In the Neolithic painted pottery bowls, there are many kinds of depicting symbols, including,,,? , etc. , may be the earliest notation in China. After the appearance of characters, special characters and decimal notation appeared in Oracle bone inscriptions in Yin Shang Dynasty, and ruler and moment were used as simple drawing and measuring tools. "Law and Discipline" records the method of expressing numbers and calculating with bamboo sticks, which is called calculation. In the early Spring and Autumn Period, the multiplication formula was called "Jiujiu", which has become a very common knowledge.
During the Spring and Autumn Period and the Warring States Period, academic prosperity produced quite wonderful and valuable mathematical ideas; In the 6th century BC, there was a simple algorithm of volume and proportion distribution, and the data of scores and angles were recorded in the examination records. In the Qin Shihuang period, the weights and measures were unified, and the decimal unit of measurement was basically adopted. The definitions of geometric nouns and geometric propositions were put forward in Mo Jing. Du Zhong Arithmetic and Xu Shang Arithmetic are the earliest mathematical monographs, but they are both lost. The ancient mathematics monograph still preserved today is Arithmetic Book, which has more than 60 subheadings and titles.
About 1 century BC, the Book of Zhou Zhi Su 'an was completed (most of the contents in the book were completed in the 7th and 6th centuries BC). The book describes the use of moments, Pythagorean theorem and its application in measurement, the theorem that the corresponding sides of similar right-angled triangles are proportional, the square root problem, the arithmetic progression problem, and the application of the ancient "quarter calendar" to calculate quite complicated fractional operations. This book is an important and valuable document.
Nine Chapters Arithmetic, an ancient mathematical masterpiece, was written in 1 century in the early Eastern Han Dynasty. This book lists 246 math problems and their solutions. * * * There are nine chapters in total: the first chapter "Square Field" introduces the calculation of land area, the formulas of square, rectangle, triangle, trapezoid, circle and ring, the approximate formulas of bow area and spherical area, and the second chapter "Millet" introduces various grain conversion ratios and the method to solve them, which is called "skillful presentation"; The third chapter "Cuǐ" introduces the distribution of materials according to grades or the proportional distribution of taxes according to certain standards, arithmetic progression, geometric series and so on. The fourth chapter "Shao Guang" introduces the method of finding the square root or square root of the side length or edge length of a known square area or cube volume, and the diameter of a known sphere volume. The fifth chapter "quotient work" introduces the calculation of solid volume, including the calculation formulas of cuboid, prism, pyramid, frustum, cylinder, cone, frustum and wedge. The sixth chapter introduces the calculation of reasonable tax sharing. According to the conditions of population, price and distance, the direct ratio, inverse ratio, complex ratio and arithmetic progression of migrant workers are calculated. The seventh chapter "insufficient profit" introduces profit and loss problem's algorithm; Chapter 8 "Equation" introduces the problem of simultaneous equation, introduces the concept of negative number and the law of addition and subtraction of positive and negative numbers. Chapter 9 "Pythagorean Theorem" introduces the application of Pythagorean Theorem and simple measurement problems. Later, famous mathematicians in history, such as Liu Hui, Zu Chongzhi, Li, Jia Xian, etc. In this paper, Nine Chapters Arithmetic is deeply studied and annotated, and many new concepts and methods are put forward, such as proof of Pythagorean theorem, double difference technique, secant technique, approximate value of pi, volume formula of sphere, solution of quadratic and cubic equations, etc.
China's ancient mathematical monographs include Pythagoras Square, Notes on Nine Chapters of Arithmetic, Arithmetic Classics of Sun Tzu, Arithmetic of Five Classics, Composition, etc. In particular, Liu Hui demonstrated most of the mathematical methods in Nine Chapters Arithmetic, and gave a clear explanation of some mathematical concepts. It laid a solid theoretical foundation for the development of mathematics in China. Zu Chongzhi put forward a more accurate pi than Liu Hui in The Book, which became a great achievement universally recognized. Jia Xian put forward the "roots of root system" and the methods of addition, subtraction, multiplication and division in the Nine Chapters of the Yellow Emperor, and also put forward the "grandson problem" in Sun Zi Shu Xue and Zhang Qiu Bai Shu.