RMI原理及在中学数学解题中的应用研究必威体育精装版.pdfVIP

摘 要 关系（relation ）—映射（mapping ）—反演（inversion ）原理，简称RMI 原理,是一种分析处理问题的普遍原则。主要适用于解决数理科学与工程技术科 学方面的有关问题，尤其广泛应用于现代数学研究，具有联系各个数学分支体 系、解决数学问题的功能，并能够实现深层次抽象化的化归，提高数学解题效 率 本论文基于对 RMI 原理理论实质的理解，重点梳理了 RMI 原理在中学数 学解题中的种种应用，从中进一步思考了 RMI 原理对中学数学解题教学的启示， 总结了采用 RMI 原理解题需要运用的策略 关 键 词：RMI 原理；化归原则；解题教学 Ⅰ RMI 原理及其在中学数学解题中的应用研究 II Abstract The method of Relation-Mapping-Inversion, abbreviated RMI method, is a general principle of analysis and solution. It is mainly used to solve some problems about mathematical science and engineering science and technology, especially widely used on modern mathematical research .It has the function of contacting various branches of mathematics and solving mathematical problems. It also can realize the more abstract naturalization and improve the efficiency of solving problems. This paper is based on understanding the theory of RMI method, and mainly arranges its various applications in solving middle school mathematical problems. And from that, it makes me begin to think of the RMI method’s affections on the teaching of solving middle school mathematical problems. Finally, I make a summary of strategies about applying RMI method to solve mathematical problems. Key words: The method of Relation-Mapping-Inversion; The theory of reduction; teaching about solving problems . Ⅱ 目 录 摘 要I Abstract II 目 录III 1 RMI 原理概述 1 1.1 一般化的 RMI 原理 1 1.2 数学中的 RMI 原理及化归原则 2 1.2.1 数学中的 RMI 原理简述 2 1.2.2 化归原则与 RMI 原理的关系 3 2 RMI 原理在中学数学解题中的应用 4 2.1 对数法