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1、2.5笛卡尔几何学的基本概念（basicconceptsofCartesiangeometry）课文5-AthecoordinatesystemofCartesiangeometryAsmentionedearlier,oneoftheapplicationsoftheintegralisthecalculationofarea.Ordinarily,wedonottalkaboutareabyitself,instead,wetalkabouttheareaofsomething.Thismeansthatwehavecertainobjects(polyg
2、onalregions,circularregions,parabolicsegmentsetc.)whoseareaswewishtomeasure.Ifwehopetoarriveatatreatmentofareathatwillenableustodealwithmanydifferentkindsofobjects,wemustfirstfindaneffectivewaytodescribetheseobjects.Themostprimitivewayofdoingthisisbydrawingfigures,aswasdonebytheanci
3、entGreeks.AmuchbetterwaywassuggestedbyReneDescartes,whointroducedthesubjectofanalyticgeometry(alsoknownasCartesiangeometry).Descartes’ideawastorepresentgeometricpointsbynumbers.Theprocedureforpointsinaplaneisthis：Twoperpendicularreferencelines(calledcoordinateaxes)arechosen,onehoriz
4、ontal(calledthe“x-axis”),theothervertical(the“y-axis”).TheirpointofintersectiondenotedbyO,iscalledtheorigin.Onthex-axisaconvenientpointischosentotherightofOanditsdistancefromOiscalledtheunitdistance.VerticaldistancesalongtheY-axisareusuallymeasuredwiththesameunitdistance,althoughsom
5、etimesitisconvenienttouseadifferentscaleonthey-axis.Noweachpointintheplane(sometimescalledthexy-plane)isassignedapairofnumbers,calleditscoordinates.Thesenumberstellushowtolocatethepoints.Figure2-5-1illustratessomeexamples.Thepointwithcoordinates(3,2)liesthreeunitstotherightofthey-ax
6、isandtwounitsabovethex-axis.Thenumber3iscalledthex-coordinateofthepoint,2itsy-coordinate.Pointstotheleftofthey-axishaveanegativex-coordinate;thosebelowthex-axishaveanegtivey-coordinate.Thex-coordinateofapointissometimescalleditsabscissaandthey-coordinateiscalleditsordinate.Whenwewri
7、teapairofnumberssuchas(a,b)torepresentapoint,weagreethattheabscissaorx-coordinate,aiswrittenfirst.Forthisreason,thepair(a,b)isoftenreferredtoasanorderedpair.Itisclearthattwoorderedpairs(a,b)and(c,d)representthesamepointifandonlyifwehavea=candb=d.Points(a,b)withbothaandbpositivearesa
8、idtolieinthefirstqu
