数形结合思想

学生：王俊 指导教师：柏明强

摘要：数形结合思想是把问题的数量关系与图形结合起来考察的一种思想方法。数形结合是把数、式与图形结合起来, 用代数的方法分析图形；用图形来直观理解数、式中的关系。通过实例揭示了数形结合思想在解决问题时的重要作用, 以及数形结合的意义。它的意义有四个方面：问题的解决过程简单化、培养创造性思维、抽象的知识形象化与加深记忆、激发兴趣。数形结合的解题方法具有直观、灵活的特点, 是数学解题中的一种重要方法, 它的应用十分广泛。主要体现下面三个方面：以形助数、以数助形、数形互动。此外要注意慎用, 不可误用。

关键词：数形结合，意义，应用，误用

The Thought of Combining Numbers and Graphs Abstract The thought of combining numbers and graphs is a method in which the relationship between numbers and graphs is considered as a whole. In this paper, through examples, its significance and application are revealed. This thought is to combine numbers ,expressions and graphs, analyze graphs with algebraic method, and understand the relationship in numbers and expressions in an intuitive manner. Its importance in addressing problems is shown in various examples. Its significance can be illustrated in the following four aspects: the simplification of process in problem-solving, the cultivation of creative thinking ,the visualization of abstract knowledge and deepening of memory, and the inspiration of interests. The features of this thought in problem-solving are visuality and flexibility. It is an important method in problem-solving, and widely used which is embodied as follows: to apply graph in handling problems concerning numbers, to utilize numbers to tackle problems concerning graphs, and to combine the former two methods. However, we should be careful using this method to avoid misuse.

Key words:The combination of numbers and graphs;Significance; Application Misuse

2