从“以率消息”看刘徽圆周率的产生过程  

Reviewing the Process of Liu Hui’s Deducing the Circular Constant Through "Modifying by Ratio"

作　　者：朱一文[1] 

机构地区：[1]上海交通大学科学史与科学哲学系,上海200240

出　　处：《自然科学史研究》2008年第1期59-70,共12页Studies in The History of Natural Sciences

摘　　要：《九章算术》圆田术刘徽注中记载了刘徽割圆术中求圆周率的方法。其中刘徽用"以率消息"的方法求得圆周率π=3927/1250的过程,争议颇多。三上义夫、沈康身、李继闵、郭书春等各家的说法不一。文章重新从《九章算术》原文考察并复原了刘徽求得圆周率π=3927/1250的过程,分析了各家说法不一的原因,讨论了"以率消息"的数学原理;认为π=3927/1250的产生过程,是数学原理加上非理性因素双重作用的结果,给了"以率消息"这个问题一个新的解释。Liu Hui’s method for deducing the circular constant is recorded in his comments to Nine Chapters on the Mathematical Art. However, there exits a dispute about how Liuhui got the circular constant π=3927/1250 through "modifying by ratio". Mikami Yoshio, Shen Kangshen, Li Jimin and Guo Shuchun all have their own explanations. This article reviews Liu Hui’s comments and recovers the process of Liu Hui’s deducing the circular constant π=3927/1250, and analyzes the cause of the difference among the scholars. The...

关 键 词：《九章算术》 圆周率 刘徽 以率消息 

分 类 号：O112[理学—数学]