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数形结合的本质是几何图形的性质反映了数量关系,数量关系解决了几何图形的性质。数形结合思想方法的应用可分为两种情况:①借助于“数”的精确性来阐明“形”的属性;②借助于“形”的直观来阐明“数”之间的关系。数形结合的基本思路:根据“数”的结构特征,构造出与之相适应的几何图形,并利用图形的特征和规律,解决数的问题;或将图形信息部分或全部转换成代数信息,削弱或消除“形”的推理部分,把要解决的“形”的问题转化为数量关系的讨论。
The nature of the combination of numbers is that the nature of the geometry reflects the quantitative relationship, and the quantitative relationship solves the nature of the geometry. The application of the method of combining figures and figures can be divided into two situations: ① the property of “shape” is clarified by means of the accuracy of “number”; ② the number of “ ”The relationship between. The basic idea of combination of numbers: According to “number ” structural features, construct the corresponding geometry, and use the characteristics and laws of graphics to solve the problem of numbers; or part or all of graphics information into algebra Information, weakened or eliminated “form ” reasoning part, the problem to be solved “form ” into a discussion of quantitative relations.