Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earlie...Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications.展开更多
A simple method to fabricate one-dimensional(1-D) and two-dimensional(2-D) ordered micro- and nano-scale patterns is developed based on the original masters from optical discs, using nanoimprint technology and soft st...A simple method to fabricate one-dimensional(1-D) and two-dimensional(2-D) ordered micro- and nano-scale patterns is developed based on the original masters from optical discs, using nanoimprint technology and soft stamps. Polydimethylsiloxane(PDMS) was used to replicate the negative image of the 1-D grating pattern on the masters of CD-R, DVD-R and BD-R optical discs, respectively, and then the 1-D pattern on one of the PDMS stamps was transferred to a blank polycarbonate(PC) substrate by nanoimprint. The 2-D ordered patterns were fabricated by the second imprinting using another PDMS stamp. Different 2-D periodic patterns were obtained depending on the PDMS stamps and the angle between the two times of imprints. This method may provide a way for the fabrication of complex 2-D patterns using simple 1-D masters.展开更多
基金research projects“Elements of Continuity between Mathematical Writings from the Thirteenth to the Fifteenth Century in China(十三至十五世纪中国数学著作连续性Y950051)”“Transmission of the Knowledge of Science and Technology along the Silk Road(丝绸之路科技知识传播Y921011012,Director:Guo Yuanyuan郭园园)”of the Institute for the History of Natural Sciences,Chinese Academy of Sciences.The paper has been copyedited by John Moffett。
文摘Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications.
基金supported by the National Natural Science Foundation of China(Nos.11504259,21575098 and 21505098)the Shanxi International Cooperation Project(No.2015081019)+2 种基金the Shanxi Scholarship Council(No.2013-038)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(No.2015123)the Scientific Research Starting Foundation from Taiyuan University of Technology(No.tyut-rc201162a)
文摘A simple method to fabricate one-dimensional(1-D) and two-dimensional(2-D) ordered micro- and nano-scale patterns is developed based on the original masters from optical discs, using nanoimprint technology and soft stamps. Polydimethylsiloxane(PDMS) was used to replicate the negative image of the 1-D grating pattern on the masters of CD-R, DVD-R and BD-R optical discs, respectively, and then the 1-D pattern on one of the PDMS stamps was transferred to a blank polycarbonate(PC) substrate by nanoimprint. The 2-D ordered patterns were fabricated by the second imprinting using another PDMS stamp. Different 2-D periodic patterns were obtained depending on the PDMS stamps and the angle between the two times of imprints. This method may provide a way for the fabrication of complex 2-D patterns using simple 1-D masters.
