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. This only shows that Zhoupian Shu Jing is an earlier one among the known materials. Nine Chapters Arithmetic is the most important of ten arithmetic books, which comprehensively and completely introduces all aspects of mathematics in ancient Han Dynasty. Its influence on the development of ancient mathematics in the future is as profound as that of Euclid's Elements of Geometry in ancient Greece (about 330-275 BC) 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. There is no title of Nine Chapters Arithmetic in Hanshu Yiwenzhi, but there is a book Arithmetic by Xu Shang and Du Fu, so some people infer that it may also include the works of Xu and Du Fu. 1984, Shu Shu bamboo slips were unearthed from Zhangjiashan Tomb in Jiangling, Hubei Province in the early Western Han Dynasty. It is estimated that the book was written more than a century and a half before the nine chapters of arithmetic, and its content is very similar to the nine chapters of arithmetic, and some calculation problems are basically the same as the nine chapters of arithmetic.
It can be seen 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 in a long period, although some of its algorithms may have existed before the Western Han Dynasty. As the title of the book shows, the book is divided into nine chapters. One * * * collects 246 mathematical problems, and together with the solutions of each problem, it is divided into nine categories, each of which is 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 on simultaneous equations, which is essentially the same as that taught in middle schools. 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.
affect
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. As a world-famous scientific work, Nine Chapters Arithmetic has been translated and published in many languages.
Sunzi suan Jing
This book was written in the fourth and fifth centuries, and the author's life and writing time are not clear. Sun Tzu's Art of War was handed down in three volumes. The paper describes the vertical and horizontal alternation system and the rules of multiplication and division, and illustrates the algorithm of calculating scores and the method of calculating Kaiping with examples.
China was the first country in the world to adopt decimal system for counting, which was widely used in the Spring and Autumn Period and the Warring States Period, that is, it strictly followed decimal system. The only information about the calculation method is contained in Sun Zi's calculation. Sunzi Suanjing is a three-volume book, which was written in the 4th century. The first volume of the book is a systematic introduction to the calculation rules, and the second volume has the famous "unknown things", also known as the "grandson problem". Volume 3 1 is the ancestor of the problem of "chickens and rabbits in the same cage" in later generations, and later spread to Japan, which became the calculation of cranes and turtles. In the book, it is described as follows: "Today, chickens and rabbits are in the same cage, with 35 heads above and 94 feet below. The geometry of chicken and rabbit? These four sentences mean: there are several chickens and rabbits in a cage, counting from the top, there are 35 heads; It's 94 feet from the bottom. How many chickens and rabbits are there in each cage?
It is of great significance to Volume 26: "There are unknown things today. Three and three numbers leave two, five and five numbers leave three, and seven and seven numbers leave two. What is the geometry of things? Answer: "Twenty-three". Sun Tzu's calculation not only provides the answer, but also gives the solution. Qin, a great mathematician in the Southern Song Dynasty, further initiated the research work of congruence theory and popularized the problem that "things are unknown". German mathematician Gauss (K.F.Gauss.A.D.1777-1855) clearly wrote the above theorem in "Arithmetic Inquiry" published in 180 1 year. In a.d. 1852, the British Christian priest William ((﹝alexander· Wiley 18 15- 1887) spread the solution to the problem of "unknown things" in Sun Tzu's Calculations to Europe. Marty was born in a.d./kloc. Cao Wu suan Jing is an applied arithmetic book for local administrators (the author is unknown, but some people think it is Zhen Luan). The book is divided into five chapters: Cao Tian, Agropyron cristatum, Jicao, Cangcao and Caojin, so it is called "Cao Wu suan Jing". The solution of the problem is easy to understand, and the numerical calculation tries to avoid fractions. This book contains 67 questions. Its author and age are not recorded. Ouyang Xiu's Book of the New Tang Dynasty (Volume 59) and Records of Arts and Literature (Volume 59) contain "Zhen Luan Wu Cao Shu Jing", and other books have similar records. Zhen Xuan was born around 535-566 AD.
This is the frontispiece of the Southern Song Dynasty publication "Wu Cao Shu Jing", which was engraved in Jiading five years in the Southern Song Dynasty (12 12). Cao Wu suan Jing is a mathematical work in ancient China. The author is Zhen Luan of the Northern Zhou Dynasty (Zun Shu, from Wuji, Hebei). He is familiar with astronomical calendars, and was once a doctor in Li Si and a satrap in Hanzhong. Li Tang, Feng Chun and others made notes on it. Zhang Qiujian's classic calculation book was written by Zhang Qiujian in the late 5th century. There are problems in the application of the greatest common divisor and the least common multiple, and there is no problem of Zhu difference sequence. The most famous is the indefinite equation group-Hundred Chicken Problem, but its solution is not specified. Xiahou Yang Shujing is probably the work of the Northern Wei Dynasty. This paper briefly introduces the fast calculation rules and fractional rules of multiplication and division, and explains the rules of division by law, division by steps, reduction and division, square root and cube. In addition, the application and popularization of decimals are completely different from the representation. When the calculation result is odd, the decimal part below the text is represented by the names of length units such as minutes, centimeters, millimeters and silk. "Hundred chickens problem" is a famous mathematical problem in Zhang Qiujian's suan Jing, which gives a solution to an indefinite system of equations composed of two equations with three unknowns. The question of a hundred chickens is: "there is a chicken today, which is worth five;" One mother hen is worth three; Chicks, chicks are worth one. Buy 100 chickens for every 100 yuan, and ask the chicken geometry. According to the meaning of the question.
Since Zhang Qiujian, Chinese mathematicians have been deeply studying the hundred chickens problem, which has almost become synonymous with indefinite equations. From the Song Dynasty to the Qing Dynasty, the mathematical research on hundred chickens has achieved good results. Wang Xiaotong wrote Ji Gu Shu Jing. In May of the eighth year of Tang Wude (625), Wang Xiaotong wrote the book "Jigu Shujing" in Chang 'an, which is the earliest existing book for solving cubic equations in China.
Wang Xiaotong's Ji Gu Shu Jing is the only work written by scholars in the Tang Dynasty. Wang Xiaomo lived mainly in the late 6th century and early 7th century. He came from a civilian background and began to devote himself to mathematics in his teens. He was an official in the Sui Dynasty on the basis of calendar calculation, and he was retained after entering the Tang Dynasty. He worked as a doctor of arithmetic in the early years of the Tang Dynasty, and was later promoted to Tong Zhilang and Tai Shicheng. I have been engaged in mathematics and astronomy all my life. In the sixth year of Tang Wude (623), the solar eclipse calculated by Fu's Wuyin Yuanli was inconsistent with the actual astronomical phenomena, so he was assigned to study the problems existing in Fu's calendar with Lang Zhongzu of the official department. In the ninth year of Tang Wude (626), he and Dali Qing made a letter to proofread Fu Li, and corrected more than 30 mistakes, and handed them over to a surname for execution. Wang Xiaotong's "Ancient Arithmetic" has always been regarded as a mathematical textbook of imperial academy Institute of Mathematics, and it is regarded as a mathematical classic, so it was later called "Ancient Arithmetic Classic". One volume of the whole book (the new and old Tang books are called four volumes, but the number of questions in one volume is consistent with Wang Xiaotong's self-report, so there may be some differences in the classification of volumes) * * * Twenty questions. The first topic is to calculate the declination number of the moon, which belongs to the calculation of astronomical calendar. The second to fourteenth questions are the construction calculation problems of civil water conservancy projects such as building an observatory, building dams, digging ditches, building granaries and cellars. Questions 15 to 20 are Pythagoras problems. These problems reflected the actual needs of construction calculation of civil water conservancy projects such as canal digging, Great Wall construction and large-scale urban construction. 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 masterpiece Calculation of Pi (accurate to the seventh place after the decimal point) was included in Sui Shu Chronicle.