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数与形是数学中的两个最古老、也是最基本的研究对象,它们在一定条件下可以相互转化.所谓数形结合,就是根据数与形之间的对应关系,通过数与形的相互转化来解决数学问题的思想.它包括两种情形:或者借助于数的精确性来阐明形的某种属性;或者借助于形的几何直观性来阐明数之间的某种联系,即“以数助形”和“以形助数”两个方面,通过这两个方面,可以使抽象的数学语言、数量关系与直观的图形、位置关系巧妙地结合起来,可以使复杂问题简单化、抽象问题具体化,从而起到优化解题的目的.
Numbers and shapes are the two oldest and most basic research objects in mathematics. They can be transformed into each other under certain conditions. The so-called combination of numbers and shapes is based on the correspondence between numbers and shapes, through the interaction between numbers and shapes. The idea of translating to solve mathematics problems. It consists of two situations: either elucidation of certain properties of the form by means of the precision of the number; or elucidation of a connection between numbers by means of the geometric intuition of the form, ie “ With two aspects, the number of ”help“ and ”to help", through these two aspects, the abstract mathematics language, the quantitative relationship and the intuitive graphics, and the positional relationship can be combined skillfully, and the complex problems can be solved. The simplification and abstraction of the problem are concrete, so as to optimize the problem.