数形结合思想在解题中的应用 【毕业论文】

本科毕业论文（2010届）题目数形结合思想在解题中的应用学院数学与信息工程学院专业数学与应用数学班级2006级数学班学号学生姓名指导教师完成日期2010年5月I摘要数形结合是数学研究和学习中的重要思想和解题方法，用数形结合方法可以使复杂问题简单化、抽象问题具体化；能够变抽象的数学语言为直观的图形、抽象思维为形象思维，有助于把握数学问题的本质。所谓数形结合就是根据数学问题的条件和结论之间的内在联系分析其代数含义，又揭示其几何直观，使数量关系与空间形式和谐结合在一起的方法。通过“以形助数”和“以数辅形”这两大题型的具体分析，揭示出“数”与“形”之间的紧密关系，从而把问题优化，获得解决。关键词数形结合线性规划数量关系IIABSTRACTCOMBININGTHEOPERATIONWITHFIGUREISTHESTUDYOFMATHEMATICSANDLEARNINGTHEIMPORTANTTHINKINGANDPROBLEMSOLVINGMETHODS,WHICHCANSIMPLIFYCOMPLICATEDPROBLEMS,SPECIFYTHEABSTRACTONES,ANDTURNTHEABSTRACTSHAPESANDTHOUGHTTOBEVISUAL,ANDISACCORDINGLYHELPFULTOGRASPTHEESSENCEOFMATHEMATICSTHESOCALLEDCOMBINATIONISANAPPROACH,WHICHNOTONLYANALYZEMEANINGOFALGEBRA,BUTALSODISCLOSETHESIGNIFICANCEOFGEOMETRYACCORDINGTOTHEINSIDERELATIONSHIPOFCONDITIONSANDCONCLUSIONS,ANDHARMONIOUSLYCOMBINESTHEFORMOFNUMBERANDSPACEASONETHISARTICLEWILLSETFORTHTHETIGHTCONTACTBETWEENALGEBRAANDGEOMETRYTHROUGHOUTTHEANALYSISOFTWOTYPICALSTYLES“GEOMETRYHELPSUNDERSTANDALGEBRA”AND“ALGEBRAHELPSUNDERSTANDGEOMETRY”,INORDERTOSOLVERELEVANTPROBLEMSWELLKEYWORDSTHECOMBINATIONOFALGEBRAANDGEOMETRYTHELINEARPROGRAMMINGQUANTITATIVERELATIONSHIPIII目录1引言12以形助数,代数问题几何化221以形助数解决集合问题222以形助数解决取值范围问题323以形助数解决解含参数问题424以形助数解决不等式问题G252G24以形助数G8726G2001数G7509值G252G25以形助数在解析几何中的G5224用G262G26G1523助于复G5191G19766G990的G9869解决复数问题G273G714以数辅形,几何问题代数化G2731用代数方法解决G5191G19766几何问题G2732用代数方法解决G12447体几何的问题G28参G13783G7003G1049811G16886G17778121数形结合思想在解题中的应用APPLICATIONOFTHEFIGUREANDSHAPECOMBINATIONINSOLVINGPROBLEMS1引言A2A0A1A3A4A5A6A7A2A8A9A10A11A12A13A14A15A16A17A18A19A20A7A21A22A25A26A2A11A14A23A24A27A28A10A25A31A23A29A1A24A27A30A32A7A35A36A33A34A7A2A8A9A10A37A12A13A14A15A38A39A40A41A42A43A25A46A44A36A2A8A9A10A30A32A45A47A14A7A48A51A33A34A25A46A44A36A47A14A7A48A51A30A32A45A2A8A9A10A33A34A25A29A1A49A50A52A53A22A7A2A0A33A34A54A55A32A58A59A56A32A25A61A57A60A53A22A62A63A17A14A22A62A63A64A65A66A67A33A34A7A62A68A37A69A70A71A23A2A14A38A39A7A62A68A69A70A35A74A72A2A0A73A75A76A77A25A80A78A72A79A8A81A79A58A84A82A11A83A82A7A85A86A87A25A71A36A2A11A14A28A10A40A41A88A35A91A92A89A90A76A77A25A10A93A94A95A96A88A97A98A33A34A99A2A32A7A69A70A25A102A99A2A15A100A101A50A52A97A98A103A104A25A36A47A14A105A13A7A97A98A9A10A106A107A45A99A2A15A105A13A7A99A2A9A10A35A110A108A5A109A111A112A113A25A70A92A2A0A114A115A116A117A1A118A119A17A120A121A25A72A122A37A2A21A105A13A58A69A86A37A123A124A105A13A125A126A40A41A21A127A9A10A25A102A99A2A69A70A19A20A97A98A33A34A25A130A26A128A126A88A132A129A97A98A0A35A134A41A25A97A98A0A87A131A133A81A77A135A61A132A136A7A33A34A25A139A137A138A140A141A142A143A144A58A126A69A145A82A58A32A146A17A69A140A33A34A25A149A147A31A148A150A151A99A2A69A70A152A153A88A154A155A7A132A136A35A158A49A72A156A99A11A3A99A2A0A7A19A20A87A25A97A98A33A34A7A99A2A32A31A23A157A159A160A161A7A69A70A162A163A25A166A164A165A167A7A127A102A35A170A168A2A37A14A7A169A72A28A10A25A135A171A49A97A98A0A172A152A88A99A2A32A7A166A173A174A175A25A31A49A131A133A99A2A0A11A2A0A141A129A7A176A34A175A166A88A177A178A7A54A55A48A25A72A2A0A132A34A87A25A181A102A2A14A38A39A62A68A25A71A23A179A180A33A34A7A175A83A182A14A25A46A44A36A47A14A48A51A33A34A30A32A45A2A8A9A10A41A19A20A25A134A44A36A2A8A9A10A33A34A30A32A45A47A14A48A51A41A19A20A25A1A183A1A2A150A14A46A1A14A150A2A25A49A2A0A33A34A184A185A32A58A53A22A33A34A175A83A32A35A2A0A0A186A87A25A135A185A187A23A2A7A188A189A37A14A7A19A20A25A192A133A7A23A102A2A14A38A39A62A68A132A34A35A193A190A191A194A195A85A198A199A2A0A23A19A20A3A4A5A6A7A8A7A9A10A37A12A13A14A15A7A196A0A35A201A2A14A38A39A71A23A179A180A2A0A33A34A7A159A202A11A38A197A105A13A7A169A72A28A10A25A204A141A129A18A99A2A143A200A25A206A203A205A18A97A98A54A55A25A49A2A8A9A7A207A208A209A210A37A12A13A14A15A7A54A55A14A22A211A212A58A11A213A94A38A39A72A157A40A25A216A141A214A102A64A65A38A39A25A218A215A132A34A62A217A25A49A33A34A32A2192A17A220A58A32A221A17A184A25A130A26A152A153A132A136A35A224A151A49A102A88A2A14A38A39A7A69A70A25A225A133A33A34A183A222A223A26A132A25A228A132A70A184A226A230A199A2A201A37A199A14A201A23A157A21A227A229A25A233A231A13A232A234A235A135A23A199A2A201A11A199A14A201A7A227A229A7A93A157A35A238A236A237A239A59A195A85A198A199A2A240A14A76A241A54A55A25A14A241A2A76A219A242A243A25A2A14A38A39A244A245A246A25A249A247A141A114A232A248A250A35A201A127A102A2A251A252A253A254A255A16A0A1A2A3A4A5A124A198A20A6A25A1A2A253A7A251A8A9A10A11A12A50A25A13A14A15A10A17A255A8A9A18A19A21A58A22A23A10A253A24A17A255A25A8A9A26A134A10A17A255A27A28A11A12A10A29A20A30A25A1A2A31A32A199A253A201A10A33A34A50A35A199A251A201A10A36A84A50A25A37A38A39A40A41A124A42A253A17A255A25A8A9A18A43A251A134A0A44A45A199A253A201A10A33A34A50A25A46A61A47A48A49A34A252A210A51A166A54A17A255A52A53A27A10A43A251A55A56A6A25A0A163A57A55A59A10A60A62A63A48A64A27A10A43A251A134A25A65A98A66A67A210A68A254A51A253A251A252A253A10A69A70A71A3A72A73A54A74A75A10A253A24A17A255A76A77A9A58A78A79A9A80A61A81A82A74A75A69A83A85A251A75A69A83A80A166A86A87A88A89A253A24A17A255A10A90A91A92A93A94A80A224A87A72A32A95A253A251A252A253A10A96A97A80A225A99A17A255A100A101A102A103A254A80A228A254A97A19A229A80A61A104A105A14A15A10A106A107A51A0A1A2A108A109A110A111A69A70A2A112A80A113A114A115A116A166A43A80A117A253A70A43A80A3A118A119A120A121A69A83A10A122A123A51A253A251A252A253A10A69A70A96A97A125A117A10A126A127A254A96A128A35A254A55A11A129A17A255A116A80A127A68A130A253A10A131A132A58A149A131A17A255A116A80A127A68A14A253A35A133A135A130A253A17A255A116A51A3A4A136A53A253A251A252A253A69A70A127A254A255A116A10A27A32A137A199A3A251A86A253A201A35A199A3A253A138A251A201A110A5A96A84A139A140A6A141A142A67A512以形助数,代数问题几何化A143A144A78A79A61A81A145A146A69A147A25A148A86A152A254A51A150A151A25A153A86A143A144A78A79A24A154A35A152A254A253A24A25A28A253A24A24A154A116A10A155A0A96A15621以形助数解决集合问题A43A157A97A28A158A253A10A155A0A159A157A97A160A6A25A53A6A54A161A162A74A75A10A158A253A17A255A25A127A254A255A16A164A153A86A165A193A43A167A32A253A168A58A43A75A11A253A251A252A253A10A69A70A96A97A25A169A169A71A3A72A17A255A78A79A9A58A251A75A9A25A137A103A170A171A58A78A79A58A19A229A58A172A34A173A174A254A51A1751A176A73A177A22450A24A178A179A10A180A181A182A77A183A116A25A184A185A186A187A180A10A16638A25A185A186A188A180A10A16641A25A185A189A190A180A10A16627A230A204A184A185A186A187A180A206A184A185A186A188A180A10A16632A204A184A185A186A188A180A206A184A185A189A190A180A10A16621A25A191A185A189A190A180A206A184A185A186A187A180A10A16620A17A59A16A184A185A110A133A181A180A10A166A99A192A194A1953A196A431A197A200A202A198A126A203A43A52A157A25A59A16A184A185A133A181A180A10A166A205A194A196A207A208A209A200A197A25A184A185A186A187A180A10A166A198203238X（A211A212A213A214A215A216A217A218A219A220A221213241X（A211A212A213A214A215A222A223A218A219A220A221202127X（A211A212A226A227A231A232A212A233A221502212032202127213241203238XXXX（A234A23517XA236A237A238A214A215A239A240A241A218A219A22017A211A24222以形助数解决取值范围问题A24312A244A245A246A2473COS,|0,3SINXMXYYPICCA206A117OAOCOB21A32A228A134A236A27A39XA73A135A153AA58BA33A124A35A118A34A28A29A36A37A300,2CA580,CA32A26A134A236A27CBXAXY2A9A49A38A6AA58BA58CA141A124A322420ACBCC120ACBCC2000C3142A154630BCCA1183210CBYXACBO6A1170CA118210BA11821BA158A10A4BA55A3021A3524以形助数解决不等式问题A2485A78A8A137A132A212XXA53A40A8A1A198A164A137A132A21A132A41A1531200202202XXXXXXA44A42A43A66A67A6912YXA70A71A72A752YXA70A113A74A70A166A76A77A79A70A168A120A80A43A82A83A71A43A51A52A54A70A42A68A56|ABXXXXX,A118QTAN,XX2122142A25A30A228A32A30XX2A25A1582XA33A34A201A48A35A211A118QTANA11A14A15A16A1942A211A164A13A36A104A25A101A24A37A38A11A39A40A27A132A174A87A41A219A42A25A129A43A25A64A44A221A45A25A99A47A37A38A49A50A51A52A25A53A55A11A223A56A57A238A58A59A60A61A62A225A63A198A34A24A65A53A33A67A51A226A25A53A67A24A33A68A69A70A57A201A72A102A24A53A73A74A11A64A76A77A79A227A80A81A82A37A38A85A83A25A86A88A90A187A230A132A38A85A191A57A91A92A95A96A97A98A100A103A105A106A107A109A110A111A112A113A114A115A119A120A121A122A112A123A125A114A100A103A105A106A127A123A119A137A128A125A130A131A133A109A110A112A232A134A135A123A192A136A138A112A115A235A95A96A141A142A144A145A112A146A147A148A236A149A150A151A152A107A100A153A109A110A111A91A92A138A237A154A155A100A154A156A157A148A159A160A161A103A162A163A239A166A123A167A168A200A169A170A171A173A175A148A103A176A173A175A177A178A179A180A112A113A114A15211参考文献A181A182A184A185A186A188A189A190A193A194A196A197A202A203A204A205A207A208A209A212A194A220A222A224A203A229A231A181A233A184A189A234A240A241A242A244A245A244A246A247A248A249A249A250A247A251A252A253A254A255A250A249A248A43A250A249A2A1A248A3A45A0A4A8A9A5A6A7A10A11A12A13A14A15A16A17A18A48A19A1A20A3A8A50A21A22A23A24A247A248A249A249A251A247A252A248A254A255A55A248A43A251A2A1A2A3A45A25A26A8A16A9A5A27A18A6A7A10A11A28A29A6A30A31A1A20A3A8A50A21A32A33A34A247A248A249A249A55A247A252A248A249A254A255A248A35A35A1A35A3A66A36A37A8A6A7A10A11A38A39A12A6A40A13A14A15A16A17A18A1A20A3A8A69A41A23A24A40A42A40A34A247A248A249A249A251A247A250A250A252A250A254A255A250A250A253A43A250A250A44A1A253A3A72A46A47A8A9A49A6A7A10A11A12A29A6A23A40A15A16A17A18A1A20A3A8A50A21A51A52A53A34A247A248A249A249A251A247A252A250A35A254A255A248A253A35A1A44A3A79A54A56A8A6A7A10A11A12A57A15A6A40A13A14A15A16A17A18A1A20A3A8A83A58A59A60A40A34A247A248A249A249A35A252A2A254A255A250A249A2A43A250A249A253A1A87A3A88A61A8A9A5A6A7A10A11A62A63A12A13A14A15A16A17A18A1A20A3A8A50A21A51A52A53A34A247A248A249A249A251A247A252A250A254A255A250A55A250A1A55A3A45A64A8A93A65A67A68A70A71A16A6A7A10A11A73A63A22A13A63A1A20A3A8A100A74A75A76A23A24A40A42A40A34A247A248A249A249A55A247A250A35A252A250A254A255A250A249A35A43A250A249A253A1A251A3A104A77A78A8A9A5A6A7A10A11A63A12A13A14A15A16A80A18A1A20A3A8A108A81A59A82A84A40A40A34A247A250A251A251A55A247A252A35A254A255A44A2A43A44A35A1A250A249A3STEPHANIEJMORRIS,THEPYTHAGOREANTHEOREMJ,DEPARTMENTOFMATHEMATICSEDUCATIONJWILSON,EMT669A1A250A250A3GIANLUCAFUSAI,CORRIDOROPTIONSANDARCSINELAWJANNAPP1PROBABVOLUME10,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