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数形结合是一个数学思想方法,包含“以形助数”和“以数辅形”两个方面,其应用大致可以分为两种情形:或者是借助形的生动和直观性来阐明数形之间的联系,即以形作为手段,数为目的,比如应用函数的图像来直观地说明函数的性质;或者是借助于数的精确性和规范严密性来阐明形的某些属性,即以数作为手段,形作为目的,如应用曲线的方程来精确地阐明曲线的几何性质。
The combination of number and shape is a method of mathematics, which includes two aspects of “helping number” and “numbering auxiliary”. Its application can be roughly divided into two situations: it can be vivid and intuitive with the aid of shape. To clarify the connection between numbers, that is, to use shape as a means and number for the purpose of, for example, visualizing the nature of a function by using the image of a function; or by clarifying the shape by means of the precision of the number and the strictness of the specification. Attributes, that is, numbers as a means, shape as a goal, such as the application of curve equations to accurately clarify the geometric properties of the curve.