Chinese Mathematics In The 13th Century
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| 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.
| Author | : Yan Li |
| Publisher | : |
| Total Pages | : 312 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : |
This volume presents a record of mathematical developments in China over a period of more than 2000 years. It goes into greater detail than ever previously available in English. Because the emphasis in Chinese mathematics is on algorithms rather than proofs, readers will find results such as Bezout's theorem and Horner's method appearing in a very different context from the familiar tradition of Euclidean deductive geometry. The Chinese always preferred algebraic methods, and by the 13th century A.D. they were the best algebraists in the world. The original Chinese point of view is retained by the translators. They have supplemented the text with short explanatory comments and references to all relevant reference sources available in the West. An extensive bibliography is included, creating a work which will appeal to general readers interested in Chinese history as well as historians of 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.
| Author | : Yoshio Mikami |
| Publisher | : |
| Total Pages | : 366 |
| Release | : 1913 |
| Genre | : Mathematics, Chinese |
| ISBN | : |
| 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.
| Author | : Christopher Cullen |
| Publisher | : |
| Total Pages | : 158 |
| Release | : 2004 |
| Genre | : Mathematics, Chinese |
| ISBN | : |
| Author | : Victor J. Katz |
| Publisher | : Princeton University Press |
| Total Pages | : 712 |
| Release | : 2007-08-05 |
| Genre | : Mathematics |
| ISBN | : 9780691114859 |
In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.
| Author | : Ho Peng Yoke |
| Publisher | : Routledge |
| Total Pages | : 261 |
| Release | : 2004-03-01 |
| Genre | : History |
| ISBN | : 1134430671 |
Though there are a number of well-written works on Chinese divination, there are none that deal with the three sophisticated devices that were employed by the Chinese Astronomical Bureau in the eleventh century and for hundreds of years thereafter. Chinese experts applied the methods associated with these devices to both weather forecasting and to the interpretation of human affairs. Hidden by a veil of secrecy, these methods have always been relatively little known other than by their names. The first work in any language to explore these three methods, known as sanshi (three cosmic boards), this book sheds light on a topic which has been shrouded in mystery for centuries, having been kept secret for many years by the Chinese Astronomical Bureau.
| Author | : Victor J. Katz |
| Publisher | : Princeton University Press |
| Total Pages | : 592 |
| Release | : 2016-11-01 |
| Genre | : Mathematics |
| ISBN | : 0691156859 |
Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.
| Author | : Catherine Jami |
| Publisher | : Oxford University Press |
| Total Pages | : 453 |
| Release | : 2012 |
| Genre | : History |
| ISBN | : 0199601402 |
Jami explores how the emperor Kangxi solidified the Qing dynasty in 17th-century China through the appropriation of the 'Western learning', and especially the mathematics, of Jesuit missionaries. This text details not only the history of mathematical ideas, but also their political and cultural impact.
