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 the Northern Song Dynasty, completed the Nine Chapters of Yellow Emperor's Fine Grass 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 diagram of "the origin of alchemy", which shows that "Jia Xian used this technique". This is the famous "Jiaxian Triangle", or "Yang Hui Triangle". Jia Xian's "Method of Increasing, Multiplying and Opening" for higher-order square roots is also recorded in "Detailed Explanation of Algorithms in Chapter Nine".
Jiaxian Triangle is called Pascal Triangle in western literature and was rediscovered by French mathematician B Pascal in 1654.
Qin: Count 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, Guangdong) 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, he studied mathematics in seclusion in Hangzhou, and wrote the famous Shu Shu Jiu Zhang in 1247. The book "Shu Shu Jiu Zhang" 18 volume, 8 1 title, is divided into nine categories (Wild Goose, Shi Tian, Tianjing, Prediction, Foraging, Money Valley, Architecture, Military Service, Market Easy). 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: Circular 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.
Zhu Shijie: Four Yuan Jade Sword
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).
Zu Chongzhi (AD 429-500) was born in Laiyuan County, Hebei Province during the Northern and Southern Dynasties. He read many books on astronomy and mathematics since childhood, studied hard and practiced hard, and finally made him an outstanding mathematician and astronomer in ancient China.
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/ 133 as the secret rate, where 355/. Is the fraction whose denominator is within 1000, which is closest to π. It is impossible to prove how Zu Chongzhi got this result. If he tries to find it according to Liu Hui's "secant" method, he will have to calculate 16384 polygons inscribed in the circle. How much time and energy will it take! 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".
-Liu Hui
Liu Hui (born around 250 AD) is a very great mathematician in the history of Chinese mathematics, and 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."
Lee Liu
Liu Hui (born around 250 AD) is a very great mathematician in the history of Chinese mathematics, and 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.
Jia Xian
Jia Xian was an outstanding mathematician in the Northern Song Dynasty in ancient China. The Nine Chapters of Yellow Emperor's Arithmetic Fine Grass (nine volumes) and Arithmetic Ancient Collection (two volumes) have been lost.
His main contribution is to create the "Jiaxian Triangle" and the method of multiplication and multiplication, which is the positive root method for finding the higher power. At present, the principle and procedure of mixed division in middle school mathematics are similar, while the multiplication and division method is more neat, simple and programmed than the traditional method, so it shows its superiority, especially when it comes to high power. This method was put forward more than 700 years before the conclusion of European mathematician Horner.
Qin
Qin (about 1202- 126 1) was from Anyue, Sichuan. He was once an official in Hubei, Anhui, Jiangsu, Zhejiang and other places, and was demoted to Meizhou (now Meixian County, Guangdong Province) around 126 1, and soon died. He, Yang Hui and Zhu Shijie are also called the four great mathematicians in Song and Yuan Dynasties. In his early years in Hangzhou, he visited the Taishi and learned mathematics from a hermit. 1247, he wrote the famous Shu Shu Jiu Zhang. The book "Shu Shu Jiu Zhang" has a total of 18 volumes and 8 1 title, which is divided into nine categories. Its most important achievements in mathematics-"the sum of large calculations" (a solution of congruence group) and "the solution of positive and negative square roots" (a numerical solution of higher-order equations) made this Song Dynasty arithmetic classic occupy a prominent position in the history of medieval mathematics.
Ye Li
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 attacked by the Mongols in 1232, and went to study in seclusion, and was later hired by Kublai Khan of Yuan Shizu. 1248 was written in "Circular Sea Mirror", the main purpose of which was to explain the method of arranging equations with astronomical elements. "Astrology" 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. Another mathematical work by Ye Li, Yi Gu Yan Duan (1259), also explains Heaven.
Zhu Shijie
Zhu Shijie (about 1300), whose real name is Han Qing, lives in Yanshan (near Beijing today). He "traveled around the lake and sea with famous mathematicians for more than 20 years" and "gathered scholars by following the door" (Mo Ruo and Ancestral Differences: A Preface to Four Ideals). 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 China's mathematical peak in the Song and Yuan Dynasties. Among them, the most outstanding mathematical creations are quadrature (formulation and elimination of multivariate higher-order equations), superposition (summation of higher-order arithmetic progression) and invited difference (interpolation of higher-order).
Chungchi Tsu
Zu Chongzhi (AD 429-500), a native of Laiyuan County, Hebei Province, was an outstanding scientist in the Southern and Northern Dynasties. He is not only a mathematician, but also familiar with astronomical calendar, machinery manufacturing, music and other fields, and is an astronomer.
Zu Chongzhi's main achievement in mathematics is the calculation of pi, which is 3. 14 15926.
Zuhuan
Zu Chongzhi's son, Zuxuan, and his father, Zu Chongzhi, 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.
Yang Hui
Yang Hui was an outstanding mathematician and mathematical educator in the Southern Song Dynasty. /kloc-in the middle of the 0/3rd century, he was active in Suzhou and Hangzhou with many works.
His famous math books have five kinds and 21 volumes. He has written twelve volumes (126 1 year), two volumes (1262), three volumes (1274) and two volumes (field ratio multiplication and division algorithm).
In his Algorithm for Extracting Odds from Ancient Times, he introduced various forms of "vertical and horizontal graphs" and related construction methods. "Overlap" was Yang Hui's research on higher-order arithmetic progression after Shen Kuo's "Gap Product". In Classification, Yang Hui reclassified 246 problems in Nine Chapters of Arithmetic into nine categories according to the order of solving problems from shallow to deep, such as multiplication and division, division rate, coincidence rate, exchange, quadratic decline, overlapping product, surplus and deficiency, equation, Pythagorean and so on.
Zhao Shuang
Zhao Shuang was a mathematician in Wu Dong during the Three Kingdoms period. He once annotated the Pythagorean Arithmetic Classics. In his annotation of the Pythagorean Arithmetic Classics, there is a full text of more than 500 words, with a lost figure. 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 (where A >: 0, A>0), and gave the proof of "gravity difference technique" by using the area relation of geometric figures in the solar altitude map annotation. The method used by astronomers in the Han Dynasty to measure the height and distance of the sun is called gravity difference technique.