applied geometry应用几何

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1、Page25VocationalMathIAppliedGeometryAlLehnen,MadisonAreaTechnicalCollegeAppliedGeometryThewordgeometryinGreekmeans“earthmeasurement”andhaditsoriginsinproblemsassociatedwithsurveying.Inthesenotesweareconsideringplaneorflattwo-dimensionalgeometry.(Solidg

2、eometrystudiesobjectsinthreedimensions.)Thefundamentalnotionsusedtodescribeplanarobjectsarepointsandlines.Twodifferentpointsdefineoneandonlyonelinethatpassesthroughbothofthemandtheshortestdistancebetweenthetwopointsisalongthisline.Weshallusecapitallett

3、erssuchasAtolabelpointsandapairofletterssuchasABtolabelthesegmentofthelinebetweenAandB.Linesegmentsaremeasuredinunitsoflengthsuchasfeetormeters.Twolinesinaplaneeitherintersectatasinglepointorareparallel.Wherethelinesmeetfour“openings”oranglesareformeda

4、sshownbelow.ThesymbolÊisusedforthewordangle.Inordertolabelanglesseveralconventionsareused.Asshownintheabovepicture,thepointwherethelinesintersectAiscalledthevertexofthefourangles.Theseparateanglesarethennamedbyindicatingapointoneachofthetwolineswhichac

5、tassidesoftheangle.ThusÊBADistheanglewithvertexatAandwithsidesthatincludesegmentsABandAD.ThissameanglecouldalsobelabeledasÊDAB.Alessprecisebutmoreconvenientnotationistolabelanglesbyasingleletterornumber,providedthatthesymbolisplacedappropriatelyinthedi

6、agram.Forexample,intheabovediagramÊ1=ÊEAD.ThemostcommonlyusedmeasureforanglesisthedegreesystemdevelopedbytheBabyloniansover3000yearsago.Theydecidedforreasonsofeasydivisibilitybywholenumberstodivideacircleinto360equalunitsofanglecalledadegreeandsignifie

7、dbythesymbolE.Forprecisesurveyingorproblemsinastronomyasmallerunitisrequired.Thisleadtotheminutewhichis1/60’thofadegreeandthesecondwhichis1/60’thofaminute.ThesymbolforminuteisN,whilethesymbolforsecondisO.Page25VocationalMathIAppliedGeometryAlLehnen,Mad

8、isonAreaTechnicalCollegeThus,wehaveand.AnangletothenearestsecondcouldbespecifiedasÊ4=37E29N54O,thisnotationiscalledDMSforDegreeMinuteSecond.ToavoidfractionsthissameanglecouldbegiveninDD(DecimalDegrees)as.WecouldalsogofromDDtoDMSasfollow