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用数学美的思想方法指导解题是数学思维的重要策略。在解题过程中数学美的思想能启发引导我们去进行直觉思维,使思维过程跃过分析推理的细节,凭感觉去发现问题的内在联系。所以,“美的观点一旦与数学问题的条件与结论的特点结合,思维主体就能凭借已有的知识和经验产生审美直觉,从而确定解题的总体思路或入手方向。”一、追求简洁美,探索解题捷径简明就是一种美。法国哲学家狄德罗说:“算学中所谓美的问题,是指一个难以解决的问题,而所谓美的回答,则是指对于困难而复杂的问题的简单回答。”有
It is an important strategy of mathematics thinking to use mathematics and ideology to guide problem solving. In the process of solving problems, the thought of mathematics can inspire and guide us to carry out intuition thinking, make the thinking process jump over the details of analytical reasoning, and use the feeling to discover the inner relationship of the problem. Therefore, once “the idea of beauty is combined with the characteristics of the conditions and conclusions of the mathematical problem, the subject of thinking can rely on existing knowledge and experience to produce an aesthetic intuition, so as to determine the overall thinking or direction of the problem.” First, the pursuit of simplicity and beauty, It is a kind of beauty to explore and solve short cuts. The French philosopher Diderot said: “The so-called beauty problem in mathematics refers to a problem that is difficult to solve, and the so-called beauty response refers to a simple answer to a difficult and complex problem.”