Abstract

Chinese mathematics has a long history. One of the important achievements of Chinese mathematics is the procedure for square root extraction carried out with counting rods. However, previous studies have paid less attention to the Confucian method tradition. Confucian scholars in the Han dynasty disputed on “To rule a county of a thousand chariots” of the Analects, in which a mathematical problem was hidden and the procedure was not written down. Huang Kang of the Liang dynasty commented on this excerpt, and used diagrams to extract square root, which was different from the procedure carried out with counting rods, and was the origin of Confucian method for square root extraction. After that, Kong Yingda and Jia Gongyan of the Tang dynasty, Xing Bing and Zhu Xi of the Song dynasty, Xu Qian of the Yuan dynasty, Liu Baonan of the Qing dynasty continued discussing Confucian methods in their study of Confucianism. On the other side, in the Mathematical Procedures of the Five Canons, Zhen Luan of the West Zhou dynasty used the square root extraction procedure carried out with counting rods to comment on the same excerpt of the Analects. Li Chunfeng of Tang dynasty commented on the Mathematical Procedures of the Five Canons. Zhen and Li tried to unify the mathematical procedures, but they failed. Dai Zhen of Qing dynasty edited ancient mathematical books, and highly evaluated the Mathematical Procedures of the Five Canons. After the later Qing period, the specialty and independence of mathematics was highly confirmed. So the mathematicians' explanations were gradually accepted, and the Confucians' methods were gradually forgotten.

Key Words

Analects; To rule a county of a thousand chariots; Procedure for square root extraction; Mathematical Procedures of the Five Canons; Confucianism

Citation: Zhu, Y. 'The Historical Evolution of Confucian Procedure for Square Root Extraction: The Case of Scholars' Commentaries on "To Rule a County of a Thousand Chariots" of the Analects' [J]. Journal of Dialectics of Nature, 2019, 41(2): 49-55.

Download: The Historical Evolution of Confucian Procedure for Square Root Extraction: The Case of Scholars' Commentaries on "To Rule a County of a Thousand Chariots" of the Analects