Determining the position(ding wei)is a method of dealing with the order of magnitude and unit of the product or quotient of the actual problem.The earliest record can be seen is Yang Hui's"SuanFaTongBianBenMo"of the Southern Song Dynasty.By the Ming Dynasty,the counting rods was gradually replaced by abacus,and the method of determining the position was developed in the books of Wu Jing,Wang Wensu,and Cheng Dawei,which was summarized as a complete abacus positioning system.With the introduction of European manual calculation,Chinese mathematicians combined it with traditional positioning methods to develop manual calculation positioning methods with the characteristics of Chinese and Western integration.By combing the history of the development and change of the method of determining the position,it is pointed out from the perspective of arithmetic that different calcu-lation orders and modes lead to different expressions of the positioning method,reflecting the different cognitions of the multiplication and division opera-tion and the number itself in different periods.At the same time,the evolution of the multiplication and division algorithm under different arithmetic tool systems is glimpsed by the change of the positioning method,especially the transformation process from counting rods to abacus,which shows that this is not a simple change of calculation tools,but also accompanied by the internal transformation of arithmetic and rules.
关键词
定位法/杨辉/王文素/珠算/位值制
Key words
Ding-Wei/Yang Hui/Wang Wensu/abacus/place value system
维普
万方数据