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

Adviser： Professor ZHU HanminThis dissertation is a study of the Mathematical text, Shu數Numbers andReckoning (hereafter SHU), on the Bamboo Strips owned by the Yuelu Academy ofHunan 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 Qindynasty (212BCE). Through sorting the strips, transliterating the original Chinesecharacters, editing and interpreting the texts, this dissertation has provided a thoroughstudy of the SHU. It reveals for the very first time a great deal new information aboutthe nature of Chinese mathematics in the third century BCE and beyond. It alsoprovides new materials for studying the economy, legal codes, and military affairs inthe 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 thebamboo strips such as lengths, positions of rope binding, numbers of columns and ofChinese characters on a strip, and top and bottom empty spaces. It also describes howthe broken strips were pieced together (19cases), and how to connect the strips tomake the contents of their texts coherent, to restore the missing characters or insertthe corrected ones (80more or less completed problems with questions, methods, andanswers;19cases of having the methods alone;3strips containing measurement ofweights and measures; and34strips recording the exchange rates among differentgrains). 2．Transliteration of the Original ScriptsIt has provided transliterations of the original scripts on236strips.(Note: somestrips 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 numberregardless it is complete or broken).3．CommentariesThe commentaries include explanations of the meanings of certain Chinesecharacters, verifications of the calculations and answers of the original texts, andanalysis of the mathematical principles or formula had been used.4．Comparison and Analysis⑴A Comparison of the SHU with算數書A Book on Numbers and Computations,and九章算術General Mathematical Methods for Nine CategoriesA comparison about the contents, algorithms, and terminologies in the SHU withcorresponding ones in the Suan Shu Shu算數書A Book on Numbers andComputations (hereafter SSS), and Jiuzhang Suanshu九章算術GeneralMathematical 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 SSSand/or JZSS. The types of questions in the SHU cover eight categories of the JZSSexcept Fangcheng方程(Rectangular Arrays)(Note: Two problems in the SHU aresimilar to the ones in Junshu (Fair Distributions), but the method used is not the samealgorithm in the JZSS). Unlike the SSS which has69specific names or titles for theproblems, the SHU virtually does not have any of them. Similar problems appear oftenin group in the SHU, but problems in the SSS are isolated or independent.⑵The Mathematical Contents of the SHUThe SHU provides new sources for studying ancient Chinese mathematics. Forinstance, one problem on a buried log in the SHU indicates that the contents of theGougu category勾股of the JZSS have their origins in the mathematical texts ofpre-Qin dynasty. The problem gives us new materials to investigate applications ofthe 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 sourcesfor investigating the development of the algorithm. The problems related to theCuifen category衰分suggest the sophisticated algorithms for dealing withproportions.The correct calculations for the areas of a rectangular, trapezoid, and a circularfield, as well as that for the volumes of truncated cone and pyramid indicate the highlevel of Chinese geometry during the Qin-dynasty. Moreover, one problem in the SHUalso suggests that the concept of mass density had been developed.⑶New Materials on Economy, Legal Codes, and Military Affairs in the Qin Dynasty.Some problems on yutian輿田(one kind of rental farmland) and zhuwuquan租誤券(correcting tax mistakes) in the SHU provide an new insight for understanding thetaxation on the farmland. We now have better knowledge of the difference betweenyutian輿田(one kind of taxable farmland) and shuitian稅田(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舂粟(husked millet) and on haocheng秏程(norm forwastage) provide information on grain gathering, processing, and other productionactivities. They also reveal the regulations on fresh and dried goods, and verify themeasurement unit of shi/dan石.The exchange rate between volume and weight of certain grain and that amongdifferent grains are recorded. These rates indicate the relationship among exchange offarm products, distribution, and storing goods.The problem on the art of setting a military camp reveals some details of militaryaffairs 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 merelysimilar 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 threetexts, 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 mathematicalalgorithms. The description styles of some problems suggest that mathematics in theQin dynasty had been undergoing abstraction and theorization.5．The SHU provides some materials on the economy, legal codes and militaryaffairs of the Qin society. These materials may be records of reality, and are valuablereferences to be consulted with other unearthed documents of the same period.