李俨与中国古代圆周率

Li Yan and the π in the History of Ancient Chinese Mathematics

以李俨、严敦杰的学术通信和已发表的论著相对照 ,讨论李俨对四个有争议问题在不同时期的看法和取舍态度。这四个问题是 :(1 )刘歆的圆周率 ;(2 )《九章·圆田术注》中“晋武库”一段及圆周率3 92 71 2 50 的作者是谁 ;(3 )如何阐释《隋书·律历志》中关于量器的记载 ;(4 )祖冲之是如何得到圆周率3 551 1 3 的。李俨对这些问题的讨论 ,能反映他作为一代科学史宗师的研究思路、学术风格和嘉勉后学的长者风范。他关于史料和算理相结合的研究方法 ,对科学史研究中论点的“假定”性质的看法 ,对今天的数学史乃至科学史研究仍有意义。

The π (ratio of the circumference of a circle to its diameter) has been paid much attention to in the study on the history of Chinese mathematics, and several problems have been in dispute until recently. This paper reveals several Li Yan's letters concerning π to Yan Dunjie. Comparing the arguments of these letters with his published works, it discusses Li Yan's viewpoints and choices on four outstanding questions in different times. The four questions are: (1) Liu Xin' π; (2) Who is the author of the paragraph about the ‘Jin Wuku’ (Jin's Storeroom of Weaponry) from the annotations on the yuantianshu (method of circular field) of the Nine Chapters on Mathematical Procedures and the π 3927/1250; (3) how to explain the record about the capacity measures in the Lǜlizhi (records of the music temperaments and calendars) of the Suishu (History of the Sui Dynasty); (4) How did Zu Chongzhi gain his π 355/113. Through the discussions, the paper reflects Li Yan's train of thought in research, academic style, and venerable demeanour. The author points out: Li Yan's way of research that historical materials are to be combined with mechanism of computing processes, and his viewpoint that an inference of the study on history of science is essentially a hypothesis, are significant to today's study on the history of mathematics, or even to the study on the history of science.