(1) is an arithmetic material.
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, "One horizontal and one rigid, one positive and one negative, and the whole is 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 the weights and measures, Xiahou Yang Suanjing records: "Ten times one, a hundred times two, a thousand times three and a thousand times four; Ten is first class, one hundred is second class, one thousand is third class, and ten thousand is fourth class. "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.
In arithmetic, we should also put forward the problem of "Sun Tzu's calculation of classics" in the third century A.D., which was developed by Qin in the Song Dynasty (A.D. 1247) as a technique of "seeking greatness". 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.
(2) Materials belonging to algebra
Since he explained equations in the eighth volume of Nine Chapters Arithmetic, China has kept brilliant achievements in the field of numerical algebra.
The equation chapter of "Nine Chapters Arithmetic" first shows that the positive and negative techniques are accurate and unchangeable, just as we are learning elementary algebra from the four operations of positive and negative numbers, and 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.
There are cubic equations in the form of x3+px2+qx=A and x3+px2=A, which were recorded in China in the Tang Dynasty in the 7th century. Wang Xiaotong got a numerical solution by "dividing 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.