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数和形是数学研究的基本对象,数形结合作为一种重要的解题方法,它把代数式的精确刻画与几何图形的直观形象描述结合起来,有利于启迪思路,探求解题途径。数量关系如果借助图形性质,可使许多抽象问题直观而形象化。而有些涉及图形问题转化为数量关系问题,又可获得简单而快捷的解法。数和形是相辅相成的两个方面,充分利用数形结合思想来解题,往往可使解法别开生面。
Number and shape are the basic objects of mathematics research. The combination of number and shape is an important method of solving problems. It combines the accurate description of algebraic style with the visual image description of geometric figures, which is conducive to inspiring ideas and exploring solutions. If the quantitative relationship depends on the nature of the graph, many abstract problems can be intuitively visualized. Some of them involve the transformation of graphical problems into quantitative relationships, and they also provide simple and quick solutions. Number and shape are two aspects that complement each other. Making full use of the idea of combining numbers and shapes to solve problems can often make the solution unique.