferred from the existing literature that Yang Hui worked as a local administrative officer in the Southern Song Dynasty, and he traveled all over Suzhou and Hangzhou, signing five kinds of mathematics books, with a total volume of 2 1 volume.
(1) major works
Yang Hui left a large number of works in his life, namely: Detailed Explanation of Nine Chapters' Algorithms (12), Daily Algorithms (II) (1262) and Multiplication and Division to Change the Background (1274).
The current version of "Detailed Explanation of Nine Chapters Algorithm" is not complete, and its arrangement is also chaotic. As can be seen from the Preface, the book gives a detailed explanation of 80 problems in Annotation, Annotation in Tang Dynasty and Jia Xian's Nine Chapters Arithmetic in the Northern Song Dynasty. On the basis of nine chapters and nine volumes of arithmetic, three volumes have been added, one is a graph, and the other is about multiplication and division algorithm, before the ninth chapter. One volume is a compilation of categories, which occupies the first number at the end of the book. The multiplication and division method of volume L, the decay and anti-decay problems of volume 2 square field, volume 3 millet, volume 4 decay point and volume 6 quotient work are all lost. Volume 4 is divided into the second half, volume 5 is the remnant of Yongle Dadian, and the rest is the Yi Family Hall Series. Judging from the style of the incomplete volume, the book has a good understanding of the nine chapters of arithmetic.