Nine Chapters Arithmetic is an ancient mathematical monograph of China, and it is the most important one among the ten computational classics. Nine Chapters Arithmetic inherited the development of mathematics in the pre-Qin period, and was edited and edited by many scholars after entering the Han Dynasty. Written in the early years of the Eastern Han Dynasty (A.D. 1 century), it is the crystallization of the joint efforts of several generations. Its appearance marks the formation of China's ancient mathematical system. Most of the later ancient mathematicians began to study and study mathematics from Nine Chapters Arithmetic, and many people commented on it, among which Liu Hui (AD 263) and Li (AD 656) were the most famous. Both Tang and Song Dynasties were clearly defined as textbooks by the state. 1084 was published by the Northern Song Dynasty, and it was the earliest printed mathematics book in the world. Nine Chapters Arithmetic was introduced to Korea and Japan in Sui and Tang Dynasties. Now it has been translated into Japanese, Russian, German, English, French and other languages.
There are 246 math problems in Nine Chapters Arithmetic, which are divided into nine chapters. Its main contents are as follows: The first chapter is the calculation of the research field area of "square field"; The second chapter is "millet", which studies the conversion of grain-grain ratio; Chapter 3 "Decreasing scores" studies the problem of proportional distribution; The fourth chapter is "few but wide", where the area, volume, length of one side and diameter are known. Chapter 5 "Business Work", studying geotechnical engineering and volume calculation; The sixth chapter, "lose-lose", studies the reasonable allocation of taxes; Chapter seven is "insufficient profit", that is, the problem of dual management; Chapter 8 "Equation" studies the problem of linear equations; Chapter 9 "Pythagorean Theorem" is solved by Pythagorean Theorem.
Chapter nine mathematical achievements of arithmetic;
(1) put forward the complete rules of four fractional operations, such as divisibility, reduction, addition, subtraction, multiplication and division, which was earlier than Europe 1400 years ago;
(2) Put forward a complete set of proportional theory. It was not until the end of 15 that a similar method was formed in the west.
(3) cholesky decomposition is introduced, and its procedures are basically consistent with the existing procedures. This is the earliest multi-digit and fractional root rule in the world. It laid a foundation for China to lead the world in numerical solution of higher order equations for a long time.
(4) The linear equations are expressed by the separation coefficient method, which is equivalent to the existing matrix. The direct division used to solve linear equations is consistent with the elementary transformation of matrices. This is the earliest solution of completely linear equations in the world. In the west, it was not until17th century that the complete rules for solving linear equations were put forward.
(5) Introduce and use negative numbers, and put forward the law of addition and subtraction of positive and negative numbers, which is exactly the same as modern algebra; When solving linear equations, the multiplication and division of positive and negative numbers are actually performed. This is a great achievement in the history of world mathematics, which broke through the range of positive numbers for the first time and expanded the number system. Foreign countries didn't realize negative numbers until the 7th century.
(6) Put forward the general solution formula of Pythagorean number problem. In the west, it was not until the 3rd century that similar results were achieved, which was about 3 centuries later than the arithmetic in Chapter 9.
(7) area formulas of various polygons, circles, arches, etc. Be proposed.
Zhouyi suanjing, formerly known as Zhouyi, is an ancient astronomical work in China, which was written around 100 BC and involved some mathematical contents. These mathematical contents include: four operations of integers and fractions, arithmetic progression and first-order interpolation, explicit expression of the general form of Pythagorean theorem and Pythagorean measure, which are applied to Kaiping method. Zhou Piai suan Jing is an important work in the history of the development of ancient mathematics in China.
Zhouyi suanjing, formerly known as Zhouyi, is an ancient astronomical work in China, which was written around 100 BC and involved some mathematical contents. These mathematical contents include: four operations of integers and fractions, arithmetic progression and first-order interpolation, explicit expression of the general form of Pythagorean theorem and Pythagorean measure, which are applied to Kaiping method. Zhou Piai suan Jing is an important work in the history of the development of ancient mathematics in China.