Zhu Shijie (1249- 13 14), a native of Yanshan (present-day Beijing), was a mathematician and educator in the Yuan Dynasty, and engaged in mathematics education all his life. It has the reputation of "the greatest mathematician in the medieval world". Zhu Shijie developed the "Quaternary Technique" on the basis of celestial sphere technique at that time, that is, he listed the polynomial equation of higher degree and its elimination method. In addition, he also created the "superposition method", that is, the summation method of high-order arithmetic progression, and the "trick", that is, the high-order interpolation method. His main works are "Arithmetic Enlightenment" and "Meeting with Siyuan".
Zhu Shijie "traveled around the lake and sea as a famous mathematician for more than 20 years" and "gathered scholars by following the door" ("Mo Ruo and Zu Yi: Preface to the Meeting of Siyuan"). Zhu Shijie's representative works in mathematics include "Arithmetic Enlightenment" (1299) and "Meeting with the Source" (1303). Zhu Shijie's book "Arithmetic Enlightenment" is a well-known mathematical masterpiece, which spread overseas and influenced the development of mathematics in South 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).
During the Song and Yuan Dynasties, four outstanding mathematicians, Li, Yang Hui and Zhu Shijie, appeared in the heyday of mathematics in China, and Zhu Shijie was one of them. Zhu Shijie is a civilian mathematician and math educator. Zhu Shijie studied nine chapters of arithmetic diligently all his life, bypassing other algorithms and becoming a famous mathematician in Yuan Dynasty.
life experience
After the Yuan Dynasty unified China, Zhu Shijie traveled around the world as a mathematician for more than 20 years, and many people learned from him. When he arrived in Guangling (now Yangzhou), he "followed the door and gathered scholars". He fully inherited the mathematical achievements of predecessors, not only absorbed the celestial science in the north, but also absorbed the positive and negative formulas, various daily algorithms and popular songs in the south. On this basis, he conducted creative research, and for the purpose of summarizing and popularizing all kinds of mathematical knowledge at that time, he wrote "Enlightenment of Arithmetic" (3 volumes), and also wrote "Siyuan-Siyuan Encounter" (3 volumes), which was published in: 65433. The book clearly puts forward the multiplication rule of positive and negative numbers, gives the concept and basic properties of reciprocal, summarizes some new multiplication formulas and radical operation rules, summarizes some quick formulas of multiplication and division, and applies the method of setting auxiliary unknowns to solving linear equations. The main content of Siyuan's encounter is the establishment and solution of multivariate higher order equations. Including Qin's numerical solution of higher-order equations and his celestial sphere skills. Zhu Shijie's academic research.
Among the mathematicians in Song and Yuan Dynasties, Zhu Shijie's work is of special significance. If many mathematicians are compared to mountains, Zhu Shijie is the highest and most majestic mountain. Standing at the height of Zhu Shijie's mathematical thought, we will feel that "other mountains are dwarfed under the sky." . The significance of coming to Shijie's works is to sum up the mathematics of Song and Yuan Dynasties and make it reach a new height in theory. This is mainly manifested in the following three areas. The first is equation theory. In establishing equations. Jiangzhou's staging method has prepared for the art of heaven, and has the idea of finding equivalent polynomials. Dong He is a pioneer of celestial art, but their equations are still bound by geometric thinking. Ye Li basically got rid of this bondage and summed up a set of fixed celestial art procedures, which made celestial art mature. In solving the equation, Jia Xian gave the method of increasing, multiplying and opening, and Liu Yi used the positive and negative flat method to find the positive root of the quartic equation. On this basis, Qin solved the numerical problem of higher-order equations. At this point, the establishment and solution of the univariate higher order equation have been realized. Linear equations have existed since ancient times, so they have the conditions for generating multivariate higher power equations. Li Dezai's binary operation and Liu Dajian's ternary operation appeared one after another, and Zhu Shijie's quaternary operation is the summary and improvement of binary operation and ternary operation. Since four elements have filled the upper, lower, left and right sides of the constant term, the equation theory has obviously come to an end.
From Dong Yuan to Ye Li, the fractional equation developed gradually. Zhu Shijie broke through the limitation of rational number formula and began to deal with irrational number equation. Secondly, the higher-order arithmetic progression is studied. Shen Kuo's gap product technique was the first to study high-order arithmetic progression, and Yang Hui gave a series of summation formulas of second-order arithmetic sequence, including the gap product technique. On this basis, Zhu Shijie studied the summation of second-order, third-order, fourth-order and even fifth-order arithmetic progression in turn, and found that. He mastered the unified formula of triangular crib. He also found the internal relationship between superposition technology and interpolation method, and gave the standard quartic interpolation formula by using superposition formula. Third, he studies geometry. Before the Song Dynasty, geometry research could not be separated from Pythagorean and area and volume. Yiji Valley in Jiangzhou also studied the area problem. Ye Li began to notice the relationship between elements in the round city factor and got some theorems. However, more general situations cannot be generalized. Zhu Shijie not only summarized the Pythagoras and quadrature theory of predecessors, but also went further on the basis of Ye Li's thought. He deeply studied the quantitative relationship between pythagorean and geometric elements in a circle, and found two important theorems-projective theorem and chord power theorem. He also began to notice the relationship between elements in solid geometry. Zhu Shijie's work makes the object of geometry research go deep from the whole figure to the figure, which embodies the progress of mathematical thought.
Famous anecdote
/kloc-At the end of 0/3, the war-torn motherland was unified by the Yuan Dynasty, and the destroyed economy and culture flourished rapidly. For the sake of national prosperity and security, Mongolian rulers respect knowledge, select talents and push all sciences to a new height. One day, by the scenic Slender West Lake in Yangzhou, a teacher came and hung a sign in front of his apartment, which read in big letters: "Teacher Zhu Songting of Yanshan specializes in teaching four elements." A few days later, Zhu Shijie's front door was crowded with people who were curious about knowledge. Just as Zhu Shijie was accepting students' registration, suddenly, a lot of shouting caught his attention. I saw a semi-old Xu Niang dressed in satin and silver, chasing a young girl, beating and cursing: "You bitch, didn't you catch a lot of money?" Do you want to be a good family? I am afraid that you voted for the wrong baby and will not think about it in the next life. " The girl was beaten so badly that even the clothes inside her were torn. The girl curled up into a ball and asked her to fight, but she didn't go back with her. When Zhu Shijie saw that the road was rough, he came forward to ask. Xu Niang, a half-aged man, saw a nosy person and sneered, "Do you want to be keen? You give me fifty taels of silver, and the girl is yours! " Zhu Shijie was furious at this. "Can't I pay fifty taels of silver?" . You can't run amok in broad daylight. Is there no king's law? "Old Xu Niang said sarcastically," you poor wretch, what are you talking about? Silver is the king. I won't fight if you can pay fifty taels of silver. "
Zhu Shijie was so angry that he took out 50 taels of silver from his pocket, threw it in front of Xu Niang, picked up the girl and went back to his teaching place. It turns out that old Xu Niang is a lady, and the girl's father borrowed her 10 silver. Due to natural disasters, he could not repay the silver, so he had to sell his daughter to pay his debts. I happened to meet Zhu Shijie today and let this girl out of her misery. Later, under the careful instruction of Zhu Shijie, the girl also learned a lot of mathematics and became Zhu Shijie's right-hand man. In a few years, the two became husband and wife. Therefore, there is a saying among Yangzhou people: Zhu Hanqing taught and educated people in Yuan Dynasty. Saving people from fire and water, a big marriage.
Yangzhou anecdote
From this, we know that Zhu Shijie was born in Beijing. /kloc-In the late 3rd century, he spent more than 20 years as a famous mathematician, and Zhu Shijie finally settled in Yangzhou, where he studied mathematics and gave lectures. He attracted many scholars to engage in academic exchanges. Yangzhou is located at the intersection of north and south, where various academic ideas are integrated; At that time, Yangzhou's printing industry was very developed and it was the national book publishing center. Two books reflecting Zhu Shijie's achievements in mathematics, Arithmetic Enlightenment and Thinking of the Source, were printed and published in Yangzhou in the third year of Yuan Dade (1299) and the seventh year of Yuan Dade (1303) respectively. ***3 volumes, divided into 20 subjects, including 259 math problems. At the beginning of the book, Zhu Shijie gave 18 commonly used mathematical songs and various commonly used mathematical constants, including: 99 pieces of multiplication, 99 pieces of division (exactly the same as the abacus calculation formula later), zero pieces of weight, counting rules, decimal method, metrological conversion, pi, plus or minus multiplication and division rules, and root. The text includes multiplication and division and its flexible algorithm, multiplication and division, celestial technology, solving linear equations, and higher-order arithmetic progression summation. The book covers almost all aspects of mathematics at that time, forming a relatively complete system, which can be said to be a good mathematics textbook. Luo Shilin, a scholar in Yangzhou in Qing Dynasty, said that "the enlightenment of arithmetic" was "as shallow as reality", and such comments were very pertinent.
"Meet with Siyuan" is the representative work of Zhu Shijie's carefully arranged research results for many years. The book is divided into 3 volumes, 24 subjects and 288 questions. All the problems in the book are related to solving equations or equations. Among them, there are four unknown 7 questions, three unknown 13 questions, two unknown 36 questions and one unknown 232 questions. The preface lists four kinds of five diagrams such as Jia Xian Triangle, and gives examples of solving celestial sphere, binary, ternary and quaternary techniques. The last three are the column methods and solutions of binary, ternary and quaternary higher-order equations respectively. The book's greatest contribution is the creation of the four-element elimination method, which solves the problem of multivariate higher-order equations. Another great achievement in the book is to systematically solve the problems of higher-order arithmetic progression summation and higher-order differential method. Before Zhu Shijie, there was a way to understand the equation in ancient Chinese mathematics-"Tianyuan Shu", which solved the equation by setting "Tianyuan as so-and-so", so-and-so as (x). Zhu Shijie not only inherited the celestial sphere technique, but also extended the solution of equations from binary and ternary to quaternary. When there is more than one unknown quantity, in addition to the unknown Tianyuan (X), we also set up soil element (Y), human element (Z) and matter element (U), and then list binary, ternary or even quaternary simultaneous equations and solve them. In Europe, the solution of simultaneous linear equations began in16th century, and the study of simultaneous equations of multiple degrees began in18th and19th century. Zhu Shijie's "celestial skills" were more than 400 years earlier than those in Europe.
Zhu Shijie's research on "stacking" actually obtained a general solution to the higher-order arithmetic progression summation problem. Since the Song Dynasty, there has been a study on the summation of higher-order arithmetic progression in China. There are overlapping problems in the works of Shen Kuo (103 1- 1095) and Yang Hui (126 1- 1275).
"Meet with Siyuan" is a brilliant mathematical masterpiece, a master of mathematics in the Song and Yuan Dynasties, and the highest-level mathematical work in ancient China. Researchers in the history of modern mathematics spoke highly of Philip Burkart's encounter. George Sarton, a famous expert in the history of science, said that "Meeting with Siyuan" is "one of China's most important mathematical works and one of the most outstanding mathematical works in the Middle Ages". Joseph Needham, who wrote History of Science and Technology in China, commented on the meeting between Zhu Shijie and Philip Burkart in this way: "His previous mathematicians failed to touch the mysterious truth contained in this extensive and profound work".
Unfortunately, after Zhu Shijie, there were no profound mathematical works in Yuan Dynasty, and there were few new mathematical works in Han, Tang, Song and Yuan Dynasties, and many of them were even lost. In the thirty-seventh year of Qianlong (1772), when the Siku Quanshu Library opened, many ancient mathematical classics were discovered, but Zhu Shijie's works were not discovered, so they were not compiled at first. 1799, Ruan Yuan, Li Rui and others didn't introduce Siyuan's meeting when they compiled A Family Biography of Mathematics. Soon after, Ruan Yuan inspected the book in Zhejiang, and immediately compiled it into Sikuquanshu, which was handed over to Li Rui for proofreading (unfinished) and later carved by He Yuanxi. This is the first reprint of Siyuan Meeting since the first edition of 1303. From 65438 to 0839, Luo Shilin, a scholar from Yangzhou, published a book "Siyuan Meets Fine Grass" after years of research, and Luo Shi made a fine grass on every question in the book "Siyuan Meets Fine Grass". Just like Luo Shilin's second edition of Meet with Siyuan, arithmetic enlightenment is still missing. Later, Luo Shilin "heard that North Korea took the Book of Poetry as the arithmetic topic", so he asked people to find a reprint engraved by Jin Shizhen, the governor of the whole state of North Korea in the seventeenth year of Shunzhi (1660) in Beijing. In this way, "Arithmetic Enlightenment" was reprinted in Yangzhou, which is the mother of the existing version of the book.
Zhu Shijie's two outstanding mathematical works in Yuan Dynasty were both completed and engraved in Yangzhou. After hundreds of years of loss, it was discovered, collated and annotated by Yangzhou scholars, and reprinted and published in Yangzhou. This shows that Yangzhou has a very important position in the history of mathematics development in China.
In 2022, the articles of association of Chongqing Three Gorges Medical College have been published, which mainly includes the ge