Ten-day stem and twelve branches form 60 names such as Jiazi, Yechou, Bingyin and Dingmao, and record the date of 60 days; In the Zhou Dynasty, Qian Yin was used again.
The eight diagrams formed by the Yang symbol indicate that eight things have developed into sixty-four hexagrams, representing sixty-four things.
The method of measuring height, depth, width and distance by moments in the early Western Zhou Dynasty was mentioned in the Book of Weekly Parallel Calculation in the first century BC, and the Pythagorean-shaped three hooks were quoted.
The fourth chord, the fifth chord and the moment of the ring may be examples of circles, for example. It is mentioned in the Book of Rites that the children of aristocrats in the Western Zhou Dynasty should learn numbers and records from the age of nine.
As one of the "six arts", number has begun to become a special course.
During the Spring and Autumn Period and the Warring States Period, calculation has been widely used and decimal notation has been used, which has made great contributions to the development of mathematics in the world.
This exhibition is of epoch-making significance. During this period, econometrics was widely used in production, and mathematics was improved accordingly.
The contention of a hundred schools of thought in the Warring States period also promoted the development of mathematics, especially the dispute of rectifying the name and some propositions were directly related to mathematics. Logician school
They think that the abstract concepts of nouns are different from their original entities. They put forward that "rules can't be round" and put "freshman" (
Infinity) is defined as "nothing" and "little one" is defined as "nothing". He also suggested that "one foot pestle, take half of it every day,
Never exhausted "and other propositions.
Mohism believes that names come from things, and names can reflect things from different sides and depths. Mohist school gave some mathematical definitions. Such as circular,
Square, flat, straight, secondary (tangent), end (point), etc.
Mohism disagrees with the proposition of "one foot" and puts forward the proposition of "non-half" to refute that a line segment is infinitely divided into two.
If you divide it, there will be a "non-half" that can't be divided. This "non-half" is a point.
The famous scholar's proposition discusses that a finite length can be divided into an infinite sequence, while the Mohist proposition points out the changes and results of this infinite division.
. The discussion on the definition and proposition of mathematics by famous scholars and Mohists is of great significance to the development of China's ancient mathematical theory.
The Formation of Ancient Mathematics System in China
Qin and Han dynasties were the rising period of feudal society, with rapid economic and cultural development. It was during this period that the ancient mathematical system of China was formed.
Its main symbol is that arithmetic has become a specialized subject, and the emergence of mathematical works represented by Nine Chapters of Arithmetic.
Nine Chapters Arithmetic is a summary of the development of mathematics during the establishment and consolidation of feudal society in the Warring States, Qin and Han Dynasties. As far as its mathematical achievements are concerned, it can be called.
World famous mathematical works. For example, the operation of quartering, the current technique (called three-rate method in the west), square root and square root (including the numerical solution of quadratic equation),
Surplus and deficiency technique (called double solution in the west), various formulas of area and volume, solution of linear equations, addition and subtraction rules of positive and negative operations, Pythagorean solution (
Especially the Pythagorean theorem and the method of finding Pythagorean number), the level is very high. Among them, the solution of equations and the addition and subtraction of positive and negative numbers are developed in world mathematics.
The exhibition is far ahead. As far as its characteristics are concerned, it forms an independent system centered on calculation, which is completely different from ancient Greek mathematics.
"Nine Chapters Arithmetic" has several remarkable characteristics: it adopts the form of mathematical problem sets divided into chapters according to categories; These formulas are all developed from calculating symbols.
Yes; Mainly arithmetic and algebra, rarely involving graphic properties; Attach importance to application and lack of theoretical explanation.
These characteristics are closely related to the social conditions and academic thoughts at that time. During the Qin and Han Dynasties, all science and technology should have been established and consolidated at that time.
The feudal system and the development of social production services all emphasize the application of mathematics. Finally, the book Nine Chapters of Arithmetic written in the early years of the Eastern Han Dynasty ruled out war.
The famous scholars and Mohists who appeared in the contention of a hundred schools of thought during China's period attached importance to the discussion of noun definition and logic, and emphasized the close combination with production and life at that time.
Mathematical problems and their solutions completely accord with the development of society at that time.
Nine Chapters Arithmetic spread to Korea and Japan in Sui and Tang Dynasties, and became the mathematics textbook of these countries at that time. Some of its achievements are like ten.
The advanced system, today's skills, and the remaining skills have also spread to India and Arabia, and have spread to Europe through India and Arabia, which has promoted the development of mathematics in the world.
Development.
The Development of Ancient Mathematics in China
Metaphysics, which appeared in Wei and Jin dynasties, was not bound by Confucian classics in Han dynasty and was active in thought. It advocates victory, but it also uses logical thinking and analysis.
Meaning, these are conducive to the theoretical improvement of mathematics. Zhao Shuang of Wu annotated Zhou Kuai, and Xu Yue of Wei Chu wrote Nine Chapters of Arithmetic at the end of Han Dynasty.
During the Wei and Jin Dynasties, Liu Hui's Nine Chapters Arithmetic Notes and Nine Chapters Double Difference Diagram both appeared in this period. Zhao Shuang and Liu Hui worked in ancient China.
The mathematical system laid the theoretical foundation.
Zhao Shuang was one of the earliest mathematicians who proved and deduced mathematical theorems and formulas in ancient China. He added in the book "Zhou Kuai Shu Jing"
Pythagoras Square Diagram and Annotations and Daily Height Diagram and Annotations are very important mathematical documents. In Pythagoras Square Diagram and Annotations, he proposed to use string diagram.
Prove Pythagorean theorem and five formulas for solving Pythagorean form; In Sunrise Picture, he proved the weight difference formula widely used in Han Dynasty with the graphic area.
Zhao Shuang's work is groundbreaking and plays an important role in the development of ancient mathematics in China.
Liu Jicheng, who was contemporary with Zhao Shuang, developed the thoughts of the famous Mohist school in the Warring States Period, and advocated that it was particularly important for some mathematical terms.
The concept of mathematics is strictly defined, and it is considered that mathematical knowledge must be "analyzed" in order to make mathematical works concise and rigorous and beneficial to readers. he
The annotation of Nine Chapters Arithmetic is not only a general explanation and derivation of the methods, formulas and theorems of Nine Chapters Arithmetic, but also in the process of discussion.
China has made great progress. Liu Hui created secant technology, proved the formula of circle area with the idea of limit, and calculated pi by theoretical method for the first time.
Yes 157/50 and 3927/ 1250.
Liu Hui proved by infinite division that the volume ratio of right-angled square cone to right-angled tetrahedron is always 2: 1, which solved the key problem of general solid volume.
Title. When proving the volume of square cone, cylinder, cone and frustum, Liu Hui put forward the correct method to solve the volume of sphere completely.
After the Eastern Jin Dynasty, China was in a state of war and north-south division for a long time. Zu Chongzhi and his son's job is to count the number of people in the south after the economic and cultural shift to the south.
On the basis of Liu Hui's Notes on Nine Chapters of Arithmetic, they greatly promoted traditional mathematics. he
Our mathematical work mainly includes: calculating pi between 3.1415926 ~ 3.1415927; Put forward the principle of ancestor (constant sky); Put forward again and again.
Solutions of equations, etc.
Presumably, Zu Chongzhi calculated the inscribed area of regular polygon 6 144 and regular polygon 12288 on the basis of Liu Hui secant method, and thus obtained this.
A result. He also obtained two fractional values of pi by a new method, namely the approximate ratio of 22/7 and the density ratio of 355/ 1 13. Zu Chongzhi's works made China.
In the calculation of pi, it is about a thousand years ahead of the west;
Zu Chongzhi Zi Zu (Riheng) summed up Liu Hui's related work and put forward that "if the potential is the same, the product cannot be different", that is, two solids with the same height, if it
If the horizontal cross-sectional area at any height is equal, the two solid volumes are equal, which is the famous axiom of our ancestors (sunward). Zu (Riheng) applied this axiom.
And solved Liu Hui's unsolved spherical volume formula.