数学史与数学教育(HPM)的一个案例——刘徽的“割圆术”与微积分

刘徽的“割圆术”是中国数学史上的重要成就之一,其中包含着中国数学家对无限问题的独特认识和致用的处理方式.很多高等数学教科书在讲述极限概念时大都提及,但所述,并未体现刘徽本意.刘徽的“割圆术”是为证明圆面积公式而设计出来的一种方法,其融合了庄、墨两家理解和处理无限问题的方法,并且使用了数列极限的“夹逼准则”和不可分量可积的预设.通过这些相关知识的历史考察,试图以HPM的方法来辅助解决极限概念教学的难题.

Some Remarks on LIU Hui's Cyclotomic Method

LIU Hui's Cyclotomic Method is one of the greatest achievements of the history of mathematics in China,even in the world,in which the special approach to understand the infinity and the method to solve it are presented.Moreover it is not mentioned in the textbook of advance mathematics that LIU Hui maybe used Squeeze Theorem and the precondition of inseparable quantity integrable.It is maybe helpful to understand the concept of limit easily by historical survey of the LIU Hui's Cyclotomic Method.