iCHSTM 2013 Programme • Version 5.3.6, 27 July 2013 • ONLINE (includes late changes)
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The meanings of 筭 Suan in the Jiuzhang Suanshu
Xu Yibao | Borough of Manhattan Community College, The City University of New York, United States

The Chinese character, 筭 Suan, appears 66 times in the text of the Jiuzhang suanshu 九章筭术 (Nine Chapters on the Art of Mathematics), as well as in the commentaries by Liu Hui and Li Chunfeng and his associates. The character has different meanings in different contexts. It may refer to one kind of algorithm, to a type of taxation, to arithmetic, or to mathematics in general. Also, it may be used to form special mathematical terms together with other characters, for example 借筭 jie suan and 筹筭 chou suan. In Chapter 8, Fang Cheng, it appears in connection with three specific numbers: 100, 77, and 124. In this context the correct interpretation of the meaning of suan is crucial for correctly understanding the specific procedures of the Fang Cheng (Rectangular Arrays) method as stated in the original text, and as it is used in a new method provided by Liu Hui in his commentary. This presentation will offer a new interpretation of the meanings of suan in the Nine Chapters, and in particular, in Chapter 8.