Empty And The Full, The: Li Ye And The Way Of Mathematics - Geometrical Procedures By Section Of AreasWorld Scientific, 20 de març 2020 - 276 pàgines During Song (960 to 1279) and Yuan (1279 to 1368) dynasties, China experienced a peak in high-level algebraic investigation through the works of famous mathematicians such as Qin Jiushao, Zhu Shijie, Yang Hui and Li Ye. Among these is Li Ye's short treatise on a curious ancient geometrical procedure: The Development of Pieces of Areas According to the Collection Augmenting the Ancient Knowledge (Yigu yanduan). The aim of this monography is to contradict traditional scholarship which has long discredited the importance of Li Ye's treatise, considering it a mere popular handbook. The author aims to show that Li Ye's work actually epitomizes a completely new aspect of ancient Chinese mathematics: a crossroad between algebra, geometry, and combinatorics containing elements reminiscent of the Book of Changes (Yi Jing). As well as Li Ye used field measurement as pretext for investigations on quadratic equations and Changes, the present study uses Li Ye's small treatise as pretext for philosophical investigations on link between mathematics and their history. The real topic of the study is the exploration of another expression of proof and generality in Chinese mathematics. This book not only completes the edition of Li Ye's works and presents new features of Chinese mathematics, but also fills a gap in the translation of Chinese mathematics treatises.It is the first book entirely dedicated to the diagrammatic practice of algebra in the history of Chinese mathematics. This practice is more important than expected. While being a monograph, the book is short and detailed enough to be used by students in class. It can also be used as an entry door to the research field of history of Chinese mathematics. |
Continguts
General Presentation | 1 |
Text Diagram and Equation | 27 |
Operations on Pieces of Areas | 85 |
Order Analogy and Reduction | 139 |
CONCLUSION | 209 |
Appendix A Supplements | 213 |
Appendix B Chinese Glossary | 235 |
Appendix C Chinese Names | 239 |
241 | |
251 | |
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Empty and the Full, The: Li Ye and the Way of Mathematics - Geometrical ... Charlotte-V Pollet Previsualització no disponible - 2020 |
Frases i termes més freqüents
adjunct algebraic algorithm Ancient knowledge Augmenting the Ancient Celestial Source procedure Chemla and Guo Chinese Chinese mathematics Circle Measurement circular field circular pond circumference Collection Augmenting commentary constant divisor counting rods counting surface Development of Pieces diagonal diagrams diameter discourse dividend empty fang four Gnomon Hui’s Methods inner pond intentionally left blank Lam Lay-Yong Li Ye Liu Hui Methods of Computation middle square Mirror of Circle multiply mutual sum Nine Chapters Old Procedure operations perimeter Pieces of Areas polynomials practitioner Problem 18 Problem 46 Qin Jiushao quadratic equations real area rectangles removed root extraction Sea Mirror Section of Pieces self-multiplying shang Song Dynasty square field square of side square pond square root statement Step subtract three squares tian yuan top position transformations translation treatise unknown visualisation Volkov width xiafa Ye’s yields Yuan Dynasties yuan shu Zhou Zhu Shijie