构造法逆向思维逆向构造法数学论证

摘 要合理运用构造法与逆向思维解决数学问题往往会起到事半功倍的效果。文章将构造法和逆向思维两者结合在一起，提出逆向构造法的概念，讨论其特点与作用，并通过实例说明逆向构造法在代数、几何与概率等数学命题论证中的应用。关键词：构造法；逆向思维；逆向构造法；数学论证AbstractRational application of structural method and reverse thinking to solve mathematical problems often results in twice the result with half the effort. Combining the construction method and reverse thinking, this paper puts forward the concept of reverse construction method, discusses its features and functions, and illustrates the application of reverse construction method in propositional argumentation of algebra, geometry and probability through examples.Key words: Construction method; Reverse thinking; Reverse construction; Mathematical reasoning目 录1 引言………………………………………………………………………………P52 逆向构造法的内涵………………………………………………………………P52.1 逆向思维………………………………………………………………………P52.2 构造法…………………………………………………………………………P62.3 逆向构造法的含义……………………………………………………………P62.4 逆向构造法的特点……………………………………………………………P72.5 逆向构造法的作用……………………………………………………………P73 运用逆向构造法论证的若干实例………………………………………………P73.1 逆向构造法在代数类的解题应用……………………………………………P73.2 逆向构造法在几何类的解题应用……………………………………………P113.3 逆向构造法在概率类问题解决中的应用……………………………………P134 总结………………………………………………………………………………P13参考文献……………………………………………………………………………P15致谢…………………………………………………………………………………P16数学论证的一种方法——逆向构造法1 引 言数学是一门严谨并且抽象的学科，并不单纯只是依照公式、定理、法则等来解题，而是要有自己的思考...