Zhu Shijie

Zhu Shijie

Zhu Shijie (1249-1314), Han Qing, Songting, Han nationality, Yanshan (now Beijing), mathematician and educator of Yuan Dynasty, devoted his life to mathematics education. It is known as "the greatest mathematician in the Middle Ages".

Zhu Shijie developed the "quaternion technique" on the basis of tianyuanshu at that time, that is, listing the quaternion high-order polynomial equation and the method of elimination. In addition, he also created the "stacking method", that is, the summation method of higher order arithmetic sequence, and the "difference technique", that is, the high-order interpolation method.

His main works are enlightenment of mathematics and four yuan jade mirror.

Profile

Zhu Shijie "toured the lake and sea for more than 20 years as a famous mathematician" and "gathered scholars after the gate" (Mo ruo, Zu Yi: preface to Siyuan Yujian).

In the song and Yuan Dynasties, there were four outstanding mathematicians in the heyday of Chinese mathematics: Qin Jiushao, Li Ye, Yang Hui and Zhu Shijie. Zhu Shijie is a common mathematician and mathematical educator. All his life, Zhu Shijie studied nine chapters of arithmetic, bypassed other algorithms, and became a famous mathematician in Yuan Dynasty.

Life experience

After the unification of China in the Yuan Dynasty, Zhu Shijie traveled around as a mathematician for more than 20 years, and many people studied from him. When he came to Guangling (now Yangzhou), he "followed the door and gathered scholars.". He inherited the predecessors' mathematical achievements in an all-round way. He absorbed not only the tianyuanshu of the north, but also the positive and negative Fangshu of the south, various daily algorithms and popular rhymes. On this basis, he carried out creative research, and wrote enlightenment of Mathematics (Volume 3) for the purpose of summarizing and popularizing all kinds of mathematical knowledge at that time Published in 1999 and 1303. From simple to profound, the Enlightenment of mathematics starts with the multiplication of one digit, and then goes all the way to the latest mathematical achievement at that time, tianyuanshu, which seems to form a complete system.

In the book, the multiplication rule of positive and negative numbers is clearly put forward, the concept and basic properties of reciprocal are given, some new multiplication formulas and radical operation rules are summarized, and some quick calculation formulas of multiplication and division are summarized, and the method of setting auxiliary unknowns is used to solve linear equations. The main content of Siyuan Yujian is quaternion, that is, the establishment and solution method of multivariate higher-order equations. Qin Jiushao's numerical solution of higher order equation and Li Ye's tianyuanshu are included.

In the song and Yuan Dynasties, Zhu Shijie's work is of special significance. If many mathematicians are compared to mountains, Zhu Shijie is the largest and most magnificent mountain. Standing at the height of Zhu Shijie's mathematical thought and overlooking the traditional mathematics, we will have the feeling of "looking at all the mountains and small".

The significance of Zhu Shijie's work 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 the aspect of formulation of equations, Jiang Zhou's stage method has made preparations for tianyuanshu. He has the idea of looking for equivalent polynomials. Dongyuanma and chandao are the pioneers of tianyuanshu, but their derivation of equations is still constrained by geometric thinking. Li Ye basically got rid of this constraint and summed up a set of fixed tianyuanshu procedures, which made tianyuanshu mature. In solving the equation, Jia Xian gives the method of increasing multiplication and opening, Liu Yi uses the positive and negative square method to find the positive root of the quartic equation, and Qin Jiushao solves the numerical solution of the higher order equation on this basis. So far, the establishment and solution of univariate higher order equation have been realized. The linear equations have existed since ancient times, so they have the conditions for the generation of multivariate higher-order equations. Li dezai's dualism and Liu Dajian's Sanyuan appeared one after another. Zhu Shijie's quaternion is the summary and improvement of dualism and Sanyuan. Since quaternion has occupied the upper, lower, left and right parts of the constant term, the development of equation theory here is obviously over. In terms of the types of equations, the equations before tianyuanshu were all integral equations.

From Dongyuan to Liye, fractional equation was developed gradually. Zhu Shijie broke through the limitation of rational equation and began to deal with irrational equation. The second is the study of higher order arithmetic series. Shen Kuo's gap product technique is the first to study the higher order arithmetic series. Yang Hui gives a series of summation formulas of the second order arithmetic series including the gap product technique. On this basis, Zhu Shijie studied the summation of second order, third order, fourth order and even fifth order isochromatic Series in order to find its law and master the unified formula of triangular buttress. He also found the internal relationship between stacking and interpolation, and gave the standard quartic interpolation formula by stacking formula. The third is the study of geometry. Before the Song Dynasty, geometry research was inseparable from Pythagorean and area and volume. Jiang Zhou's Yi Gu Ji also takes the area problem as the research object. Li Ye began to pay attention to the relationship between the elements in the Yuancheng factor and obtained some theorems, but failed to extend them to more general cases. Zhu Shijie not only summarized the previous Pythagorean and quadrature theory, but also further studied the quantitative relationship of geometric elements in Pythagorean shape and circle on the basis of Li Ye's thought, and found two important theorems -- projective theorem and chord power theorem. In solid geometry, he also began to pay attention to the relationship between the elements in the figure. Zhu Shijie's work makes the object of geometry research from the whole figure to the inside of the figure, which reflects the progress of mathematical thought.

Famous anecdotes

At the end of the 13th century, the war-torn motherland was unified by the Yuan Dynasty, and the destroyed economy and culture flourished quickly. In order to prosper the country, Mongolian rulers respected knowledge, selected talents, and pushed all kinds of science to a new peak.

One day, on the Bank of the beautiful Slender West Lake in Yangzhou, a teacher came and hung a signboard in front of his apartment, which read in big characters: "Mr. Zhu Songting of Yanshan, specializing in four yuan skills.". A few days later, Zhu Shijie's door was crowded with people seeking knowledge. Just as Zhu Shijie was receiving students to sign up, he suddenly called a curse to attract his attention.

Xu Niang, wearing silk and silver, chased a young girl and scolded: "You cheap woman, if you don't pay for a lot of silver, do you want to be a lady of a big family? I'm afraid you've got the wrong baby. Don't think about it in your next life." The girl was beaten to pieces, even her inner clothes were torn. The girl curled up in a ball, let her fight, also don't go back with her. Seeing injustice, Zhu Shijie went forward to ask. Seeing that a meddler appeared, Xu Niang laughed and said, "do you want to fight against injustice? If you give 50 liang of silver, the girl will be yours!"

Seeing this, Zhu Shijie said angrily, "can't I take out 50 taels of silver. In broad daylight, they act recklessly. Is there no royal law

That half old Xu Niang sarcastically says: "you poor devil, still talk about King's law, silver is king's law, if you can take out 50 Liang silver, I won't fight."

Zhu Shijie is very angry. He grabs 50 taels of silver from his pocket, falls in front of Xu Niang, pulls up the girl and goes back to his teaching place. It turned out that Xu Niang was the bustard of the prostitute's house, and the girl's father had to sell his daughter to pay off the debt because he borrowed 10 taels of money from the bustard and couldn't pay back the money due to natural disasters. Today, I happened to meet Zhu Shijie and saved the girl from suffering.

Later, under the careful guidance of Zhu Shijie, the girl knew a lot about mathematics and became Zhu Shijie's right-hand assistant. Within a few years, they became husband and wife. Therefore, there is still a saying in Yangzhou: Zhu Hanqing of the Yuan Dynasty taught and educated people. To save a man from suffering is a great success in marriage.

Related works

Zhu Shijie has been engaged in mathematics research and education for a long time. He has traveled around as a famous mathematician for more than 20 years, and many people come to study. Zhu Shijie's representative works of mathematics are enlightenment of Mathematics (1299) and jade mirror of four elements (1303). The Enlightenment of mathematics is a famous work of popular mathematics, which has spread abroad and influenced the development of mathematics in Korea and Japan. "Four yuan jade mirror" is another symbol of the peak of mathematics in song and Yuan Dynasties in China. Among them, the most outstanding mathematical creations are "four yuan technique" (multiple high-order equation formulation and elimination method), "stacking method" (higher-order arithmetic sequence summation) and "zhaocha technique" (high-order interpolation method).

Zhu Shijie inherited the achievements of Qin Jiushao, Li Ye and Yang Hui in mathematics science, and gave creative development. He wrote some famous works such as enlightenment of mathematics and four yuan Yujian, which pushed ancient mathematics to a higher level and formed the peak of Chinese mathematics in song and Yuan Dynasties. The Enlightenment of mathematics was published by Zhu Shijie in 1299, the third year of Dade reign of emperor Chengzong of Yuan Dynasty. The book consists of three volumes and 20 doors, with a total of 259 questions and corresponding answers. From multiplication and division to tianyuanshu, the highest achievement in the development of mathematics at that time, this book introduces all aspects of mathematics at that time.

It is a famous enlightening book with complete system, simple content and easy to understand. Later, this work spread to Korea, Japan and other countries, and published the reprinted edition and annotated edition, which had a certain impact. And "four yuan jade mirror" is a brilliant mathematical masterpiece. It is highly praised by the researchers of modern mathematics history, and is considered to be the most important and most contributing mathematics masterpiece in ancient Chinese mathematics science works. Siyuan Yujian was written in 1303, the seventh year of Dade. It consists of three volumes, 24 doors and 288 questions. This paper introduces Zhu Shijie's research and achievements in the solution of multivariate higher-order equations, namely, quaternion method, and the calculation of higher-order isochromatic series, namely, stacking method and zhaocha method.

"Tianyuan Shu" is to set "Tianyuan is XX", that is, XX is X. But when there is more than one unknowns, in addition to the unknowns Tian Yuan (x), we also need to set the land yuan (y), human yuan (z) and matter yuan (U), and then list the two elements

Chinese PinYin : Zhu Shi Jie