Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of dou...Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.展开更多
The transcription of the Suanshu Shu算數書(a bamboo book of mathematics)in simplified Chinese characters offers a new opportunity to explore the history of Chinese mathematics in ancient times.This paper analyzes the ...The transcription of the Suanshu Shu算數書(a bamboo book of mathematics)in simplified Chinese characters offers a new opportunity to explore the history of Chinese mathematics in ancient times.This paper analyzes the style and structure of the Suanshu Shu and makes comparisons with the Nine Chapters on Mathematical Procedures and a number of other texts in various social contexts.It will be shown that the Suanshu Shu was compiled from at least two sources,and that no direct textual interplay exists between the Suanshu Shu and the Nine Chapters,although both share the same origins in the Pre-Qin period when the major mathematical methods in the Nine Chapters came into being.It will also be shown that the Suanshu Shu was accomplished with the methods used in certain mathematical books in the Pre-Qin period or their results,which later led to the Nine Chapters,and by accommodating the actual conditions of the lower government administration.The Suanshu Shu is significant for establishing the evolution of algorithmic mathematics from the Warring States period to the Han dynasty.展开更多
This paper gives a review of Nine Chapters on the Mathematical Art,Companion and Commentary by Shen Kangshen in collaboration with J.N.Crossley and Anthony W.-C. Lun.In the beginning the paper overviews briefly the Ru...This paper gives a review of Nine Chapters on the Mathematical Art,Companion and Commentary by Shen Kangshen in collaboration with J.N.Crossley and Anthony W.-C. Lun.In the beginning the paper overviews briefly the Russian,Japanese,English,German and French translations of Jiuzhang Suanshu during the past 50 years.Then it introduces the whole process in the preparation of the book.The paper focuses on the content and quality of the translation,and gives some examples to show how the authors carefully select words and special terms appropriately corresponding to (Chinese and the equivalent English. There are also in it some passages to )indicate that the translation work is indeed trustworthy,faithful and elegant.Finally,the paper sums up the merits of the Book in gathering togethering all that is good in Jiuzhang Suanshu itself,Liu Hui′s & Li Chunfeng ′s Commentaries and the Sea Island Manual, as well as in providing a lot of supplementary materials and new notes.展开更多
文摘Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.
基金Prof.Guo Shuchun and Prof.Chen Meidong陈美东assisted with the completion of the Chinese version of this paper.In addition,Prof.Joseph W.Dauben has guided its revision in English.John Moffett copyedited the English translation.The author would like to express his heartfelt appreciation to all of them.
文摘The transcription of the Suanshu Shu算數書(a bamboo book of mathematics)in simplified Chinese characters offers a new opportunity to explore the history of Chinese mathematics in ancient times.This paper analyzes the style and structure of the Suanshu Shu and makes comparisons with the Nine Chapters on Mathematical Procedures and a number of other texts in various social contexts.It will be shown that the Suanshu Shu was compiled from at least two sources,and that no direct textual interplay exists between the Suanshu Shu and the Nine Chapters,although both share the same origins in the Pre-Qin period when the major mathematical methods in the Nine Chapters came into being.It will also be shown that the Suanshu Shu was accomplished with the methods used in certain mathematical books in the Pre-Qin period or their results,which later led to the Nine Chapters,and by accommodating the actual conditions of the lower government administration.The Suanshu Shu is significant for establishing the evolution of algorithmic mathematics from the Warring States period to the Han dynasty.
文摘This paper gives a review of Nine Chapters on the Mathematical Art,Companion and Commentary by Shen Kangshen in collaboration with J.N.Crossley and Anthony W.-C. Lun.In the beginning the paper overviews briefly the Russian,Japanese,English,German and French translations of Jiuzhang Suanshu during the past 50 years.Then it introduces the whole process in the preparation of the book.The paper focuses on the content and quality of the translation,and gives some examples to show how the authors carefully select words and special terms appropriately corresponding to (Chinese and the equivalent English. There are also in it some passages to )indicate that the translation work is indeed trustworthy,faithful and elegant.Finally,the paper sums up the merits of the Book in gathering togethering all that is good in Jiuzhang Suanshu itself,Liu Hui′s & Li Chunfeng ′s Commentaries and the Sea Island Manual, as well as in providing a lot of supplementary materials and new notes.
