Different Cultures of Computation in Seventh Century China from the Viewpoint of Square Root Extraction

International audienceThe aim of this paper is to bring to light a previously unknown geometrical method for extracting the square root in seventh century China. In order to achieve this goal, a seventh century commentary by the scholar Jia Gongyan, 賈公彥, on a Confucian canon, the Rites of Zhou Dynasty [Zhouli 周禮], is analysed. This is compared with the commentary by his contemporary Li Chunfeng,李淳風, which is referred to in another mathematical book , the Mathematical Procedures of the Five Canons , [ Wujing Suanshu 五經筭術 ]. Although these two scholars probably knew each other , they used very different methods to solve the same problem in relation to square root extraction. It is argued that the differences mainly lie in two aspects : firstly , Jia Gongyan mostly made use of geometry while Li Chunfeng used counting rods ; secondly , the two methods had different geometrical interpretations. Given the fact that the method of square root extraction Jia Gongyan uses is one among many other methods he employed in mathematics , and it has the same features as the others ; moreover , other commentators on the Confucian Canons use similar mathematical methods , this paper closes with a general discussion on mathematical cultures. It is suggested that there were three elements to mathematical practice in seventh century China : geometry , counting rods , and written texts. The interplay and structure between the three elements is seen to influence mathematical practices