中學数学解题方法研究反证法本科.doc

毕业论文（设计） 题目：中学数学解题方法研究——反证法 English Title : Study On The Reductio Ad Absurdum In Secondary School Mathematics 摘 要 反证法在中学数学解题过程中的一种极其重要的数学方法，特别是对于一些直接证明比较难的问题来说，使用反证法去证明，将会变成非常简单，思路非常的清晰，因此反证法在中学数学解题得到了较为广泛的应用。反证法它主要是运用了一种逆向思维的逻辑进行解题，它是先提出一个与命题的结论相反的假设。然后，从这个假设出发经过正确的推理，导致矛盾，从而否定相反的假设，达到肯定原命题正确的一种方法。 因此在中学数学解题过程中，常使用反证法的学生能够更容易通过逻辑推理获得答案，进一步巩固学习成绩，提升逻辑思辨能力。 本文主要介绍反证法的概念、来源、本质、基本思想以及反证法在中学数学中各个方面的一些应用。对于反证法的使用时注意事项和使用反证法时的解题步骤做了一些的论述。 关键字：反证法；立体几何；平面几何 ABSTRACT A reductio ad absurdum in secondary school mathematics problem solving process is extremely important mathematical methods, especially for directly prove more difficult, the use of reductio ad absurdum to prove, will become very simple, very clear ideas, so the reductio ad absurdum inthe secondary school mathematics problem solving has been more widely used. The reductio ad absurdum that it is mainly using the logic of reverse thinking, problem solving, it is first put forward a contrary assumption and the conclusion of the proposition. Then proceed from this assumption correct reasoning, lead to contradictions, thereby negating the opposite assumption, to achieve a certainly correct the original proposition. In secondary school mathematics problem solving process, students often use reductio ad absurdum can be more easily obtained through logical reasoning answer to further consolidate the academic performance, enhance logical thinking ability. This paper describes the reductio ad absurdum of the concept, the source, nature, the basic idea of reductio ad absurdum in mathematics in secondary schools in all aspects of the application. Some discussion of the use of reductio ad absurdum of the Notes and the use of reductio ad absurdum of the problem-solving steps. Key words: reduction to absurdity; solid geometry; geometry  目 录 摘 要 I 绪 论 1 1. 反证法的概念与来源 2 1.1 反证法的概念 2 1.2 反证法的来源 2 1.2.1 古希腊的反证法 2 1.2.2 中国古代数学的反证法 3 1.2.3 反证法的其他来源 4