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构造法证明不等式毕业论文 精品

构造法证明不等式毕业论文 精品

宁波大学理学院本科毕业设计(论文) 编号: 本科毕业设计(论文) 题目: 构造法证明不等式 Constructing method to prove inequality I 摘 要 【摘要】1978 年, 《参考消息》第四版刊载了当年在布加勒斯特举行的第二十届国际数学奥林匹克竞赛题。由此, 国内数学教育界才第一次知道,世界上有“国际奥林匹克竞赛” (陈计、叶中豪《初等数学前沿》 ) 。加之时代因素,由 这则小消息作为发端,国内数学界形成了一波研究数学竞赛,研究初等数学的高潮。四十多年来,对这两者的研究延 续不断,可谓方兴未艾。作为一种极富创新精神的方法,构造法被广泛的运用于中学数学竞赛的各个部分。而构造法 在证明不等式方面,其独创性和巧妙性往往让人叹为观止。仅仅在国内,每年都有数以百计的关于构造法解题的论文 涌现,可见这一方法的吸引力之大。 本文一共分为四章章。第一章对构造法进行概述,即讲述了构造思想及构造法的历史和目前国内外对这一思想 与方法的研究现状,指出构造法解题所应遵循的规则。第二章则是构造法解题的模型概述,比较全面的总结了构造法 证明不等式的基本数学模型,对模型产生的思维过程进行剖析。第三章结合数学竞赛、高考的众多实例对各个模型进 行说明,对一些问题给出新的解答,从中体会构造法的迷人之处,窥见数学之美。第三章四章是结语。对比近三十年 的文献,本文的创新之处在于将加强命题证明不等式作为构造法证明不等式的一种新模型作了一些探索,对思维构造 过程作了相应论述,对某些模型的构造思维生发过程给予比较细致的剖析。 【关键词】构造法;构造思想;模型。 。 宁波大学理学院本科毕业设计(论文) 英文题目 Constructing method to prove inequality Abstract 【ABSTRACT】 In 1978, the fourth edition of the references published in those days the twentieth international mathematical Olympiad in Bucharest contest questions.thus,Domestic mathematics education to know for the first time, there are of the international Olympic competition in the world (Chen meter, Ye Zhonghao the frontiers of elementary mathematics). Combined with the age factor, by the small message as a start, formed a wave study maths at home, the climax of elementary mathematics research. For more than forty years, the study of the two prolonged, just. As a kind of innovative method, structure method is widely used different parts of the secondary school mathematics competition. And constructing method to prove inequality in terms of its originality and clever tend to surprise. Just at home, every year hundreds of papers about construction method of problem solving, visible appeal of this method. This article altogether is divided into three chapters. First chapter is to outline of construction method, which tells the structure thought and method of history and the study of the thought and method at home and abroad present situation, points out that the construction should follow the rules to solve problems. The second chapter is the key, of constructing method to prove inequality of basic mathematical model, and combining the math competition, the university entrance exam of many examples, to experience the enchantment of the construction method from them to see the beauty of math. The third chapter is epilogue. Contrast to nearly three decades of literature, the innovation of this paper lies in that will strengthen the proposition to prove inequality as a new model of constructing method to

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