Who are the authors of Nine Chapters of Arithmetic ?

Nine Chapters of Arithmetic was written in the early years of the Eastern Han Dynasty, not a one-man work, but by many people to modify and supplement, at present only known Han Beiping Marquis Zhang Cang (?) 152 B.C.) and Geng Shouchang (c. mid-1st century B.C.) were involved in the collection, addition and deletion work.

Liu Hui was a great mathematician between the Wei and Jin dynasties and had annotated this book. Liu Hui annotated the "Nine Chapters of Arithmetic" in the fourth year of Emperor Jingyuan of Wei Yuan (263 AD) and wrote a volume of "Heavy Difference". The current name of "Heavy Difference" is "Island Arithmetic", and it is included in the "Ten Books of Arithmetic" together with "Nine Chapters of Arithmetic".

Nine Chapters of Arithmetic is a mathematical treatise written by Zhang Cang and Geng Shouchang in ancient China.

Nine Chapters of Arithmetic contains a total of 246 mathematical problems divided into nine chapters. Their main contents are:

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.

Chapter 4 "Shaoguang": know the area and volume, and find the length of one side and the length of the diameter; The method of opening the square and opening the square is introduced.

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 separating coefficients is used to represent the system of linear equations, which is equivalent to 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.

A general formula for the Pythagorean number problem is proposed: if a, b, and c are the Pythagorean hooks, strands, and chords, respectively, then m>n. In 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.

Nine Chapters of Arithmetic is the crystallization of the research of many mathematicians since the Western Han Dynasty, and the famous mathematicians Zhang Cang, Geng Shouchang and others in the early Western Han Dynasty have increased or subtracted from him.

The book is divided into 9 chapters, collecting solutions to 246 mathematical problems, including the world's most advanced fractional quadruple and proportional algorithm at that time.

There are also various algorithms for area volumes and the problem of measuring using the Pythagorean theorem, as well as methods of opening and squared.

In particular, for the first time in the history of mathematics in the world, the concept of negative numbers and the rules of addition and subtraction of positive and negative numbers were recorded. The impact of this book on the development of mathematics in ancient China was great. It marks the formation of a complete system of ancient mathematics in China.

He not only occupies an important position in the history of Chinese mathematics, but also influenced Korea and Japan, and has been translated and published in many foreign languages.

The authors of "Nine Chapters of Arithmetic" are Zhang Cang and Geng Shouchang. The author of "Nine Chapters of Arithmetic" is a mathematical treatise written by Zhang Cang and Geng Shouchang in ancient China. It is the most important of the Ten Books of Calculation, 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 200 B.C., Zhang Cang collected the official mathematical data accumulated since 1000 B.C. and compiled the Nine Chapters of Arithmetic, which became the original version of the Nine Chapters of Arithmetic, which was later compiled, revised, and commented on by many scholars, and finally combined into one book.

Impact:

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.