Mathematics in Song and Yuan Dynasties is the peak of mathematics development in China.

After the unification of China in the Northern Song Dynasty, agriculture, handicrafts and commerce flourished rapidly, and science and technology advanced by leaps and bounds. 1 1 century to14th century (Song and Yuan Dynasties), computational mathematics reached its peak, which was the heyday of unprecedented prosperity and fruitful achievements in ancient Chinese mathematics. During this period, a number of famous mathematicians and mathematical works appeared, which are listed as follows: Jia Xian's Nine Chapters of the Yellow Emperor (165438+mid-20th century), Gu Gen Lun (65438+mid-2nd century), Shu Jiu Chapters (1247) and. Yang Hui's nine-chapter algorithm [126 1], daily algorithm [1262] and Yang Hui's algorithm [1274- 1275], Zhu Shijie's arithmetic enlightenment [65438] achieved in many fields. The main tasks are:

Around A.D. 1050, Jia Xian of the Northern Song Dynasty (the year of birth and death is unknown) created a method of "increasing, multiplying and opening" in the Nine Chapters of the Yellow Emperor to open any higher power. It was not until A.D. 18 19 that the Englishman William George Horner came up with the same method. Jia Xian also listed the binomial theorem coefficient table, and the similar "Basga Triangle" did not appear in Europe until17th century. (The Nine Chapters of the Yellow Emperor Arithmetic Fine Grass has been lost)

During the period of 1088- 1095, Shen Kuo put forward the "gap product method" from the production practice problems such as the number of restaurants and the volume of terraces, and began to study the high-order arithmetic progression summation, and established the correct summation formula. Shen Kuo also put forward the theory of "meeting circle" and obtained the first approximate formula of arc length in the history of ancient mathematics in China. He also used the idea of logistics to analyze and study the relationship between logistics food supply and troop transportation.

In A.D. 1247, Qin in the Southern Song Dynasty popularized the multiplication and division method in Shu Shu Jiu Zhang, and described the numerical solution of higher order equations. He listed more than 20 solutions of higher-order equations from practice, the highest of which is the decagonal equation. It was not until16th century in Europe that the Italian Scipio Del Ferro proposed the solution of cubic equation. Qin also systematically studied the theory of primary congruence.

In A.D. 1248, Ye Li (Li Zhi, 1 192- 1279) wrote The Sea Mirror for Measuring the Circle, which was the first work to systematically discuss the "celestial technique" (one-dimensional higher-order equation) and was an outstanding achievement in the history of mathematics. In the round sea mirror? In the Preface, Ye Li criticized the fallacy of belittling scientific practice and treating mathematics as "poor skills" and "playing with things and getting tired of it".

In A.D. 126 1 year, Yang Hui (the year of birth and death is unknown) in the Southern Song Dynasty used "piling technique" to find the sum of several kinds of high-order arithmetic progression. In A.D. 1274, he also described the "Nine-fold Agile Method" in his book The Origin of Multiplication and Division Transformation, and introduced various calculation methods of multiplication and division. In A.D. 1280, Wang Xun and Guo Shoujing listed the interpolation formula of triple difference when compiling the calendar method of the Yuan Dynasty. Guo Shoujing also found two formulas equivalent to the present spherical triangle by geometric method.

In A.D. 1303, Zhu Shijie of Yuan Dynasty (date of birth and death unknown) wrote a jade mirror with four elements. He extended "Tianshi skill" to "four-element skill" (four-element simultaneous equation) and put forward a solution to eliminate elements. It was not until A.D. 1775 that etienne bezout, a Frenchman in Europe, proposed the same solution. Zhu Shijie also studied the summation of finite series, and on this basis, obtained the interpolation formula of higher-order difference. Until 65438 to 1678, the Englishman James Gregory and the Englishman Isaac Newton put forward the general formula of European interpolation.

In the 4th century A.D./KLOC-,people in China already used abacus. Before modern computers appeared, abacus was a simple and effective computing tool in the world.

In addition, other achievements include the new development of Pythagorean method, the research of solving spherical right triangle, the research of vertical and horizontal diagram (magic square), the concrete application of decimal, the appearance of abacus and so on.

During this period, folk mathematics education also developed, and the exchange of mathematics knowledge between China and Islamic countries also developed.

Reference:

History of Mathematics in Song and Yuan Dynasties/View/27 dbdf6648d7c1c708a145ba.html