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1、FlatlandFlatlandbyEdwinA.Abbott18841FlatlandPART1THISWORLDSECTION1OftheNatureofFlatlandIcallourworldFlatland,notbecausewecallitso,buttomakeitsnatureclearertoyou,myhappyreaders,whoareprivilegedtoliveinSpace.ImagineavastsheetofpaperonwhichstraightLines,Triangl
2、es,Squares,Pentagons,Hexagons,andotherfigures,insteadofremainingfixedintheirplaces,movefreelyabout,onorinthesurface,butwithoutthepowerofrisingaboveorsinkingbelowit,verymuchlikeshadows--onlyhardwithluminousedges--andyouwillthenhaveaprettycorrectnotionofmycoun
3、tryandcountrymen.Alas,afewyearsago,Ishouldhavesaid"myuniverse:"butnowmymindhasbeenopenedtohigherviewsofthings.Insuchacountry,youwillperceiveatoncethatitisimpossiblethatthereshouldbeanythingofwhatyoucalla"solid"kind;butIdaresayyouwillsupposethatwecouldatleast
4、distinguishbysighttheTriangles,Squares,andotherfigures,movingaboutasIhavedescribedthem.Onthecontrary,wecouldseenothingofthekind,notatleastsoastodistinguishonefigurefromanother.Nothingwasvisible,norcouldbevisible,tous,exceptStraightLines;andthenecessityofthis
5、Iwillspeedilydemonstrate.PlaceapennyonthemiddleofoneofyourtablesinSpace;andleaningoverit,lookdownuponit.Itwillappearacircle.Butnow,drawingbacktotheedgeofthetable,graduallyloweryoureye(thusbringingyourselfmoreandmoreintotheconditionoftheinhabitantsofFlatland)
6、,andyouwillfindthepennybecomingmoreandmoreovaltoyourview,andatlastwhenyouhaveplacedyoureyeexactlyontheedgeofthetable(sothatyouare,asitwere,actuallyaFlatlander)2Flatlandthepennywillthenhaveceasedtoappearovalatall,andwillhavebecome,sofarasyoucansee,astraightli
7、ne.ThesamethingwouldhappenifyouweretotreatinthesamewayaTriangle,oraSquare,oranyotherfigurecutoutfrompasteboard.Assoonasyoulookatitwithyoureyeontheedgeofthetable,youwillfindthatitceasestoappeartoyouasafigure,andthatitbecomesinappearanceastraightline.Takeforex
8、ampleanequilateralTriangle--whorepresentswithusaTradesmanoftherespectableclass.Figure1representstheTradesmanasyouwouldseehimwhileyouwerebendingoverhimfromabove;figures2and3representtheTradesman,