A Study Of The Mathematical Text,Shu数Numbers And Reckoning,on The Bamboo Strips Owned By The Yuelu Academy Of Hunan University

This dissertation is a study of the Mathematical text, Shu数Numbers and Reckoning (hereafter SHU), on the Bamboo Strips owned by the Yuelu Academy of Hunan University. The bamboo strips were newly discovered primary documents. Their dating should be no later than the thirty-fifth year of the First Emperor of Qin dynasty (212BCE). Through sorting the strips, transliterating the original Chinese characters, editing and interpreting the texts, this dissertation has provided a thorough study of the SHU. It reveals for the very first time a great deal new information about the nature of Chinese mathematics in the third century BCE and beyond. It also provides new materials for studying the economy, legal codes, and military affairs in the Qin Dynasty.The main contents of this dissertation are as follows:1. Descriptions of the Bamboo StripsThis dissertation has detailed descriptions of the physical properties of the bamboo strips such as lengths, positions of rope binding, numbers of columns and of Chinese characters on a strip, and top and bottom empty spaces. It also describes how the broken strips were pieced together (18cases), and how to connect the strips to make the contents of their texts coherent, to restore the missing characters or insert the corrected ones (81more or less completed problems with questions, methods, and answers;19cases of having the methods alone;3strips containing measurement of weights and measures; and34strips recording the exchange rates among different grains). 2. Transliteration of the Original ScriptsIt has provided transliterations of the original scripts on234strips.(Note:some strips are broken pieces, part of which can be put together as the complete ones. While clearing and sorting out the strips, each one is given a unique number regardless it is complete or broken).3. CommentariesThe commentaries include explanations of the meanings of certain Chinese characters, verifications of the calculations and answers of the original texts, and analysis of the mathematical principles or formula had been used.4. Comparison and Analysis(1) A Comparison of the SHU with算数书A Book on Numbers and Computations, and九章算术General Mathematical Methods for Nine CategoriesA comparison about the contents, algorithms, and terminologies in the SHU with corresponding ones in the Suan Shu Shu算数书A Book on Numbers and Computations (hereafter SSS), and Jiuzhang Suanshu九章算术General Mathematical Methods for Nine Categories (hereafter JZSS) had been carried out. Some problems in the SHU are unique, and some others can be found also in the SSS and/or JZSS. The types of questions in the SHU cover eight categories of the JZSS except Fangcheng方程(Rectangular Arrays)(Note:Two problems in the SHU are similar to the ones in Junshu (Fair Distributions), but the method used is not the same algorithm in the JZSS). Unlike the SSS which has69specific names or titles for the problems, the SHU virtually does not have any of them. Similar problems appear often in group in the SHU, but problems in the SSS are isolated or independent.(2) The Mathematical Contents of the SHUThe SHU provides new sources for studying ancient Chinese mathematics. For instance, one problem on a buried log in the SHU indicates that the contents of the Gougu category勾股of the JZSS have their origins in the mathematical texts of pre-Qin dynasty. The problem gives us new materials to investigate applications of the so-called Pythagorean Theorem in the pre-Qin times. The problems related to the excess and deficiency algorithm yinbuzu盈不足,especially the one I pieced together which has3unknowns, provide excellent sources for investigating the development of the algorithm. The problems related to the Cuifen category衰分suggest the sophisticated algorithms for dealing with proportions.The correct calculations for the areas of a rectangular, trapezoid, and a circular field, as well as that for the volumes of truncated cone and pyramid indicate the high level of Chinese geometry during the Qin-dynasty. Moreover, one problem in the SHU also suggests that the concept of mass density had been developed.(3) New Materials on Economy, Legal Codes, and Military Affairs in the Qin Dynasty.Some problems on yutian舆田(one kind of rental farmland) and zhuwuquan租误券(correcting tax mistakes) in the SHU provide new insides for understanding the taxation on the farmland. We now have better knowledge of the difference between yutian舆田(one kind of taxable farmland) and shuitian税田(taxable farmland); and that of the different tax rates for xitian枲田hemp-grown farmland)and hetian禾田(grain-grown farmland).The problems on chongsu春粟(husked millet) and on haocheng耗程(norm for wastage) provide information on grain gathering, processing, and other production activities. They also reveal the regulations on fresh and dried goods, and verify the measurement unit of shi/dan石.The exchange rate between volume and weight of certain grain and that among different grains are recorded. These rates indicate the relationship among exchange of farm products, distribution, and storing goods.The problem on the art of setting a military camp reveals some details of military affairs of Qin dynasty. The major points presented in this dissertation are:1. There are several mathematical books had already existed in the Qin dynasty. The SHU probably is a copy from one or more of them.2. While some problems in the SHU are almost identical and others are merely similar to those in the SSS or the JZSS, the three texts are not necessary correlated. More specifically, it is not the case that one is the direct source for another. The three texts, however, may share some common origins.3. The SHU preserves application problems of some ancient Chinese algorithms.4. The SHU as a whole demonstrates characteristics of practical mathematical algorithms. The description styles of some problems suggest that mathematics in the Qin dynasty had been undergoing abstraction and theorization.5. The SHU provides some materials on the economy, legal codes and military affairs of the Qin society. These materials may be records of reality, and are valuable references to be consulted with other unearthed documents of the same period.