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在探求某些问题的解题途径时,如果能运用所学的代数、几何、三角知识,把数与形结合起来进行探索,往往能化繁为简,化难为易,收到良好的效果,且能使学生对所学知识融汇贯通,综合运用,提高解题能力,下面仅就初中数学中,代数、几何、三角三门科相互联系,相互渗透的某些方面,举一些例子,谈一点粗浅的看法. 一、代数与几何的相互沟通 1.用代数方法解几何题. 法国数学家笛卡尔在“思维的法则”中,曾提出运用方程的观点来解决世间的一切问题.他设计的模式是:
When exploring problem solving approaches for certain problems, if we can use the algebra, geometry, and trigonometry knowledge we have learned and combine the number with the shape to explore, we can often simplify the complexity, make things difficult, and receive good results. It enables students to integrate the knowledge they have learned and use them comprehensively to improve their problem-solving abilities. In the following, we will give some examples of some aspects of interrelation between algebra, geometry, and triangular trilogy in junior middle school mathematics. A superficial point of view. First, the communication between algebra and geometry. 1. Solving geometric problems using algebraic methods. French mathematician Descartes in the “The laws of thinking,” has proposed the use of equations to solve all problems in the world. He designed The pattern is: