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1、Draft,May,1997MATHEMATICSANDARTMarcFrantzDepartmentofMathematicalSciencesIUPUI402NorthBlackfordStreetIndianapolis,Indiana46202-3216mfrantz@math.iupui.educbyMarcFrantz1997.Allrightsreserved.ALSCNIEThisprojectwassupported,inpart,OINTCbytheANnfENationalSci
2、enceFoundationFONOpinionsexpressedarethoseoftheauthorsUIONDATandnotnecessarilythoseoftheFoundationLinearPerspective1.BasicResultsFigure1(a).Figure1(b).TakeagoodlookattheimagesinFigure1.Figure1(a)isadetailfromanillumi-natedmanuscriptcalledtheTresRichesH
3、eures,paintedbytheLimbourgbrothers,Paul,HermannandJean,inthe fteenthcentury.Figure1(b)isadetailfromaneighteenthcenturyoilpaintingbytheItalianartistCanaletto(GiovanniAntonioCanal),entitledViewoftheGrandCanaltowardsthePallazzoContarinidagliScrigni.Ofallth
4、ethingsonemightnoticeabouttheseworks,wewouldliketofocusononespeci caspect,namelytheillusionofdepthinthree-dimensionalspace,whichisfarmoree ectiveandbelievableinthepaintingontheright.Giventhattheartistsineithercasewereconsideredverycompetentintheirtime,i
5、twouldappearthatsomethinghappenedinEuropebetweenthe fteenthcenturyandtheeighteenthcenturythataddedapowerfulnewtooltotheartist'stoolbox.Thesomething"wastheRenaissance,aperiodofvigorousandcreativeactivityintheartsandsciences.Thepowerfulnewtoolwasamathema
6、ticaltechniquecalledlinearperspective,"orjustperspective."Anillusionofdepthisnotnecessarilythemostimportantaspect
7、orevenanecessaryaspect
8、ofasuccessfulpainting.Butwheneverthee ecthasbeenneeded,ithasbeenfoundthataknowledgeofmathematicsisanindispensablet
9、oolinachievingit.Infact,thisiswhywehavechosentocomparetwopaintingsfromEurope,fornowherewasthee ectofperspectiveuponartmoredramatic.Moreover,theuseofmathematicalperspectiveisperhapsmoreimportanttodaythaneverbefore,ifoneconsidersmoderncreativemediasuchas
10、lmmaking,computergraphics,andvirtualrealitythathavebeenmadepossiblebyadvancesintechnology.1Figure2.Computer-aidedperspectivehelpsbringtolifealandscapewithdinosaursinJurassicPark.Theideabehindtheconceptoflinearperspective"isillus
