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数形结合思想就是通过数与形之间的相互转化来解决数学问题,包括以形助数和以数赋形两个方面。利用它可以使复杂问题简单化,抽象问题具体化。华罗庚教授曾说过:“数缺形时少直观,形缺数时难入微。”因此数形结合思想是一种重要的数学思想。而通常我们在教学中用代数知识解决几何问题较多,用几何知识解决代数问题涉及较少,本文就重点举几个用几何图形解决代数问题以渗透数形结合思想的实例,以飨读者。一、用几何图形解决代数式的最小值问题例1已知:x为任意实数,求代数式
The idea of combining numbers with numbers is to solve mathematical problems through the mutual transformation between numbers and forms, including two aspects: form aids and numbers. It can be used to simplify complex issues, abstract issues specific. Professor Hua Luogeng once said: “The number of lack of shape less intuitive, when the number of missing form into. ” Therefore, mathematical combination of ideas is an important mathematical thinking. Usually, we use algebraic knowledge in teaching to solve more geometric problems and deal with algebra problems with less geometric knowledge. This article focuses on several examples of using algebraic problems to solve algebra problems and to penetrate the idea of combining numbers with readers. First, the use of geometry to solve the minimum algebraic problem Example 1 Known: x is any real number and find algebraic