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数形结合就是把抽象的数学语言、数量关系与直观的几何图形、位置关系结合起来,通过“以形助数”或“以数解形”将抽象思维与形象思维相结合,可以使复杂问题简单化,抽象问题具体化,从而起到优化解题途径的目的.应用数形结合思想可以解决以下问题:①实数与数轴上的点的对应关系;②函数与图像的对应关系;③曲线与方程的对应关系;④以几何元素和几何条件为背景,建立起来的概念,如,复数、三角函数等;⑤所给的等式或代数式的结构含有明显的几何及数的特征,构造出与之相适应的几何图形,并利用图形的特征和规律来解决数的问题;或将图形信息部分转换成代
The combination of numbers combines the abstract mathematical language, the quantitative relationship with the intuitive geometry and the positional relationship, combines the abstract thinking with the image thinking through Which can make the complex problem simple and the abstract problem concrete, so as to optimize the way of solving the problem.Application of the combination of shape and ideology can solve the following problems: (1) the correspondence between the real number and the axis point; (2) the correspondence between the function and the image ; ③ Correspondence between curves and equations; ④ Concepts based on geometric elements and geometric conditions, such as complex numbers, trigonometric functions, etc. ⑤ Equations or algebraic structures are given with significant geometric and numerical features , To construct the geometry corresponding to it, and to use the features and laws of the figures to solve the problem of numbers; or to convert part of the graphic information into generation