ESHS/HSS Annual Meeting

Yang Hui’s (fl. 13th century) Methods of Computation with Place-Value Notations and Their Variations in Later Mathematical Works

• In Event: Diagrammatic Computations and Their Symbolic Aspects (III)

English Abstract

Mathematical Methods of Yang Hui (1274, 1275) is a comprehensive collection of mathematical
treatises of the thirteenth century with an orientation of popularization of mathematics. This
presentation focuses on the sections related to notations and arithmetic computation in this work. A large number of arithmetic operations and shortcut procedures are recorded in detail through counting-rod notation, in which the spatial arrangement of the symbols and the connecting lines between them capture the dynamic process of computation. Many of the pithy formulas and specially designed algorithms are shaped by the ephemeral process of physically arranging counting rods on a plane. Some of these computational methods were later inherited and further developed by Wu Jing’s Great Compendium of The Nine Chapters on Mathematical Methods with Analogies of the 15th century. Under the category of “written calculation” (xiesuan), we begin to see cases in which numbers written directly in Chinese characters participate in the computational process. On the one hand, some of these cases differ significantly from earlier texts in which numbers represented by counting-rod symbols directly entered into arithmetic operations. On the other hand, certain “written calculation” methods still exhibit prominent features of the place-value system, thereby continuing the computational principles found in Yang Hui’s algorithms. This presentation attempts to analyze the role played by place-value notations, as well as the references to them within pithy formulas, in recording and expressing arithmetic procedures.

Author

• Célestin Xiaohan ZHOU, The Institute for the History of Natural Sciences, Chinese Academy of Sciences