关于三角形等周问题的讲授思路研究

Research on Teaching Ideas about Triangular Isoperimetric Problems

摘要: 三角形等周问题是非常古老的问题，在维吉尔的史诗《埃涅阿斯纪》中就出现了等周问题的影子。三角形等周问题是中学中经常用到的知识点，在一些中考，高考中会涉及三角形等周问题的变式。三角形等周问题的本质就是最值问题，但是大多数学生只知道这个知识点的结论，没有掌握其思想，这对于学生在面对一些相关变式题时会无从下手。本文基于这个问题，进行教学设计，对三角形等周问题这个知识点的进行详细证明，旨在让学生“知其所以然”，激发学生的好奇心。

Abstract: The triangle isoperimetric problem is a very old problem. The shadow of the isoperipheral problem appears in Virgil’s epic “Aeneid”, and the triangle is the simplest of the isoperipheral problems. The problem of triangle isosperimeter is a knowledge point often used in middle schools. In some high school entrance examinations and college entrance examinations, variations of the problem of triangle isosperimeter will be involved. The essence of the triangle isosperimeter problem is the optimal value problem, but most students only know the conclusion of this knowledge point and do not grasp its ideas. This makes it difficult for students to start when facing some related variant questions. Based on this problem, this article carries out teaching design and provides detailed proof of the knowledge point of the triangle isosperimeter problem, aiming to let students “know why” and stimulate students’ curiosity.