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1、AnImaginaryTaleCopyright©1998byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,3MarketPlace,Woodstock,OxfordshireOX201SYAllRightsReservedFifteenthprinting,andfirstpaperbackprint
2、ing,withanewprefaceandappendixesbytheauthor,2007PaperbackISBN-13:978-0-691-12798-9PaperbackISBN-10:0-691-12798-0TheLibraryofCongresshascatalogedtheclotheditionofthisbookasfollowsNahin,PaulJ.Animaginarytale:thestoryof[thesquarerootofminusone]/PaulJ.Nahin.p.cm.Ont.p.“[thesq
3、uarerootofminusone]”appearsasaradicalover“–1”.Includesbibliographicalreferencesandindexes.1.Numbers,Complex.I.Title.QA255.N341998ISBN0-691-02795-1(cloth:alk.paper)515'.9—dc2197-52082BritishLibraryCataloging-in-PublicationDataisavailableThisbookhasbeencomposedinTimesRomanP
4、rintedonacid-freepaper.∞pup.princeton.eduPrintedintheUnitedStatesofAmerica151617181920DEDICATEDTOMYMOTHERKATHERINEDOROTHYMARKFELDERANDTOTHEMEMORYOFMYFATHERPAULGILBERTNAHIN(1916±1990)ThispageintentionallyleftblankANotetotheReaderANIMAGINARYTALEhasaverystronghistoricalcompo
5、nenttoit,butthatdoesnotmeanitisamathematicallightweight.Butdon'treadtoomuchintothateither.Itisnotascholarlytomemeanttobereadonlybysomemythical,elitegroup,suchastheonedescribedinthe1920sfablethatclaimedtherewereonlytwelvepeopleintheworldwhoreallyunderstoodEinstein.Ï21haslo
6、nglaboredunderasimilarfalsestoryofunfathomablemystery.TheFrenchphilosophicalgeniusoftheEnlightenment,DenisDiderot,wroteofmathe-maticiansthattheyªresemblethosewhogazeoutfromthetopsofhighmoun-tainswhosesummitsarelostintheclouds.Objectsontheplainbelowhavedisappearedfromview;
7、theyareleftwithonlythespectacleoftheirownthoughtsandtheconsciousnessoftheheighttowhichtheyhaverisenandwhereperhapsitisnotpossibleforeveryonetofollowandbreathe[thethinair].ºWell,inthisbooktheairisalmostalwaysatsea-levelpressure.Largechunksofthisbookcan,infact,bereadandunde
8、rstoodbyahighschoolseniorwhohaspaidattentiontohisorherteachersinthestandardfareofpre-collegecour
