“在哲学中正确的作法通常是考虑相似的东西,虽然这些东西彼此相距甚远”(亚里斯多德语).类比的实质就是根据两个对象之间的相似,把信息从一个对象转移给另一个对象.科学史上很多重大发现,往往发端于类比,类比被誉为科学活动中“伟大的引路人”.同样数学解题中,类比会使我们获得猜想,探明解题方向,为最终解决问题奠定基础. 例题设f(x)是定义在R上的偶函数,其图象关于直线x=1对称,对任意x1,x2∈ “The correct approach in philosophy is usually to consider similar things, although these things are far apart from each other” (Aristotle). The essence of analogy is to transfer information from one object to another based on the similarity between two objects. An object. Many major discoveries in the history of science often originate analogy. Analogy is known as the “great guide” in scientific activities. In the same mathematics problem solving, analogy will allow us to obtain conjectures, explore the direction of problem solving, and finally solve problems. The problem lays the foundation. Example Let f(x) be an even function defined on R. Its image is symmetrical about the straight line x=1, for any x1, x2