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1、,.0"LUSAMATHEMATICALOLYMPIADS1972-1986COMPILEDANDWITHSOLUTIONSBYMURRAYS.KLAMKINTheMathematicalAssociationofAmericaNewMathematicalLibraryU.S.A.MATHEMATICALOLYMPIADS,1972-1986NEWMATHEMATICALLIBRARYPUBLISHEDBYTHEMATHEMATICALASSOCIATIONOFAMERICAEditorialCommitteeIvanNiven,Ch
2、airmanAnneliLax,EditorNewYorkUniversityJoanneElliott,RutgersUniversityBasilGordon,UniversityofCaliforniaHerbertJ.Greenberg,UniversityofDenverPeterUngarTheNewMathematicalLibrary(NML)wasstartedin1961bytheSchoolMathematicsStudyGrouptomakeavailabletohighschoolstudentsshortex
3、positorybooksonvarioustopicsnotusuallycoveredinthehighschoolsyllabus.InadecadetheNMLmaturedintoasteadilygrowingseriesofsometwentytitlesofinterestnotonlytotheoriginallyintendedaudience,buttocollegestudentsandteachersatalllevels.PreviouslypublishedbyRandomHouseandL.W.Singe
4、r,theNMLbecameapublicationseriesoftheMathematicalAsso-ciationofAmerica(MAA)in1975.UndertheauspicesoftheMAAtheNMLcontinuestogrowandremainsdedicatedtoitsoriginalandexpandedpurposes.Initsthirddecade,itcontainssomethirtytitles.U.S.A.MATHEMATICALOLYMPIADS,1972-1986Compiledand
5、withsolutionsbyMurrayS.KlamkinUniversityofAlberta33THEMATHEMATICALASSOCIATIONOFAMERICAProblemsaboutatriangleABConthesurfaceofaspherecanoftenbestbesolvedbyconsideringthewedgeshowninthecoverillustrationandthecentralanglesa,/3,andy.ThisimageiscourtesyofJamesHoffman,GANG,Uni
6、versityofMassachusetts,Amherst.©Geometry,Analysis,Numerics,andGraphicsGroup,UMASS,1988.FirstPrinting©1988bytheMathematicalAssociationofAmerica(Inc.)AllrightsreservedunderInternationalPan-AmericanCopyrightConventions.PublishedinWashington,D.C.byTheMathematicalAssociationo
7、fAmericaLibraryofCongressCatalogCardNumber88-062611CompleteSetISBN:0-88385-600-XVol.33ISBN:0-88385-634-4ManufacturedintheUnitedStatesofAmericaDedicatedtothememoryofSamuelL.GreitzerfirstchairmanoftheU.S.A.MathematicalOlympiadCommitteeandlongtimefriendandcolleague.NEWMATHE
8、MATICALLIBRARY1.Numbers:RationalandIrrationalbyIvanNiven2.WhatisCalculusAbout?byW.W.Sawyer3.AnIntroduct
