Liu Hui (about 250 AD), wei ren in the late Three Kingdoms period, was an outstanding mathematician in ancient China and one of the founders of China's classical mathematical theory. History books rarely record his birth, death and life story. According to limited historical data, he was from Zouping, Shandong Province in Wei and Jin Dynasties. Never been an official. He also occupies a prominent position in the history of world mathematics. His representative works "Nine Arithmetic Notes" and "Arithmetic on the Island" are China's most precious mathematical heritage.
Nine Chapters of Arithmetic was written in the early Eastern Han Dynasty. * * * There are solutions to 246 problems. In solving simultaneous equations, calculating four fractions, calculating positive and negative numbers, calculating the volume and area of geometric figures and many other aspects, it is among the advanced in the world. However, due to the primitive solution and the lack of necessary proof, Liu Hui made supplementary proof for it. These proofs show his creative contributions in many aspects. The solution of linear equations is improved. In geometry, the secant method is put forward, that is, the method of finding the area and perimeter of a circle by using inscribed or circumscribed regular polygons. He scientifically obtained the result that pi = 3. 14 by using secant technology. Liu Hui put forward in the secant technique that "if you cut it carefully, the loss is not great, and then you can't cut it."
In the book Island Calculation, Liu Hui carefully selected nine surveying problems, which were creative, complex and representative and attracted the attention of the West at that time.
Liu Hui has quick thinking and flexible methods, and advocates both reasoning and intuition. He is the first person who China explicitly advocated to demonstrate mathematical propositions by logical reasoning.
Liu Hui's life is a life of hard work for mathematics. Although the status is low, but the personality is noble. He is not a mediocre man who seeks fame and fame, but a great man who never tires of learning. He left a precious wealth to our Chinese nation.
Zu Chongzhi (AD 429-AD 500)
Zu Chongzhi (429-500) was an outstanding mathematician and scientist in China. People in the Southern and Northern Dynasties, Han people, the word Wen Yuan. Born in Yuanjia for six years and died in Hou Yongyuan for two years. His ancestral home is Qiu County, Fanyang County (now Laishui County, Hebei Province). Its main contributions are in mathematics, astronomical calendar and machinery. In mathematics, he wrote a book "Composition", which was included in the famous "Ten Books of Calculating Classics" as a textbook of imperial academy in the Tang Dynasty, but it was later lost. Zu Chongzhi, together with his son Zuxuan, successfully solved the problem of calculating the volume of the ball by using "Mu He Fang Gai" and got the correct formula of the volume of the ball. In mechanics, he has designed and manufactured a water hammer mill, a compass driven by copper parts, a thousand-mile ship, a timer and so on. Besides, I also study music. He is one of the few well-read figures in history.
Zu Chongzhi's outstanding achievement in mathematics is about the calculation of pi. Before the Qin and Han Dynasties, people used "the diameter of three weeks a week" as pi, which was called "Gubi". Later, it was found that the error of Gubi was too large, and the pi should be "the diameter of a circle is greater than the diameter of three weeks". However, there are different opinions on how much is left. Until the Three Kingdoms period, Liu Hui put forward a scientific method to calculate pi-"secant" which approximated the circumference of a circle with the circumference inscribed by a regular polygon. Liu Hui calculated the circle inscribed with a 96-sided polygon and got π=3. 14, and pointed out that the more sides inscribed with a regular polygon, the more accurate the π value obtained. On the basis of predecessors' achievements, Zu Chongzhi devoted himself to research and repeated calculations. It is found that π is between 3. 14 15926 and 3. 14 15927, and an approximation in the form of π fraction is obtained, with 22/7 as the approximation rate and 355/13 as the secret rate. Is the fraction whose denominator is within 16604, which is closest to π. It is impossible to prove how Zu Chongzhi got this result. If he wants to find it according to Liu Hui's secant method, he will have to work out how much time and energy it will take to inscribed 12288 polygons in this circle! It is obvious that his perseverance and wisdom in academic research are admirable. It has been more than 1000 years since foreign mathematicians obtained the same result in the secrecy rate calculated by Zu Chongzhi. In order to commemorate Zu Chongzhi's outstanding contribution, some mathematicians abroad suggested that π = be called "ancestral rate".
Zu Chongzhi exhibited famous works at that time and insisted on seeking truth from facts. He compared and analyzed a large number of materials calculated by himself, found serious mistakes in the past calendars, and dared to improve them. At the age of 33, he successfully compiled the Daming Calendar, which opened a new era in calendar history.
Zu Chongzhi and his son Zuxuan (also a famous mathematician in China) solved the calculation of the volume of a sphere with ingenious methods. They adopted a principle at that time: "If the power supply potential is the same, the products should not be different." That is to say, two solids located between two parallel planes are cut by any plane parallel to these two planes. If the areas of two sections are always equal, then the volumes of two solids are equal. This principle is based on the following points. However, it was discovered by Karl Marx more than 1000 years ago. In order to commemorate the great contribution of grandfather and son in discovering this principle, everyone also called this principle "the ancestor principle".
Other famous mathematicians in ancient China and their main contributions
▲ Zhang Qiujian-
According to Qian Baoyu's research, Zhang Qiujian, a native of Qinghe (now Linqing, Shandong Province) in the Northern Wei Dynasty, was written in 466 ~ 485 AD. The application of the least common multiple, the mutual summation of arithmetic progression elements and "Hundred Chicken Skills" are his main achievements. "Hundred Chickens Skill" is a world-famous indefinite equation problem. /kloc-Fibonacci calculation in Italy in the 3rd century, and/kloc-Alkasi in Arabia in the 5th century < < The Key to Arithmetic > and other works all have the same problems.
▲ Zhu Shijie: "Four Jade Juanjian"
Zhu Shijie (about 1300) was born in Songting, Han Qing, and lived in Yanshan (now near Beijing). He "traveled around the lake and sea for more than twenty years as a famous mathematician" and "gathered scholars by following the door". 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. "Thinking of the source meets" 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" (the formulation and elimination of multivariate higher-order equations), "overlapping method" (the summation of higher-order arithmetic progression) and "seeking difference method" (the high-order interpolation method).
▲ Jia Xian: Nine Chapters of the Yellow Emperor are Fine Grass. "
China's classical mathematicians reached their peak in the Song and Yuan Dynasties, and the prelude of this development was the discovery of "Jiaxian Triangle" (binomial expansion coefficient table) and the establishment of higher-order open method ("increase, multiply and open method") closely related to it. Jia Xian, a native of Northern Song Dynasty, completed Nine Chapters of Fine Grass in Huangdi Neijing about 1050. The original book was lost, but the main contents were copied by Yang Hui's works (about13rd century), which can be handed down from generation to generation. Yang Hui's Detailed Explanation of Nine Chapters' Algorithms (126 1) has a picture of "Learning the Original Prescription", which means "Jia Xian used this technique". This is the famous "Jiaxian Triangle", or "Yang Hui Triangle". At the same time, it records Jia Xian's "method of increasing, multiplying and opening" to the root of higher order.
Jiaxian Triangle is called Pascal Triangle in western literature and was rediscovered by French mathematician B Pascal in 1654.
▲ Qin: "Several Books and Nine Chapters"
Qin (about 1202 ~ 126 1), a native of Anyue, Sichuan, once served as an official in Hubei, Anhui, Jiangsu, Zhejiang and other places, and was exiled to Meizhou (now Meixian County, Guangdong Province) around 126 1, and soon died. Qin, Yang Hui and Zhu Shijie are also called the four great mathematicians in Song and Yuan Dynasties. In his early years in Hangzhou, "Visiting a Taishi and learning from a hermit" was written in 1247. The book "Shu Shu Jiu Zhang" 18, 8 1 title, is divided into nine categories (Wild Goose, Shi Tian, Tianjing, Prospecting, Foraging, Qian Gu, Architecture, Military Service, Market Changes). Its most important mathematical achievements —— "Dayan summation method" (one-time congruence group solution) and "positive and negative leveling method" (numerical solution of higher-order equations) made this Song Dynasty arithmetic classic occupy a prominent position in the history of medieval mathematics.
▲ Ye Li: Round Sea Mirror-Kaiyuan Art
With the development of numerical solution technology of higher-order equations, the sequential equation method came into being, which is called "Kaiyuan technique". Among the mathematical works handed down from Song Dynasty to Yuan Dynasty, Ye Li's "Measuring the Round Sea Mirror" is the first work that systematically expounds Kaiyuan.
Ye Li (1 192 ~ 1279), formerly known as Li Zhi, was born in Luancheng, Jin Dynasty. He used to be the governor of Zhou Jun (now Yuxian County, Henan Province). Zhou Jun was destroyed by the Mongolian army in 1232, so he studied in seclusion. He was hired by Kublai Khan of Yuan Shizu as a bachelor of Hanlin for only one year. 1248 was written into "Circle Survey Mirror", the main purpose of which was to explain the method of establishing equations by using Kaiyuan. "Kai Yuan Shu" is similar to the column equation method in modern algebra. "Let Tianyuan be so-and-so" is equivalent to "Let X be so-and-so", which can be said to be an attempt of symbolic algebra. Ye Li also has another mathematical work Yi Gu Yan Duan (1259), which also explains Kaiyuan.