Where are Nine Chapters of Arithmetic, Da Yan Li, Notes on the Armageddon, Zhou Kuai Shu Jing and Shi Gan Jing?

Nine chapters and nine volumes of arithmetic, the author's name is unknown. Nine Chapters Arithmetic is China's oldest mathematical work, which has been handed down to this day. Its compilation time is about the early years of the Eastern Han Dynasty. In the book? The answers to 246 application problems are collected, which belong to Tian Fang (38), Xiaomi (46), Decay (20), Shaoguang (24), Quotient (28), Accidental Loss (28), Profit and Loss (20), Equation (18) and Sentence Stock (24).

Nine Chapters Arithmetic is one of the oldest mathematical monographs in China, which was written in the Western Han Dynasty. The completion of this book has gone through a historical process. Some of the mathematical problems collected in the book were handed down in the pre-Qin period, and were edited by many people for a long time, and finally sorted out by mathematicians in the Western Han Dynasty. The content of the final version circulated today was formed before the Eastern Han Dynasty. Nine Chapters Arithmetic is China's most important classic mathematical work. Its completion laid the foundation for the development of ancient mathematics in China and played an extremely important role in the history of Chinese mathematics. This issue of Nine Chapters Arithmetic has collected 246 application questions and answers to various questions, which belong to:

Chapter 1, "Square Domain" (38): methods and algorithms for measuring the area of plane graphics, such as quadrature formulas for rectangular, triangular, circular, arc, ring and other domains, and fractional algorithms, including addition, subtraction, multiplication and division, denominator and numerator division to find the greatest common divisor, and then compare and calculate the fractional size.

The second chapter, "Su" (46): the calculation between various grain exchanges and the discussion of the proportional algorithm.

Chapter III, "Decline" (20): Proportional distribution.

Chapter 4, "Less Width" (24): the square root of multiple digits, the issuer's rule.

Chapter 5, "quotient work" (28): Calculation of solid volume.

Chapter VI "Equal Loss" (28): Deal with travel itinerary, and reasonably solve the taxation problem, especially about the time required for people to transport grain from the local area to Beijing to pay taxes, and some problems about taxation according to population, which are also mixed with attenuation, proportion and various miscellaneous problems.

Chapter 7 "Profit and Loss" (20): profit and loss problem's arithmetic is actually the present linear interpolation method, which has many names, such as trial and error method and double hypothesis method.

Chapter 8 Equation (18): the content of linear equation, and finally the indefinite equation. By calculating, the coefficients and constant terms of the equation are put into the "equation set", which is the method to solve the equation more than once in "Nine Chapters Arithmetic", and the whole elimination process is equivalent to the linear transformation in algebra. In the chapter of equation, different representations of positive and negative numbers and the rules of addition and subtraction of positive and negative numbers are put forward.

Chapter 9 "Pythagorean Theorem" (24): The method of solving application problems by Pythagorean Theorem is specially discussed.

The appearance of Nine Chapters Arithmetic marks the formal establishment of the ancient mathematical system in China, which has the following characteristics:

1 is an applied mathematics system, and the whole book is expressed in the form of applied exercises;

2. With algorithm as the main content, the book consists of questions, answers and skills, and "skills" is the main content to be elaborated;

3. Use calculation as a tool.

"Nine Chapters Arithmetic" has made many mathematical achievements, including: fractional operation, proportional problem, double solution, calculation of some areas and volumes, solution of linear equations, introduction of negative number concept and negative number addition and subtraction rules, square root, square root, solution of general quadratic equation, etc. The thinking method of Nine Chapters Arithmetic has a great influence on ancient mathematics in China. Since Sui and Tang Dynasties, Nine Chapters Arithmetic has been introduced into Korea and Japan, and has been translated into many languages.

The appearance of nine chapters arithmetic is the result of social development and long-term accumulation of mathematical knowledge, which brings together the labor achievements of mathematicians in different periods. Liu Hui, a mathematician in the Three Kingdoms period, said: "Duke Zhou used the nine-number system, and nine chapters were enough. Zhang Cang, Hou Peiping of Han Dynasty, Cheng Gengshouchang and the old farmer are all good fortune tellers. Cang et al. are called deletion and supplement because of the remnants of old texts. Therefore, the purpose of the school is different from the ancient or different, and the theory is closer. " According to Liu Hui's research results, Nine Chapters Arithmetic originated from Nine Numbers in Duke Zhou. The Nine Chapters Arithmetic he saw was edited by Zhang Cang and Geng Shouchang in the Western Han Dynasty on the basis of inheriting the legacy of the pre-Qin Dynasty, which contained a lot of supplementary contents in the Western Han Dynasty. According to historical documents and unearthed cultural relics, what Liu Hui said is credible.