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数学上总是用数的抽象性和精确性来说明形象的事实,同时又用图形的直观性来说明抽象的事实。或以数辅形,用严密的逻辑推理来精确刻画直观的形象;或以形助数,用形象的几何图形启迪抽象的代数思维。这种数形结合就是把代数式的精确刻画与几何图形的直观描述有机结合起来,实现形象思维与抽象思维的优势互补,体现了数与形之间的沟通与变换。既利于探求解题途径,又可深刻认识问题的本质。
Mathematically, the abstractness and accuracy of numbers are always used to illustrate the fact of the image, while at the same time the abstract fact is illustrated by the intuition of the figure. Or the number of auxiliary shape, with rigorous logical reasoning to accurately depict the visual image; or to help form the number of geometric figures inspired by the use of abstract algebraic thinking. The combination of number and shape combines the accurate description of algebra and the intuitive description of geometry to realize the complementary advantages of image thinking and abstract thinking, which reflects the communication and transformation between number and form. It not only helps to explore ways to solve problems but also profoundly understands the essence of the problems.