The Yang Hui Suan Fa A Thirteenth Century Chinese Mathematical Treatise
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The Nine Chapters on the Mathematical Art
| Author | : Kangshen Shen |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 636 |
| Release | : 1999 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780198539360 |
The Nine Chapters on the Mathematical Art has been the most important mathematical source in China for the past 2000 years, comparable in significance to Euclid's Elements in the West. The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science was introduced in about 1600. This volume contains the first complete English translation of the Nine Chapters, together with the illuminating commentary of Liu Hui written in the 3rd century AD and other early century commentaries and further insights provided by the translators. The Nine Chapters contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. There are methods for solving problems in areas such as land measurement, construction, agriculture, commerce, and taxation, while the Chinese commentators provide the algorithms needed to solve the problems, and explanations of how the algorithms work. The translators' commentary provides clear and accessible background material for the Western reader, explanations of technicalities, and notes on the treatment of similar or identical mathematical problems in other countries. This first, full-English translation gives us an idea of the distinctive style and important contributions that have been made by traditional Chinese mathematics.
Chinese Mathematics in the Thirteenth Century
| Author | : Ulrich Libbrecht |
| Publisher | : Courier Dover Publications |
| Total Pages | : 624 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : |
An exploration of the 13th-century mathematician Ch'in, this fascinating book combines what is known of Ch'in's life with a history of his only extant work, the Shu-shu chiu-chang. Ch'in's most original contribution to mathematics is the Chinese remainder theorem for the solution of indeterminate equations of the first degree. 1973 edition. Includes 71 figures and 85 diagrams.
Chinese Mathematics in the Thirteenth Century
| Author | : Ulrich Libbrecht |
| Publisher | : Courier Corporation |
| Total Pages | : 594 |
| Release | : 2005-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486446190 |
An exploration of the life and work of the thirteenth-century mathematician Ch'in, this fascinating book examines a range of mathematical issues that reflect Chinese life of a millennium ago. Its first part consists of four closely related studies of Ch'in and his work. The first study brings together what is known of the mathematician's life and of the history of his only extant work, the Shu-shu chiu-chang. Subsequent studies examine the entire range of mathematical techniques and problems found within Ch'in's book. The core of this book consists of an in-depth study of what modern mathematicians still refer to as the Chinese remainder theorem for the solution of indeterminate equations of the first degree. This was Ch'in's most original contribution to mathematics--so original that no one could correctly explain Ch'in's procedure until the early nineteenth century. This volume's concluding study unites information on artisanal, economic, administrative, and military affairs dispersed throughout Ch'in's writings, providing rare insights into thirteenth-century China.
A History of Chinese Mathematics
| Author | : Jean-Claude Martzloff |
| Publisher | : Springer |
| Total Pages | : 491 |
| Release | : 2007-08-17 |
| Genre | : Mathematics |
| ISBN | : 3540337830 |
This book is made up of two parts, the first devoted to general, historical and cultural background, and the second to the development of each subdiscipline that together comprise Chinese mathematics. The book is uniquely accessible, both as a topical reference work, and also as an overview that can be read and reread at many levels of sophistication by both sinologists and mathematicians alike.
Fleeting Footsteps: Tracing The Conception Of Arithmetic And Algebra In Ancient China (Revised Edition)
| Author | : Tian Se Ang |
| Publisher | : World Scientific |
| Total Pages | : 266 |
| Release | : 2004-04-06 |
| Genre | : Mathematics |
| ISBN | : 9814483605 |
The Hindu-Arabic numeral system (1, 2, 3,…) is one of mankind's greatest achievements and one of its most commonly used inventions. How did it originate? Those who have written about the numeral system have hypothesized that it originated in India; however, there is little evidence to support this claim.This book provides considerable evidence to show that the Hindu-Arabic numeral system, despite its commonly accepted name, has its origins in the Chinese rod numeral system. This system was widely used in China from antiquity till the 16th century. It was used by officials, astronomers, traders and others to perform addition, subtraction, multiplication, division and other arithmetic operations, and also used by mathematicians to develop arithmetic and algebra. Based on this system, numerous mathematical treatises were written.Sun Zi suanjing (The Mathematical Classic of Sun Zi), written around 400 AD, is the earliest existing work to have a description of the rod numerals and their operations. With this treatise as a central reference, the first part of the book discusses the development of arithmetic and the beginnings of algebra in ancient China and, on the basis of this knowledge, advances the thesis that the Hindu-Arabic numeral system has its origins in the rod numeral system. Part Two gives a complete translation of Sun Zi suanjing.In this revised edition, Lam Lay Yong has included an edited text of her plenary lecture entitled “Ancient Chinese Mathematics and Its Influence on World Mathematics”, which was delivered at the International Congress of Mathematicians, Beijing 2002, after she received the prestigious Kenneth O. May Medal conferred by the International Commission on the History of Mathematics. This should serve as a useful and easy-to-comprehend introduction to the book.
The Chinese Roots of Linear Algebra
| Author | : Roger Hart |
| Publisher | : JHU Press |
| Total Pages | : 304 |
| Release | : 2011-01-01 |
| Genre | : Mathematics |
| ISBN | : 0801899583 |
A monumental accomplishment in the history of non-Western mathematics, The Chinese Roots of Linear Algebra explains the fundamentally visual way Chinese mathematicians understood and solved mathematical problems. It argues convincingly that what the West "discovered" in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years. Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts—the classic ancient Chinese mathematics text—and the arcane art of fangcheng, one of the most significant branches of mathematics in Imperial China. Practiced between the first and seventeenth centuries by anonymous and most likely illiterate adepts, fangcheng involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra, and its practice, Hart reveals, was visual and algorithmic. Fangcheng practitioners viewed problems in two dimensions as an array of numbers across counting boards. By "cross multiplying" these, they derived solutions of systems of linear equations that are not found in ancient Greek or early European mathematics. Doing so within a column equates to Gaussian elimination, while the same operation among individual entries produces determinantal-style solutions. Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.
