1引言我国现行数学教科书(如人教版和北师大版)中,“圆的度量”这部分内容安排在6-9年级.这期间学生并未接触过极限概念,因此,对于圆的周长和面积公式,教科书并没有用严密的几何方法加以推导.关于圆周率,教科书也只是以阅读材料的形式介绍了与之相关的历史.到高中阶段,在学习极限概念时,学生仍没有机会了解圆的面积是如何严格推导出来的.在大学阶段,该主题又被视为学生在中学已经熟知的内容.因此,尽 1 Introduction In China’s current mathematics textbooks (such as the PEP and BNU), the “measure of the circle” is arranged in grades 6 to 9. During this period the students did not come into contact with the limit concept, therefore, Textbooks are not deduced by rigorously geometrical methods, and textbooks refer only to the history associated with them in the form of reading materials. By the time of their high school, students still did not learn the concept of limits The opportunity to understand how the area of ​​a circle is strictly derived is also seen in college as a subject already known to students in secondary school.