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美国著名数学家G·波利亚说:“掌握数学意味着什么?那就是善于解题。”解题的关键在于能否快速地找到正确的解题途径和方法。本文介绍的整体思维是解题策略中的一种重要思维方法,它常给某些问题的解决带来方便,它体现在解题过程中,不是着眼于问题的各个组成部分,而是根据题中的结构特点,将要解决的问题青作一个整体,通过研究问题的整体形式、整体结构或作种种整体处理后,达到顺利而又简捷地解决问题的目的。今举数例,以示一斑。例1 过圆外一点P(a,b),引圆x~2+y~2=R~2的两条切线,求经过两切点的直线方程。 (甲种本第26页24题)
The famous American mathematician G. Polya said: “What does it mean to master mathematics? That is to be good at solving problems.” The key to problem solving lies in whether or not you can quickly find the right solution approaches and methods. The overall thinking introduced in this paper is an important way of thinking in problem solving strategies. It often brings convenience to the solution of certain problems. It is reflected in the process of solving problems, not focusing on the various components of the problem, but on the basis of the problem. The structural characteristics of China and the issues to be solved are a complete one. After studying the overall form of the problem, its overall structure, or all sorts of overall treatment, it can achieve a smooth and simple solution to the problem. Here are a few examples to show. Example 1 The point P(a, b) is outside the circle and the two tangents of x~2+y~2=R~2 are drawn to find the straight line equation that passes through the two cut points. (A type of 24 questions on page 26)