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数形结合思想是初中数学众多数学思想中最重要、也是最基本的思想之一。它在初中数学中有着广泛的应用,是解决许多数学问题的有效思想。几何图形形象直观,便于理解,代数方法则具有一般性,解题过程机械化,可操作性强,便于把握。数形结合思想也就是通过数与形的灵活转换,相互作用,进而解决问题的一种思维方式,数形结合思想能发扬数之长,取形之优,使得“数量关系”与“空间形式”珠连壁合、相映生辉。正如数学家华罗庚所说:
The combination of number and shape is one of the most important and basic concepts in many mathematical ideas of junior middle school mathematics. It has a wide range of applications in junior high school mathematics, is an effective idea to solve many mathematical problems. Geometric figures intuitive, easy to understand, algebra method is a general solution to the mechanization problem, maneuverability, easy to grasp. The combination of number and shape is also a way of thinking through the flexible transformation and interaction of number and form, and then to solve the problem. The combination of number and shape can promote a long way and take shape, “Space form ” Bead wall together, glorified. As mathematician Hua Luogeng said: