I. Zhu Shijie
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".
Second, representative works
1, arithmetic enlightenment
The text of this book is divided into 3 volumes, 20 subjects and 259 questions. There are 8 questions in the volume, 1 13, including multiplication and division, rhyming and various proportional algorithms. Many problems reflect the social and economic situation of the Yuan Dynasty.
The volume of the 7 1 question has seven doors, namely, area, volume and various arithmetic problems. The second volume contains 5 doors and 75 questions, which are about fractional operation, accumulation (that is, the summation of higher-order arithmetic progression), surplus and deficiency, the solution of linear equations, astrophysics and the methods of addition, multiplication and division. The sign change of coefficient in the process of square root is also discussed.
2. Siyuan Jade Mirror
Siyuan Encounter is divided into Volume I, Volume I, Volume II and contains 288 questions, including 232 celestial arts, 36 binary arts, 3 ternary arts 13, and 7 quaternary arts. The first four questions are titled as examples, with grass (solving steps), and the remaining 284 questions are only skills without grass.
1837, Luo Shilin, a mathematician in the Qing Dynasty, compiled grass and published three volumes of Four Yuan Jade Sword Fine Grass. All problems are related to equations or equations.
This paper introduces Zhu Shijie's research achievements in solving high-order multivariate equations-"four-element method", calculating high-order arithmetic progression-"superposition method" and "inviting difference method" (finite difference method).
Third, mathematical creation.
Zhu Shijie's main contribution is to create a set of methods to eliminate unknowns, which is called quaternary elimination method. This method has been in the leading position in the world for a long time, and it was not until18th century that the French mathematician Bezot put forward the general solution of higher-order equations that Zhu Shijie was surpassed.
Apart from the four-element technique, the four-element jade mirror has two important achievements, namely, the general summation formula of higher-order arithmetic progression and the quartic equidistant interpolation formula, which are usually called the difference technique.
Extended data:
In mathematical science, Zhu Shijie comprehensively inherited the mathematical achievements of Qin, Yang Hui and developed them creatively. He wrote such famous works as Arithmetic Enlightenment, Meeting with Siyuan, which pushed the ancient mathematics in China to a new height and formed the highest peak of China's mathematics in the Song and Yuan Dynasties.
The Enlightenment of Arithmetic was published by Zhu Shijie in Yuan Chengzong Dade for three years (1299). Its system is complete, the content is simple and easy to understand, and it is a very famous enlightenment reading. This book was later spread to Korea, Japan and other countries, and reprinted and annotated editions were published successively, which had a certain influence.
Philip Burkart Meeting is a brilliant mathematical masterpiece. It is highly praised by researchers in the history of modern mathematics, and it is considered as the most important and greatest mathematical masterpiece among China's ancient mathematical scientific works.
Meeting Siyuan was written in the seventh year of Dade (1303), with three volumes, 24 doors and 288 questions. This paper introduces Zhu Shijie's research and achievements in solving multivariate higher-order equations-quaternary method and calculating higher-order arithmetic progression-superposition method and differential method.
"Tianyuan Shu" means "Tianyuan is XXX", that is, XXX is X. But when there is more than one unknown quantity, besides the unknown Tianyuan (X), it is necessary to set geographical element (Y), humanistic element (Z) and material element (U), and then list the high-order binary, ternary or even quaternary equations before solving them.
In Europe, the solution of linear equations began in16th century, and the study of high-order simultaneous equations was from 18 to19th century. Another great contribution of Zhu Shijie is the study of "piling".
He studied a series of new summation problems of crib-shaped sequences, which were summarized as "triangular crib" formula. In fact, he obtained a systematic and universal solution to this kind of arbitrary high-order arithmetic progression summation problem.
Zhu Shijie also introduced the triangle crib formula into the unique skill, pointing out that the coefficient in the unique skill formula is just the product of the triangle crib in turn, thus obtaining the unique skill formula with the fourth difference.
Baidu Encyclopedia-Zhu Shijie