Is the arithmetic of the nine chapters a must be learned by the ancient literati?

The nine chapters of arithmetic were written in the Han Dynasty, and the Han Dynasty was basically a recommendation system at that time, and these were listed as those that needed to be learned. After the Sui and Tang dynasties, the imperial examination system appeared, and there were still a lot to learn in the imperial examination in the Tang Dynasty, including arithmetic, but when the Ming and Qing dynasties were prevalent in Baguwen, there were more than 50 kinds of subjects in the regular department, such as Xiucai, Ming Jing, Jinshi, Junshi, Ming Law, Ming Zi, Ming Arithmetic, etc. Among them, the subjects of Ming Law, Ming Calculation, and Ming Characters are not taken seriously.

These books can only become textbooks for some high-tech yamen, such as the Ministry of Water Conservancy and Household Affairs, and Qin Tianjian.

I think the main thing is to study the Confucian classics, the Four Books and the Five Classics. Natural science stuff was not popular in ancient China.

In the early stage, it is necessary to learn, many famous Confucians are great mathematicians, and the astronomical calendar is all-encompassing, such as Zhang Heng, to the Sui and Tang dynasties, there is still a Ming arithmetic department, and in the Ming and Qing dynasties, there are only four books and five classics.

No, there are no hard and fast rules But the "Nine Chapters of Arithmetic" is the crystallization of the joint labor of several generations, and its appearance marks the formation of the ancient Chinese mathematical system Most of the mathematicians of later generations began to study and study mathematical knowledge from the "Nine Chapters of Arithmetic". In the Tang and Song dynasties, it was stipulated as a textbook by the state. It was engraved in 1084 by the court of the Northern Song Dynasty at that time, and it is the world's earliest printed mathematics book.

Yes, there were also ancient Chinese mathematicians, a lot of them.

The Nine Chapters of Arithmetic Bi Sanshu is from the Western Han Dynasty. The Nine Chapters of Arithmetic Hand Stool is Zhang Cang of the Western Han Dynasty in China.

A mathematical treatise written by Geng Shouchang. It is the "Ten Books of Reckoning".

The most important of these was written around the first century AD. Its author is no longer available.

It is generally believed that it has undergone additions and revisions from generation to generation, and gradually became the definitive version today, and Zhang Cang and Geng Shouchang of the Western Han Dynasty have made additions and sortings, and it has generally become a definitive version at that time. In the end, the book was written in the early period of the Eastern Han Dynasty at the latest, and most of the ones that are circulated today are in the fourth year of Emperor Jingyuan of Wei Yuan (263) during the Three Kingdoms period, Liu Hui.

Annotations to the Nine Chapters.

The influence of the later generations of "Nine Chapters of Arithmetic":The Nine Chapters of Arithmetic is the world's earliest work to systematically describe the operation of fractions; Among them, the algorithm of surplus and deficiency is an amazing creation; The chapter "Equations" is also in the history of mathematics in the world.

For the first time, negative numbers and their addition and subtraction operations are described. In terms of algebra, "Nine Chapters of Arithmetic" was the first in the history of mathematics in the world to put forward the concept of negative numbers and the rules of addition and subtraction of positive and negative numbers.

The Nine Chapters of Arithmetic is a book published in the Eastern Han Dynasty. The Nine Chapters of Arithmetic is the first mathematical monograph of Han Chinese scholars in ancient times, and it is the most important one of the ten books of arithmetic. The book is very rich in content, systematically summarizing the mathematical achievements of the Warring States, Qin, and Han dynasties.

Nine chapters of arithmetic introduction

The Nine Chapters of Arithmetic is an ancient Chinese mathematical treatise, and it is the most important of the Ten Books of Arithmetic (ten ancient arithmetic books that appeared between the Han and Tang dynasties). During the Wei and Jin dynasties, Liu Hui wrote a note for the "Nine Chapters of Arithmetic": "Zhou Hu sold the metric system and there were nine numbers, and the flow of nine numbers was the "Nine Chapters" and repented", and said that "Zhang Cang, the marquis of Pinghou in the Han Dynasty, and Geng Shouchang, the chief farmer, were all good at fortune telling."

Due to the remnants of the old texts, each is called deletion and supplementation, so the purpose of the school is different from the ancient, and the discussion is more close." According to research, Zhang Cang and Geng Shouchang of the Western Han Dynasty once made supplements.

The final book was written in the early Eastern Han Dynasty at the latest, but its basic content was basically finalized in the late Eastern Han Dynasty. There are only two kinds of mathematics books recorded in the "Han Shuyi Wenzhi" (written by Ban Gu based on Liu Xin's "Seven Strategies"), "Xu Shang Arithmetic" and "Du Zhong Arithmetic", and there is no "Nine Chapters of Arithmetic", which shows that "Nine Chapters of Arithmetic" appeared later than "Seven Strategies".

The Later Han Shu Ma Yuan Biography contains his nephew Ma Xu "well-read and good at "Nine Chapters of Arithmetic", and Ma Xu was the last in the 1st century AD.

Twenty or thirty years old. According to the official names and place names that can be used to determine the age in the "Nine Chapters of Arithmetic", it can be inferred that the current version of the "Nine Chapters of Arithmetic" was written in the second half of the first century AD. The Nine Chapters of Arithmetic divides all the mathematical problems in the book into nine categories, which are the "Nine Chapters".

Chapter 1 "Fangtian": Mainly describes the method of calculating the area of plane geometry. It includes eight methods for calculating the area of rectangles, isosceles triangles, right-angle trapezoids, isosceles trapezoids, circles, fans, bows, and rings.

In addition, the four rules of operation of fractions and the methods of finding the greatest common divisor of the numerator and denominator are systematically described.

Chapter 2 "Corn": The Proportional Conversion of Cereals; Proposed a proportional algorithm, known as the present technique; The decay chapter proposes the law of proportional distribution, which is called decay;

Chapter 3 "Decay": The Problem of Proportional Distribution; The method of opening the square and opening the square is introduced, and the procedure is basically the same as the current procedure. This is the world's first multi-digit and fractional opening rule. It laid the foundation for China to lead the world in numerical solutions of higher-order equations for a long time.

Chapter 4 "Shaoguang": know the area and volume, and find the length of one side and the length of the diameter;

Chapter 5 "Commercial Works": Earth and Stone Engineering, Volume Calculation; In addition to various three-dimensional volume formulas, there are also engineering allocation methods; Chapter 6 "Equal Loss": Reasonable Allocation of Taxes; Solve the problem of reasonable burden of enslavement with attenuation.

Today's techniques, decay techniques and their application methods constitute a complete set of proportional theories including today's positive and negative proportions, proportional distribution, complex proportions, and linkage proportions. It was not until the end of the 15th century that a similar set of methods was developed in the West.

Chapter 7 "Surplus and Deficiency": that is, the problem of double management; Three types of profit and loss problems are proposed, namely, surplus deficiency, surplus and shortfall, two surplus and two deficit, as well as some solutions to some general problems that can be turned into surplus and deficit problems by two assumptions. This is also the result of being a world leader, and after it spread to the West, it has had a great impact.

Chapter 8 "Equations": Problems of a system of equations; The method of separation coefficients is used to represent the system of linear equations, and the Pythagorean theorem solves the equivalent of the current matrix. The direct division method used to solve systems of linear equations is consistent with the elementary transformation of matrices. This is the world's first complete solution to a system of linear equations.

In the West, it was not until the 17th century that Leibniz proposed the law of solving complete linear equations. This chapter also introduces and uses negative numbers, and proposes the method of plus and minus - the addition and subtraction of positive and negative numbers, which is exactly the same as in modern algebra; When solving a system of linear equations, the multiplication and division of positive and negative numbers is actually performed. This is a major achievement in the history of world mathematics, breaking through the range of positive numbers and expanding the number system for the first time.

Abroad, it was not until the Brahma and Duo in India in the 7th century that negative numbers were recognized.

The general solution formula for the Pythagorean number problem is proposed: if a, b, and c are the Pythagorean hooks, strands, and chords, respectively, then m>nIn the West, Pythagoras, Euclid, etc., obtained only a few special cases of this formula, and it was not until the third century that Diophantus achieved similar results, which was about three centuries later than the Nine Chapters of Arithmetic.

The Pythagorean chapter still has some content, but in the West it is still a modern thing. For example, the set of formulas given in the last question of the Pythagorean chapter was not formulated by the American number theorist Dixon until the end of the 19th century abroad.