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1、TituAndreescuOlegMushkarovLuchezarStoyanovGeometricProblemsonMaximaandMinimaBirkhauser¨Boston•Basel•BerlinTituAndreescuOlegMushkarovTheUniversityofTexasatDallasBulgarianAcademyofSciencesDepartmentofScience/InstituteofMathematicsandInformaticsMathematicsE
2、ducation1113SofiaRichardson,TX75083BulgariaUSALuchezarStoyanovTheUniversityofWesternAustraliaSchoolofMathematicsandStatisticsCrawley,PerthWA6009AustraliaCoverdesignbyMaryBurgess.MathematicsSubjectClassification(2000):00A07,00A05,00A06LibraryofCongressContr
3、olNumber:2005935987ISBN-100-8176-3517-3eISBN0-8176-4473-3ISBN-13978-0-8176-3517-6Printedonacid-freepaper.c2006BirkhauserBoston¨BasedontheoriginalBulgarianedition,Ekstremalnizadachivgeometriata,NarodnaProsveta,Sofia,1989Allrightsreserved.Thisworkmaynotbet
4、ranslatedorcopiedinwholeorinpartwithoutthewrit-tenpermissionofthepublisher(BirkhauserBoston,c/oSpringerScience¨+BusinessMediaInc.,233SpringStreet,NewYork,NY10013,USA)andtheauthor,exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconne
5、ctionwithanyformofinformationstorageandre-trieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,eveniftheyarenoti
6、dentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.(KeS/MP)987654321www.birkhauser.comContentsPrefacevii1MethodsforFindingGeometricExtrema11.1EmployingGeometricTransform
7、ations..............11.2EmployingAlgebraicInequalities.................191.3EmployingCalculus.........................271.4TheMethodofPartialVariation..................381.5TheTangencyPrinciple.......................482SelectedTypesofGeometricExtremumPro
8、blems632.1IsoperimetricProblems.......................632.2ExtremalPointsinTriangleandTetrahedron............722.3Malfatti’sProblems.........................802.4ExtremalCombinatorialGeometryProblems...........883Miscellan
