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Zhang Qiujian
''Zhang Qiujian Suanjing'' (''The Mathematical Classic of Zhang Qiujian'') is the only known work of the fifth century Chinese mathematician, Zhang Qiujian. It is one of ten mathematical books known collectively as ''Suanjing shishu'' (The Ten Computational Canons). In 656 CE, when mathematics was included in the imperial examinations, these ten outstanding works were selected as textbooks. ''Jiuzhang suanshu'' (The Nine Chapters on the Mathematical Art) and ''Sunzi Suanjing ''Sunzi Suanjing'' () was a mathematical treatise written during 3rd to 5th centuries AD which was listed as one of the Ten Computational Canons during the Tang dynasty. The specific identity of its author Sunzi (lit. "Master Sun") is still ...'' (The Mathematical Classic of Sunzi) are two of these texts that precede ''Zhang Qiujian suanjing''. All three works share a large number of common topics. In ''Zhang Qiujian suanjing'' one can find the continuation of the development of mathematics from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Mathematics
Mathematics in China emerged independently by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system ( base 2 and base 10), algebra, geometry, number theory and trigonometry. Since the Han Dynasty, as diophantine approximation being a prominent numerical method, the Chinese made substantial progress on polynomial evaluation. Algorithms like regula falsi and expressions like continued fractions are widely used and have been well-documented ever-since. They deliberately find the principal ''n''th root of positive numbers and the roots of equations. The major texts from the period, ''The Nine Chapters on the Mathematical Art'' and the ''Book on Numbers and Computation'' gave detailed processes for solving various mathematical problems in daily life. All procedures were computed using a counting board in both texts, and they included inverse elements as well as Euclidean divi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Ten Computational Canons
The ''Ten Computational Canons'' was a collection of ten Chinese mathematical works, compiled by early Tang dynasty mathematician Li Chunfeng (602–670), as the official mathematical texts for imperial examinations in mathematics. The Ten Computational Canons includes: #''Zhoubi Suanjing'' (''Zhou Shadow Mathematical Classic'') #''Jiuzhang Suanshu'' (''The Nine Chapters on the Mathematical Art'') #''Haidao Suanjing'' (''The Sea Island Mathematical Classic'') #''Sunzi Suanjing'' (''The Mathematical Classic of Sun Zi'') #'' Zhang Qiujian Suanjing'' (''The Mathematical Classic of Zhang Qiujian'') #'' Wucao Suanjing'' (''Computational Canon of the Five Administrative Sections'') #''Xiahou Yang Suanjing'' (''The Mathematical Classic of Xiahou Yang'') #'' Wujing Suanshu'' (''Computational Prescriptions of the Five Classics'') #''Jigu Suanjing'' (''Continuation of Ancient Mathematical Classic'') #'' Zhui Shu'' (''Method of Interpolation'') It was specified in Tang dynasty laws on examina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imperial Examinations
The imperial examination (; lit. "subject recommendation") refers to a civil-service examination system in Imperial China, administered for the purpose of selecting candidates for the state bureaucracy. The concept of choosing bureaucrats by merit rather than by birth started early in Chinese history, but using written examinations as a tool of selection started in earnest during the Sui dynasty (581–618) then into the Tang dynasty of 618–907. The system became dominant during the Song dynasty (960–1279) and lasted for almost a millennium until its abolition in the late Qing dynasty reforms in 1905. Aspects of the imperial examination still exist for entry into the civil service of contemporary China, in both the People's Republic of China (PRC) and the Republic of China (ROC). The exams served to ensure a common knowledge of writing, Chinese classics, and literary style among state officials. This common culture helped to unify the empire, and the ideal of achievement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Nine Chapters On The Mathematical Art
''The Nine Chapters on the Mathematical Art'' () is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE. This book is one of the earliest surviving mathematical texts from China, the first being '' Suan shu shu'' (202 BCE – 186 BCE) and ''Zhoubi Suanjing'' (compiled throughout the Han until the late 2nd century CE). It lays out an approach to mathematics that centres on finding the most general methods of solving problems, which may be contrasted with the approach common to ancient Greek mathematicians, who tended to deduce propositions from an initial set of axioms. Entries in the book usually take the form of a statement of a problem, followed by the statement of the solution and an explanation of the procedure that led to the solution. These were commented on by Liu Hui in the 3rd century. History Original book The full title of ''The Nine Chapters on the Mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sunzi Suanjing
''Sunzi Suanjing'' () was a mathematical treatise written during 3rd to 5th centuries AD which was listed as one of the Ten Computational Canons during the Tang dynasty. The specific identity of its author Sunzi (lit. "Master Sun") is still unknown but he lived much later than his namesake Sun Tzu, author of ''The Art of War''. From the textual evidence in the book, some scholars concluded that the work was completed during the Southern and Northern Dynasties. Besides describing arithmetic methods and investigating Diophantine equations, the treatise touches upon astronomy and attempts to develop a calendar. Contents The book is divided into three chapters. Chapter 1 Chapter 1 discusses measurement units of length, weight and capacity, and the rules of counting rods. Although counting rods were in use in the Spring and Autumn period and there were many ancient books on mathematics such as ''Book on Numbers and Computation'' and ''The Nine Chapters on the Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of Three (mathematics)
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as the "cross your heart" method because lines resembling a heart outline can be drawn to remember which things to multiply together. Given an equation like : \frac a b = \frac c d, where and are not zero, one can cross-multiply to get : ad = bc \quad \text \quad a = \fracd. In Euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles. Procedure In practice, the method of cross-multiplying means that we multiply the numerator of each (or one) side by the denominator of the other side, effectively crossing the terms over: : \frac a b \nwarrow \frac c d, \quad \frac a b \nearrow \frac c d. The mathematical justification for the method is from the following ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hundred Fowls Problem
The Hundred Fowls Problem is a problem first discussed in the fifth century CE Chinese mathematics text '' Zhang Qiujian suanjing'' (The Mathematical Classic of Zhang Qiujian), a book of mathematical problems written by Zhang Qiujian. It is one of the best known examples of indeterminate problems in the early history of mathematics. The problem appears as the final problem in ''Zhang Qiujian suanjing'' (Problem 38 in Chapter 3). However, the problem and its variants have appeared in the medieval mathematical literature of India, Europe and the Arab world. The name "Hundred Fowls Problem" is due to the Belgian historian Louis van Hee. Problem statement The Hundred Fowls Problem as presented in ''Zhang Qiujian suanjing'' can be translated as follows: : "Now one cock is worth 5 qian, one hen 3 qian and 3 chicks 1 qian. It is required to buy 100 fowls with 100 qian. In each case, find the number of cocks, hens and chicks bought." Mathematical formulation Let ''x'' be the number o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Manuscripts
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
