互补咖啡杯问题与Pappus定理——微积分课堂的趣味案例剖析

The Problem of Complementary Coffee Cups and Pappus’s Theorem—An Analysis of Interesting Cases in Calculus Classes

摘要: 在微积分的教学过程中，如何将抽象的数学概念与实际生活相结合，激发学生的学习兴趣和解决问题的能力，是教育工作者不断探索的课题。本文以“互补咖啡杯容积比较”这一有趣的问题为切入点，探讨其在微积分教学中的应用，旨在为微积分教学提供与生活相贴近的教学案例。

Abstract: In the teaching process of calculus, how to combine abstract mathematical concepts with real life, and stimulate students’ learning interest and problem-solving ability is a subject that educators continue to explore. This paper takes the interesting problem of “comparison of volumes of complementary coffee cups” as the starting point and discusses its application in calculus teaching, aiming to provide teaching cases close to life for calculus teaching.