Study on the Logical Ideas in Chinese Ancient Mathematics from “Liu Hui’s Commentary of the Chiu Chang Suan Shu” (Research of the Relations between Calculation and Proof, Arithmetic and Logic)

Qi Zhou

doi:10.5539/ass.v5n8p9

Abstract

“Liu Hui’s Commentary of the Chiu Chang Suan Shu” is the best commentary for the most important basic book in Chinese ancient mathematics, the Chiu Chang Suan Shu, and it contains large numbers of logical reasoning and logical ideas. Abundant logical ideas and logical contents in Chinese ancient mathematics were contained in Liu Hui’s Commentary. Based on analyzing the items in Liu Hui’s Commentary and relative ancient literatures, abundant logic contents in the Commentary and the logical contents in ancient mathematics were demonstrated from three angles including concept, logical method and symbolic logic in the article. The relations between calculation and proof, arithmetic and logic in ancient mathematics were also expounded in the article, and the conclusions showed that there was proof logic or arithmetic logic existing in the ancient times of China.

Highlights

Abstract “Liu Hui’s Commentary of the Chiu Chang Suan Shu” is the best commentary for the most important basic book in Chinese ancient mathematics, the Chiu Chang Suan Shu, and it contains large numbers of logical reasoning and logical ideas
The existing “Liu Hui’s Commentary of the Chiu Chang Suan Shu” only includes words, but the mark of figure still can be seen in the commentary, and the using attention of the figure is to open out the logical references that the formula or operation rule came into existence, and to fully embody the logical idea of “using figure to explain”
A series of similar problems were listed in the Chiu Chang Suan Shu which pointed out the general solution of these problems

Summary

Introduction

Abstract “Liu Hui’s Commentary of the Chiu Chang Suan Shu” is the best commentary for the most important basic book in Chinese ancient mathematics, the Chiu Chang Suan Shu, and it contains large numbers of logical reasoning and logical ideas. (2) The reduction was the character of the logic in the arithmetic theory in Chinese ancient mathematics.

Results

Conclusion