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数”和“形”是不可分割的统一体。数形沟通,相互印证。不仅是数学研究的重要手段,也是数学解题的重要技巧。解析几何开创了用“数”研究“形”的先例,使灵活多变的几何问题转化为有程序的代数问题,解题有路可循,易于解决;反之,以“形”研究“数”,代数问题转化为几何问题,会使得问题直观形象,解法灵活、简洁,本文从几方面谈谈如何实现这一转化。 (一)利用概念的几何意义: 数学中许多代数概念都有较强的几何意义,充分应用它的几何意义剖析代数问题,可使许多繁杂的代
“Number” and “form” are inseparable unity. Number-shaped communication and mutual confirmation are not only important methods for mathematical research, but also important techniques for solving problems in mathematics. Analytic geometry has created a precedent for studying “shape” with “number”. , Transforming flexible and geometric problems into algebraic problems with programs, solving problems in a way that can be followed, and solving them easily; conversely, if you study “numbers” in “forms” and convert algebraic problems into geometric problems, you will make the problems visible. The solution method is flexible and concise. This article discusses how to achieve this transformation from several aspects. (1) Using the geometric meaning of the concept: Many algebraic concepts in mathematics have strong geometric meanings, and fully apply its geometric meaning to analyze algebraic problems. Make many complicated generations