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把图形按着一定的规律间隔地涂上颜色、把有色方格(点)和无色方格(点)看成被研究的对象,使研讨的问题变为直观,这种别具一格的解题方法称作间隔涂色法。某些数学竞赛试题,运用此法能起到意想不到的作用,对问题的理解、叙述、讨论都是有益的。下面从两方面谈谈此法的运用。一、用间隔涂色法构造命题“型模”某些数字命题的数量关系,能在间隔涂色法构造的“模型”上得到体现,直观地得到一种解释,从而得到问题的解答。例1 试用图解法证明 1+3+5+…+(2n-1)=n~2。解:用间隔涂色法构造图1,则命题的数量关系直观地体现出来。
The pattern is painted at regular intervals and colors, colored squares (points) and colorless squares (points) are regarded as the objects to be studied, so that the question of the study becomes intuitive, this unique method of solving the problem. It is called interval coloring. Certain mathematics contest questions can have unexpected effects by using this method. It is beneficial to understand, narrate, and discuss problems. Let’s talk about the use of this method in two aspects. 1. The quantitative relationship between certain numerical propositions of the propositional “pattern” constructed by the interval coloring method can be embodied on the “model” of the interval coloring method construction, and an explanation is intuitively obtained so as to obtain a solution to the problem. Example 1 Trial Graphic Method Proof 1+3+5+...+(2n-1)=n~2. Solution: Constructing Figure 1 using the interval coloring method, the quantitative relationship of propositions is visualized.