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1、Theimpossiblewilltakeonlyalittlebitlonger*.MathematicsResourcePartIIofIII:GeometryTABLEOFCONTENTSI.LINES,PLANES,ANDANGLES2II.LINES,RAYS,ANDPLANES3III.ABITONANGLES5IV.TRIANGLES:THENUMERICALPERSPECTIVE8V.TRIANGLES:MORENUMERICALPERSPECTIVE11VI.TRIANGLES:THEABSTRACTPERSPECTIVE12VII.TRIA
2、NGLES:ANEWNUMERICALPERSPECTIVE16VIII.RECTANGLESANDSQUARESANDRHOMBUSES,OHMY!20IX.CIRCLES:ROUNDANDROUNDWEGO22X.CIRCLES:ANGLESOFEVERYSORT25XI.CIRCLES:SECANTS,TANGENTS,ANDCHORDS30XII.ABOUTTHEAUTHOR34BYCRAIGCHUCALIFORNIAINSTITUTEOFTECHNOLOGYPROOFREADINGLEAHSLOANINHERFOURTHYEARWITHDEMIDEC
3、*AQUOTEOFFEREDENTERINGFIRST-YEARSTUDENTSBYANOBELPRIZEWINNINGCHEMISTATACERTAINIVYLEAGUEUNIVERSITY,ATTRIBUTEDTOTHEARMYCORPSOFENGINEERSDURINGWORLDWARII:THEDIFFICULTISBUTTHEWORKOFAMOMENT.THEIMPOSSIBLEWILLTAKEONLYALITTLEBITLONGER.ITMAKESAGOODDECATHLONMAXIM,TOO.GEOMETRYRESOURCEDEMIDECRESO
4、URCES?2001DEMIDECRESOURCESANDEXAMSGEOMETRYINTRODUCTIONTOLINES,PLANES,ANDANGLESPointLineRayAngleVertexGeometryisaspecialtypeofmathematicthathasfascinatedmanforcenturies.Egyptianhieroglyphics,Greeksculpture,andtheRomanarchallmadeuseofspecificshapesandtheirproperties.Geometryisimportan
5、tnotonlyasatoolinconstructionandasacomponentoftheappearanceofthenaturalworld,butalsoasabranchofmathematicsthatrequiresustomakelogicalconstructstodeducewhatweknow.Inthestudyofgeometry,mosttermsarerigorouslydefinedandusedtoconveyspecificconditionsandcharacteristics.Afewterms,however,e
6、xistprimarilyasCconceptswithnostrictmathematicaldefinition.ThepointisthefirstoftheseHideas.Apointisrepresentedonpaperasadot.Ithasnoactualsize;itsimplyrepresentsauniqueplace.Totherightareshownthreepoints,namedC,H,andUU(capitallettersareconventionallyusedtolabelandrepresentpointsintex
7、t).Thenextgeometricideaisthatoftheline.Alineisaone-dimensionalobjectthatextendsinfinitelyinbothdirections.ItcontainspointsandisrepresentedCasalineonpaperwitharrowsatbothendstoindicatethatitdoesindeedmHextendindefinitely.LinesarenamedeitherwithtwopointsthatlieonthelineUorwithascriptl
8、etter.CH,HC,andmall
