ESHS/HSS Annual Meeting

Reasoning, Procedures, and Computational Devices: Explanations to the Arithmetic Rules of Positive and Negative Numbers

• In Event: Mathematics and Practical Knowledge

English Abstract

The basic notion of positive and negative numbers appeared early in Chinese Mathematics, e.g., the Nine Chapters on the Art of Mathematics (九章算術 Jiu zhang suan shu). They formally appeared in the genre of 方程 fang cheng problems, which are similar to systems of linear equations in modern mathematics. While combining gain and loss in a trade can be easily done, the arithmetic rules governing the addition and subtraction of positive and negative numbers are much more complex, let alone simultaneously executing multiple arithmetic operations of mixed positive and negative numbers in solving fang cheng problems. Most historians in the 20th century attempted to explain the arithmetic rules governing these numbers in terms of modern notion of absolution values. Although their efforts lead to the same final answers, their approach do not match the explanations by Liu Hui (fl. In the 3rd century C.E.), one of the few scholars whose commentary to the Nine Chapters is still extant. By examining the manipulation of counting rods on a counting surface, the computation device of the day, we make sense of Liu Hui’s explanation and the procedures of solving fang cheng problems put forth by the Nine Chapters. We also compare Liu Hui’s with Mei Wending’s (1633-1721) explanations and somewhat different procedures, highlighting the influence by the computation devices.

Author

• Jiang-Ping Jeff CHEN, Saint Cloud State University, Minnesota