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数形结合的思想方法是一种重要的数学思想方法,它在解题中的应用是深入和广泛的。本文主要论述了数形结合思想方法在解题中的应用:一方面,以形助数即借助于图形的性质可以将许多抽象的数学概念和数量关系形象化、简单化,给人以直觉的启示;另一方面,以数助形即将图形问题转化为代数问题,以获得精确的结论;最后一方面是数形结合即“数”与“形”的信息相互转换,相互渗透。
The idea of combination of number and shape is an important method of mathematical thinking. Its application in problem solving is deep and extensive. This article mainly discusses the application of the number and shape combination method in the problem solving: On the one hand, the number of shape aids, that is, with the help of the nature of the graph, can visualize and simplify many abstract mathematical concepts and quantity relations, giving people intuition. Enlightenment; on the other hand, the mathematical assistance is about to turn the graph problem into an algebra problem to get accurate conclusions; the last aspect is the transformation of the number form combination, ie, the “number” and the “shape”, and the mutual infiltration. .