For example, the earliest known mathematical works "Zhou Zhi ·suan Jing" and "Nine Chapters Arithmetic" are all works around A.D., with a history of about 2,000 years. It is a great achievement in itself to let the mathematics books of 2000 years ago spread to the present.
At first, people learned mathematics by copying and passed on their knowledge to the next generation. Until the Northern Song Dynasty, with the development of printing, printed mathematics books began to appear, which is probably the earliest appearance of printed mathematics books in the world. Now, five kinds of mathematics books handed down from the Southern Song Dynasty, such as Zhou Kuai Shu Jing and Jiu Zhang Arithmetic, are precious cultural relics worth collecting.
From Han and Tang Dynasties to Song and Yuan Dynasties, famous arithmetic books appeared: either use China's traditional method to annotate the existing arithmetic books and put forward his own new algorithm in the annotation process; Or write a new book, innovate and create new ideas. These ancient mathematics books are the precious legacy left by mathematicians of all ages.
Ten classic books on computing
Ten books of calculation refer to ten famous mathematical works in the Han and Tang dynasties 1000 years. They used to be the textbooks of mathematics in imperial academy during the Sui and Tang Dynasties. The names of these ten books are: Weekly Calculations, Nine Chapters Calculations, Island Calculations, Five Cao Calculations, Sun Tzu Calculations, and.
Among the ten books, The Book of Weekly Parallel Calculations is the earliest. I don't know who its author is. According to textual research, it was written no later than the end of the Western Han Dynasty (the first century BC). Zhou Pi 'ai ·suan Jing is not only a mathematical work, but more accurately, it is an astronomical work about Gai Tian Shuo, a school of astronomical theory at that time. There are more complicated fractional calculations. Of course, it can't be said that these two algorithms were mastered only in the first century BC. It just shows that "Weekly Parallel Computing Book" is an earlier record in known data.
Nine Chapters of Arithmetic is the most important book among ten books, which comprehensively and completely introduces all aspects of ancient mathematics. Its influence on the later development of ancient mathematics in China is as profound as the influence of Euclid's Elements on western mathematics. In China, it has been directly used as a textbook for mathematics education for 1000 years. It also influenced foreign countries.
I don't know the exact author of Nine Chapters Arithmetic, except that Zhang Cang (20 1- 152) and Geng Shouchang were famous mathematicians in the early years of the Western Han Dynasty. Hanshu? There is no title of Nine Chapters Arithmetic in Yiwenzhi, but there is Arithmetic written by Xu Shanghe, so some people infer that it also includes Xu Hedu's works. 1984, bamboo slips of Arithmetic Book were unearthed in Zhangjiashan, Jiangling, Hubei Province in the early Western Han Dynasty. It is estimated that this book should have been written more than a century and a half before Nine Chapters Arithmetic. Some arithmetic sentences are basically the same as Nine Chapters Arithmetic, which shows that there is a certain inheritance relationship between the two books. It can be said that "Nine Chapters Arithmetic" was gradually formed after many revisions for a long time, although some of its algorithms may have existed as early as the Western Han Dynasty. As the title shows, the book is divided into nine chapters. One * * * collects 246 mathematical problems, which are divided into nine categories together with the solutions of each problem.
Judging from the mathematical achievements, the first thing to mention is that the book recorded four most advanced fractional operations and proportional algorithms in the world at that time. The algorithm of solving various area and volume problems and various measurement problems by Pythagorean theorem is also recorded. The most important achievement of Nine Chapters Arithmetic is algebra. The book records the method of square root and square root. On this basis, the numerical solution of the general quadratic equation with one variable is obtained (the first coefficient is non-negative). There is also a whole chapter about the solution of linear equations, which is essentially the same as that in middle schools now. This is 1500 years earlier than similar algorithms in Europe. In the same chapter, the concept of negative number and the addition and subtraction algorithm of positive and negative numbers were recorded for the first time in the history of mathematics in the world.
Nine Chapters Arithmetic not only occupies an important position in the history of Chinese mathematics, but also has far-reaching influence abroad. In the Middle Ages in Europe, some algorithms in Nine Chapters Arithmetic, such as fractions and proportions, may have been introduced to India first, and then to Europe through Arabia. Another example is "surplus and deficiency" (which can also be regarded as one-time interpolation method), which is called "China algorithm" in early Arabic and European mathematical works.
The third part of the Ten Books of Calculations is Calculations on the Island, which was written by Liu Hui (about 225- 295) during the Three Kingdoms period. This book talks about all the problems of measuring mathematics with benchmarks, twice, three times, and the most complicated is four times. These surveying mathematics are the mathematical basis of the very advanced cartography in ancient China. These notes can be regarded as mathematical proofs of several algorithms in Nine Chapters Arithmetic. The secant in Liu Hui's notes pioneered an important method for calculating pi in ancient China (see page 98 of this book), and he also applied the concept of limit to solving mathematical problems for the first time.
Other books in the Book of Ten Calculations also record some achievements of world significance. For example, the problem of "things are unknown" in Sun Tzu's Calculations (see page 106 of this book for the congruence solution) and the problem of "hundred chickens" (indefinite equation problem) in Zhang Qiu's Calculations are all famous.
Seal script is the work of Zu Chongzhi, a famous mathematician in the Northern and Southern Dynasties. Unfortunately, this book was lost in the Tang and Song Dynasties in the 10 century. Song people used another arithmetic book, The Book of Numerology, to fill in the blanks when they published Ten Books of Calculating Classics. Zu Chongzhi's famous book Calculation of Pi (accurate to the sixth decimal place) was recorded in Sui Shu? Legal calendar (see page 10 1 in this book).
Mathematical terms used in the book of ten calculations, such as numerator, denominator, square root, square root, positive, negative, equation, etc. , has been used to this day, some have a history of nearly two thousand years.
Arithmetic in Song and Yuan Dynasties
Ancient mathematics in China, from Han Dynasty to Tang Dynasty, has formed a relatively complete system after more than 1000 years of development. On this basis, the Song and Yuan Dynasties (from the 10th century to the 14th century) witnessed new development. The rapid development of mathematics in Song and Yuan Dynasties, numerous mathematical works and high achievements can be said to be the most brilliant page in the history of ancient mathematics in China.
Especially in the second half of the13rd century, in just a few decades, Qin (1202- 126 1) and (1 192- 1279 appeared successively.
Nine Chapters of Qin Dynasty (A.D.1247);
Ye Li's Round Sea Mirror (A.D. 1248) and An Ancient Yan Duan (A.D.1259);
Yang Hui's algorithm (AD/KOOC-0/26/KOOC-0/), daily algorithm (AD/KOOC-0/262) and Yang Hui's algorithm (AD/KOOC-0/274-/KOOC-0/275);
Zhu Shijie's Arithmetic Enlightenment (A.D. 1299) and Philip Burkart's Meeting (A.D. 1303).
Shu Shu Jiu Zhang mainly describes two important achievements: the numerical solution of higher-order equations and the first congruence solution (see pages 1 19 and 1 10 respectively). Some questions in the book need to solve ten equations, and some questions have as many as 180 answers. The relationship between line segments and inscribed circles caused by right-angled triangles is also described, which is a unique geometry in ancient Chinese mathematics. Yang Hui's works tell another important aspect of mathematics in Song and Yuan Dynasties: practical mathematics and various simple algorithms. This is a new direction with the development of social economy, which creates conditions for the emergence of abacus. Zhu Shijie's "Arithmetic Enlightenment" is worthy of being an enlightenment textbook at that time, and it is gradual. By that time, mathematics was still relatively advanced. Four-element jade mirror records two other achievements of mathematics in Song and Yuan Dynasties: four elements (see book 123 for solving higher-order equations) and higher-order arithmetic progression and higher-order differential method (see book 13 1 page).
Compared with similar achievements in the West, these achievements in the Song and Yuan Dynasties include: the numerical solution of higher-order equations is more than 500 years earlier than Horner's (1786- 1837) method, the quaternion method is more than 400 years earlier than Bezo's (1730- 1783) method, and the higher-order difference method.
The brilliant achievements recorded in the Song and Yuan Dynasties proved once again that until the middle of Ming Dynasty, China was far ahead in many aspects of science and technology.
After the Song and Yuan Dynasties, there were also many arithmetic books in the Ming and Qing Dynasties. For example, in the Ming Dynasty, there was a famous arithmetic book, Arithmetic Unification, which was a popular book about abacus calculation. After entering the Qing Dynasty, there were many arithmetic books, but such great achievements as ten calculations and calculations in Song and Yuan Dynasties were rare. Especially after the late Ming and early Qing dynasties, many arithmetic books introduced western mathematics. This reflects.
The history of mathematics development in China shows that China's mathematics has made outstanding contributions to the development of mathematics in the world, but it has gradually fallen behind in modern times. We are convinced that through hard work, China's mathematics will certainly catch up with the advanced level in the world.
Precautions:
Bezo is also translated as Pei Shu or Bi Zuo.