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基于代数思维的几何问题求解方法对比与应用分析

Comparison and Application Analysis of Geometric Problem Solving Methods Based on Algebraic Thinking

教育研讨 / 2024,6(5)：1336-1340 / 2024-10-22 47 73

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• 作者： 胡凡      陈壁廷      李孟雨      杨晓芳     
• 单位：

  成都师范学院，成都

• 关键词： 代数思维；几何问题求解；代数方法；几何结构分析
• Algebraic thinking; Solving geometric problems; Algebraic methods; Geometric structure analysis
• 摘要： 代数思维以其结构化和符号化的特性，为几何问题提供了不同于传统几何方法的独特视角。本文通过分析代数方法的逻辑框架和几何问题的本质属性，探讨了代数在解题过程中所展现的抽象与一般化能力，并结合典型的几何问题实例，展示了代数方法与几何方法在求解路径上的不同，评估了代数思维在处理复杂几何结构时的有效性与局限性。研究结果表明，代数思维不仅能够简化复杂的几何问题，还能提供新的解题思路，具有广泛的应用潜力。
• Algebraic thinking, with its structured and symbolic characteristics, provides a unique perspective for geometric problems that is different from traditional geometric methods. This article analyzes the logical framework of algebraic methods and the essential properties of geometric problems, explores the abstract and generalized abilities exhibited by algebra in solving problems, and combines typical geometric problem examples to demonstrate the differences between algebraic and geometric methods in solving paths, evaluating the effectiveness and limitations of algebraic thinking in dealing with complex geometric structures. The research results indicate that algebraic thinking can not only simplify complex geometric problems, but also provide new problem-solving ideas, with broad potential for application.
• DOI： https://doi.org/10.35534/es.0605179
• 引用： 胡凡，陈壁廷，李孟雨，等．基于代数思维的几何问题求解方法对比与应用分析［J］．教育研讨，2024，6（5）：1336-1340．