例说类比推理及其应用 2

本科生毕业论文（设计）

题 目 例说类比推理及其应用 专 业 数学与应用数学

目录

摘要 ................................................................................................................................................................ II 关键词 ........................................................................................................................................................... II Abstract ...................................................................................................................................................... III Keywords ................................................................................................................................................... III 前言 ................................................................................................................................................................. 1 1类比推理的涵义、特点和步骤 .................................................................................................................. 1 1.1类比推理的涵义 ....................................................................................................................................... 1 1.2类比推理的特点 ....................................................................................................................................... 1 1.3类比推理的步骤 ....................................................................................................................................... 2 2类比推理的作用 .......................................................................................................................................... 2 2.1预测未知目标从而实现化归 ................................................................................................................... 2 2.2发现新的命题 ........................................................................................................................................... 3 2.3发现解决问题的途径和方法 ................................................................................................................... 4 3类比推理的分类 .......................................................................................................................................... 6 3.1简单共存类比 ........................................................................................................................................... 6 3.2因果类比 ................................................................................................................................................... 6 3.3对称类比 ................................................................................................................................................... 7 3.4协变类比 ................................................................................................................................................... 7 3.5综合类比 ................................................................................................................................................... 8 4类比推理的应用 .......................................................................................................................................... 9 4.1类比推理在圆锥曲线中的应用 ............................................................................................................... 9 4.2类比推理在函数中的应用 ..................................................................................................................... 12 4.3类比推理在立体几何中的应用 ............................................................................................................. 13 4.4类比推理在定比分点中的应用 ............................................................................................................. 14 4.5类比推理在数列中的应用 ..................................................................................................................... 17 参考文献 ....................................................................................................................................................... 18 致谢 ............................................................................................................................................................... 19

例说类比推理及其应用

摘要：类比是探索问题、解决问题与发现新结果的一种卓有成效的思维方法.在数学中，类比

是发现概念、方法、定理和公式的重要手段，也是开拓新领域和创造数学新分支的重要途径.它在圆锥曲线、函数、立体几何、定比分点和数列也有广泛的应用.

关键词：类比推理；圆锥曲线；立体几何；定比分点

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Cases of analogy reasoning and its application

Abstract: The analogy is to explore the problem, solve the problem and a very fruitful way of

thinking to find new results. In mathematics, the analogy is not only important means to discover concepts, methods, theorem and formula, but also to open up new areas and create a new branch of mathematics important way. This paper mainly cases that analogical reasoning and its application in the cone curve, function, solid geometry, definite proportion and sequence.

Keywords: Analogical reasoning; conic curve; solid geometry; definite proportion

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