对称思想在几何中的应用研究 毕业论文

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1、对称思想在几何中的应用研究摘要对称思想是一种重要的数学思想，存在于数学的很多领域，我们对其应该给予足够的重视。对称思想是研究数学问题常用的思想方法，对称是一种美，数学中的对称美主要表现在几何图形的对称、式子的对称、解题方法的对称等方面。本文讨论对称思想在平面几何、解析几何、立体几何、射影几何中的应用并举例说明分析。关键词对称思想几何应用theResearchofSymmetricalIdeaintheGemmetry　　（SchoolofMathematicalScience，HuaibeiNormalUniversity，Huaibei，23500

2、0）AbstractSymmetricalideaisanimportantmathematicalthought,whichexistsinmany　areasofmathematics,ofwhichweshouldgiveenoughattention.Symmetricalideaisthinkingmethodwhichisthestudymathproblemscommonlyused.Symmetryisabeauty,thesymmetricalbeautyofmathematicsismainlymanifestedinthesym

3、met-ricalgeometricfigure,thesymmetricalformula,thesymmetricalmethodofsolvingproblem,ect.Thispaperdiscussessymmetricalideasinplanegeometry,andanalyticgeometry,three-dimensionalgeometry,projectivegeometry,andillustratestheappli-cation.KeyWords:SymmetryideaGeometricalapplication目录

4、引言··························································1一对称思想的意义·················································1二几何的对称性···················································1（一）几何公式的对称性···········································2（二）几何图形的对称性··································

5、·········2（三）对称的广泛应用·············································2三对称思想在初等数学中的应用·····································3（一）对称思想在平面解析几何中的应用······························3（二）对称思想在立体几何中的应用··································11四对称思想在高等数学中的应用····································12（一）对称思想

6、在射影几何中的应用·································12（二）对称思想在微分学中的应用···································15（三）对称思想在积分学中的应用···································16五对称思想的进一步探讨··········································18（一）数学思想方法的探讨·········································18（二）对称思想方法对教学的影响·····

7、······························191对称思想方法对学生的影响·································192对称思想方法对教师的影响·································19参考文献···························································20后记···························································21引言从中国数学发展的历程和数学本身的特征看，

8、中国数学表现出对称性、统一性等科学美学特征。中国数学美的思想方法对数学、数学教育的发展起到过积极作用，在今后