For example, the earliest known mathematical works, Zhou Piai Suan Jing and Nine Chapters Arithmetic, are all works around A.D., with a history of about two thousand 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 by copying and passed on their mathematical knowledge to the next generation. Until the Northern Song Dynasty, with the development of printing, printed mathematics books began to appear, which may be the earliest printed mathematics works in the world. There are five kinds of mathematics books handed down from the Southern Song Dynasty in Beijing Library, Shanghai Library and Peking University Library, such as Zhou Kuai Suan Jing and Jiu Zhang Arithmetic, which are even more 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 another new book and be innovative. These ancient arithmetic books, which have been handed down from generation to generation, are a 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 arithmetic books are Zhou Pian Jing, Jiu Zhang Arithmetic, Island Arithmetic, Cao Wu Arithmetic Classic, Sun Zi Arithmetic Classic, Xiahou Yang Arithmetic Classic, Zhang Qiu Arithmetic Classic, Five Arithmetic Classics, Ji Gu Arithmetic Classic and Seal Script.
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 Kuai suan Jing is not only a mathematical work, but also an astronomical work about Gai Tian Shuo, a school of astronomical theory at that time. As far as mathematical content is concerned, the book records astronomical calculations with Pythagorean theorem, and there are more complicated fractional calculations. Of course, it cannot be said that these two algorithms were not mastered until the first century BC. It can only show that "Weekly Parallel Computing Book" is an earlier record in known data.
Nine Chapters Arithmetic is the most important of ten arithmetic 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 Euclid's Elements of Geometry's influence on western mathematics. In China, it has been directly used as a textbook for mathematics education for 1000 years. It also influenced foreign countries, and Korea and Japan used it as teaching materials.
I don't know the exact author of Nine Chapters Arithmetic, except that Zhang Cang (201-kloc-0/52), Geng Shouchang and others had added or deleted it 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 there may also be works by Xu Hedu. 1984, in the early Western Han Dynasty, 67 Shu Shu bamboo slips unearthed from Zhangjiashan Tomb in Jiangling, Hubei Province were calculated more than a century and a half earlier than the nine-chapter arithmetic, and the contents were very similar. Some calculation questions were basically the same as the nine-chapter arithmetic, indicating that there was a certain inheritance relationship between the two books. It can be said that Nine Chapters Arithmetic was gradually formed after many revisions in a long period, although some of its algorithms may have existed before the Western Han Dynasty. As the title shows, the book is divided into nine chapters, and a total of 246 math problems are collected. Together with the solutions to each problem, it is divided into nine categories, and each category is regarded as a chapter.
Judging from the mathematical achievements, the first thing to mention is that the book records the most advanced quartering operation and proportional algorithm in the world at that time. The book also records the algorithm of solving various area and volume problems and various measurement problems with Pythagorean theorem. The most important achievement of Nine Chapters Arithmetic is algebra. The method of square root and square root is recorded in the book, and on this basis, a numerical solution for solving the general quadratic equation with one variable (the first term coefficient is not negative) is obtained. There is also a whole chapter about solving simultaneous equations, which is essentially the same as the method 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 a one-time interpolation method), which is called "China algorithm" in the early mathematical works of Arabia and Europe. Now, as a world-famous scientific work, Nine Chapters Arithmetic has been translated and published in many languages.
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 is all about using benchmarks to measure twice, three times, and the most complicated is four times to solve various mathematical problems of measurement. These surveying mathematics are the mathematical basis of the very advanced cartography in ancient China. In addition, Liu Hui is also famous for his annotation of Nine Chapters Arithmetic. Generally speaking, these notes can be regarded as mathematical proofs of several algorithms in Nine Chapters of Arithmetic. The secant in Liu Hui's annotation 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 Ten Calculations also recorded some achievements of world significance. For example, the problem of "I don't know the number of things" in Sun Tzu's calculation (for a solution of congruence, see page 106 of this book) and the problem of "hundred chickens" in Zhang Qiu's calculation (indefinite equation problem) are all famous. The solution of the cubic equation of Yoshitani Shujing, especially the method of listing the cubic equation by geometric method, is also very distinctive.
Seal script is the work of Zu Chongzhi, a famous mathematician in the Northern and Southern Dynasties. Unfortunately, this book was lost around the tenth century AD between the Tang and Song Dynasties. Song people used another arithmetic book found at that time to fill in the numbers when publishing the Ten Books of Arithmetic Classics. Zu Chongzhi's famous work, the 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
From Han Dynasty to Tang Dynasty, China ancient mathematics has formed a relatively complete system after more than one thousand years' development. On this basis, the Song and Yuan Dynasties (10th century to14th 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. The so-called Song and Yuan Dynasties refer to the mathematical works of these four masters, including:
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 1 19 and 1 10 respectively). Some questions in the book require the solution of decagonal equations, and some questions have as many as 180 answers. "Round Sea Mirror" and "An Ancient Yan Duan" tell about another achievement of mathematics in Song and Yuan Dynasties: celestial skills (see 12 1 page for algebraic equations); The relationship between line segments caused by right triangle and inscribed circle is also described, which is a unique geometry in China's ancient 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 rising with the development of social economy, which creates conditions for the emergence of abacus. Zhu Shijie's "Arithmetic Enlightenment" was the teaching material of enlightenment at that time, from the shallow to the deep, step by step, until the mathematics at that time was more advanced. "Encounter with Siyuan" records two other achievements of Song and Yuan Mathematics: Quaternary method (see this book 123 for solving higher-order equations) and higher-order arithmetic progression and higher-order differential method (see this 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 many arithmetic books in the Ming and Qing Dynasties. For example, there was a famous arithmetic book "Arithmetic Unity" in Ming Dynasty. This is a popular book about abacus. After entering the Qing Dynasty, there were many arithmetic books, but the great achievements contained in Classic Ten Calculations and Arithmetic in Song and Yuan Dynasties were rare. Especially after the late Ming and early Qing dynasties, many calculation books introduced western mathematics. This reflects the gradual backwardness of China's science and technology after the development of western capitalism entered the modern scientific period, and also reflects a process in which China's mathematics gradually merged into the general trend of world mathematics development.
The history of China's mathematics development shows that China's mathematics has made outstanding contributions to the development of the world's mathematics, but it only gradually fell 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 also translated Pei Shu or finished his work.