Development history of mathematics in China

About 3,000 years ago, China knew four operations of natural numbers, and these operations were just some results, which were preserved in ancient words and books. The operation rules of multiplication and division were recorded in detail in Sun Tzu's Art of War (3rd century AD). China used chips to count in ancient times. In our ancient counting, we used the same bit rate as now. The method of counting chips is to use vertical chips to represent the number of units, hundreds of digits and tens of thousands of digits. Use horizontal chips to represent tens, thousands, etc. It is also obvious in the operation process. Sun Tzu's Calculations is expressed in sixteen words. "From one to ten, one hundred stands upright and thousands of faces are equal." Like other ancient countries, the multiplication table has existed in China for a long time. China's multiplication table was called Jiujiu in ancient times. It is estimated that China had this table 2,500 years ago. At that time, people used 99 to represent mathematics. Now we can still see the wooden slips with multiplication formula of 99 left over from the Han Dynasty (1st century BC). According to the existing historical data, the fractional arithmetic in China's ancient mathematical work Nine Chapters Arithmetic (AD 1 century or so) is the earliest document in the world, and the fractional arithmetic in Nine Chapters Arithmetic is almost exactly the same as what we use now. In ancient times, learning arithmetic also began to know fractions from the measurement of quantity. Sun Tzu's Calculations of Classics (3rd century A.D.) and Summer Sun's Calculations of Classics (6th and 7th centuries A.D.) both started to talk about weights and measures before discussing scores. After describing weights and measures, Xiahou Yang's Jing suan records: "Ten times one, a hundred times two, a thousand times three and a thousand times four; One tenth, two percent, three thousandths, four thousandths. " This power of ten is undoubtedly China's earliest discovery. In the decimal notation, in the Yuan Dynasty (A.D.13rd century), it was represented by a small letter, such as 13.56 1356. Arithmetically, we should also put forward the problem of "Sun Tzu's calculation of classics" in the third century A.D., and develop it into the "big extension and seeking skills" of Qin in the Song Dynasty (A.D. 1247). This is China's remainder theorem, and the same method was only studied in Europe in19th century. In the book written by Yang Hui in the Song Dynasty (A.D. 1274), there was a table of factors within 1-300. For example, 297 is represented by "three factors plus one loss", that is, 297=3× 1 1×9, (165438). Yang Hui also used the term "conjoined addition" to describe prime numbers within 20 1-300. (II) Materials Belonging to Algebra Since the eighth volume of "Nine Chapters of Arithmetic" explained the equation, China has maintained brilliant achievements in the field of numerical algebra. The equation chapter of "Nine Chapters Arithmetic" first shows that the positive and negative method is accurate and unchangeable, just as we are learning four operations of positive and negative numbers when studying elementary algebra now, the appearance of negative numbers enriches the content of numbers. In the first century BC, there were several kinds of equations in ancient China, such as multivariate equation, univariate quadratic equation and indefinite equation. Prove the quadratic equation of one variable by using geometric figures. The emergence of indefinite equation in China more than two thousand years ago is a subject worthy of attention, which is more than three hundred years earlier than the Greek Diophantine equation we are familiar with now. Cubic equations in the form of x3+px2+qx=A and x3+px2=A were recorded by China in Wang Xiaotong's "Several Ancient Classics" in the 7th century A.D., and the digital solution was obtained by "differentiating from the square" (unfortunately, the original solution was lost). It is not difficult to imagine Wang Xiaotong's pleasure when he got this solution. He said that whoever can change a word in his work will get thousands of dollars. 1 1 century Jia Xian has invented the same numerical equation solution as Horner (1786- 1837), and we can't forget the great contribution of China13rd century mathematician Qin. In the history of mathematics in the world, the original records of equations have different forms, but in comparison, we have to push the simplicity of China's magic. The four-element technology is the inevitable product of the development of celestial technology. Serials are ancient things. Two thousand years ago, arithmetic progression and geometric sequence were discussed in Zhou Zhi than Jing and Nine Chapters Arithmetic. /kloc-At the beginning of the 4th century, China should give high praise to the calculation of Zhu Shijie series in Yuan Dynasty. Some of his works are recorded in the works of Europe18th and 9th centuries. In the 1 1 century, China had a complete binomial coefficient table and a method for compiling it. Historical documents show that the famous surplus and deficiency calculation technology was spread to Europe from China. The calculation of interpolation method can be traced back to Liu Zhuo in the 6th century in China, and the monks and nuns had interpolation methods with unequal intervals at the end of the 7th century. Before14th century, China was one of the advanced countries that studied many problems in algebra. That is, 18 and the 9th century, Li Rui (1773- 18 17) and Wang Lai (1768- 1865438) went to Li (/kloc). (3) China's geometry has developed independently for a long time from the late Ming Dynasty (16th century) to the publication of some Chinese versions of Euclid's Elements of Geometry. We should pay attention to many ancient handicrafts and achievements in architectural engineering and water conservancy engineering, which contain rich geometric knowledge. China's geometry has a long history, and reliable records can be traced back to BC15th century. In Oracle Bone Inscriptions, there are two words: rules and moments. Rules are used to draw circles and moments are used to draw squares. The shape of moments in stone carvings in the Han Dynasty is similar to that of right-angled triangles. Around the 2nd century BC, China recorded the famous Pythagorean Theorem (Pythagoras originated relatively late). The study of circle and square plays an important role in the development of ancient geometry in China. Mozi's definition of a circle is: "A circle is equal in length." A circle whose center is equal to the circumference is called a circle, which was explained more than 100 years before Euclid. And Liu Xin (? 23), Zhang Heng (78- 139), Liu Hui (263), Wang Fan (2 19-257), Zu Chongzhi (429-500), Zhao Youqin (A.D.13rd century) and others, among whom Liu Fan. Zu Chongzhi got the result π=355/ 133 more than one thousand years earlier than Europe. In Liu Hui's notes on Nine Chapters of Arithmetic, his genius for the concept of limit has been revealed many times. In plane geometry, right-angled triangles or squares are used, and in solid geometry, cones and rectangular cylinders are used for displacement, which constitute the characteristics of ancient geometry in China. Mathematicians in China are good at applying the results of algebra to geometry and proving algebra with geometric figures. The combination of numerical algebra and intuitive geometry has achieved good results in practice, which just shows that mathematicians in China18th and 9th centuries studied the tangent connectivity ratio, and Mingda Xiang (1789- 1850) used it to find ellipse circumference. These are obtained by inheriting ancient methods and exerting them (of course, we also need to absorb the essence of foreign mathematics). (4) The appearance of material trigonometry belonging to triangle is due to the development of measurement, and the spherical triangle is first produced. Ancient astronomy in China was very developed, because the knowledge of spherical measurement was known a long time ago to determine the position of stars; Plane measurement has been recorded in Weekly Shooting of Shu Jing. If the depth and distance are measured by moments. Liu Hui secant method calculates the length of each side of regular hexagon and dodecagon in a circle in radius. This answer is consistent with the value of 2sinA (A is half of the central angle), and the same principle is also applicable to Zhao Youqin's calculation of a regular quadrilateral on a circle in the12nd century. From the calculations of Liu Hui and Zhao Youqin, we can get 7.5o, 15o, 22.5o and 3000. In the ancient calendar, there was a sundial with 24 solar terms, and an eight-foot-long "table" stood upright on the ground. Due to the rotation of the earth, the sunlight projected on this "table" on the ground by each solar term is different. The ratio of these shadow lengths to the "eight-foot table" constitutes the cotangent function table (although there was no such name at that time). 13rd century, China astronomer Guo Shoujing (1231-1316) discovered three formulas on a spherical triangle. Now we use trigonometric function terms: sine, cosine, tangent, cotangent, secant, cotangent, all of which were the names of China in16th century. At that time, adding the two functions of vector and cotangent was called eight lines. /kloc-in the late 7th century, China mathematician Mei Wending (1633- 172 1) compiled a book about plane triangles and a book about spherical triangles. The book about plane triangle is called Outline of Plane Triangle, which contains the following contents: (1) the definition of trigonometric function; (2) Solving right triangle and oblique triangle; (3) The quadrature of a triangle containing a circle and a square; (4) measurement. This is not far from the content of modern plane triangle. Mei Wending also wrote a book about famous multiplication and difference formulas on triangles. /kloc-After the 8th century, China also published many trigonometry books.