旋转在数学解题中发挥的重要作用（the important role of rotation in solving mathematical problems）

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1、旋转在数学解题中发挥的重要作用（Theimportantroleofrotationinsolvingmathematicalproblems）DataworthhavingFromtheusualstudy,accumulationandsummaryWherethereisaproblem,theremustbesomePleasealsocriticizeandcorrectme!TheimportantroleofrotationinsolvingmathematicalproblemsDawuCo

2、untyhighschoolChenJieChenRuishopAbstract:rotationisakindoftransformationofplanegeometryItistocircleacertainfigureintheplane(thecenterofrotation)Rotateanangle(rotationangle)inacertaindirectionConstructanewgraphUsingtheshapeofarotatedfigureThetraitofnotchang

3、inginsizeSoastofindawaytosolveproblems[Keywords]arouseinterest,optimizeintegration,mastermethod,difficulttoeasyFirst,createscenariosStimulatestudents'interestinrotationManlivesontheearthTheearthalwaysmovesroundthesunandrotatesfromwesttoEastMakespring,summe

4、r,autumnandwinterclearallyearroundThetrains,planes,andshipsthatwetravelarealltyresofwheelsTherailsandpropellerskeptturningusroundtoourdestination;theclockhungontheblackboardintheclassroomThesecondhourandminutenon-stoprotationBringustoabettertomorrowWaitLif

5、eisfullofspinSpinninggivesuscouragetoliveRotationaddswisdomtoourproblemsolvingRotationgivesusagreatdealofpowertosolvedifficultproblemsDEG[1]casesofdeltaABCDeltaDEFtorotatearoundthefixedpointOpositionFigure1(1)whatisthecenterofrotation?Whatistheangleofrotat

6、ion?Howmanyrotationanglesdoyouhave?Whatkindofrelationshipdotheyhave?(2)whereisthepositionoftherotatingpointAandtherotatingpointBrespectively?(3)whatistherelationshipbetweenthelinesegmentOAandthelengthofOD?WhataboutOBandOF,OCandOE?(4)theABCaroundthepointOan

7、drotatedby90DEGIfyougetaGHKConnectAG,BH,CKHowmanyisoscelesrighttrianglesarethereinthepicture?(5)theABCOafterthe180degreerotationaroundafixedpointIfyougetaGHKThepositionrelationshipbetweentheABCvalueandGHKis.SABCSDeltaDeltaDeltaGHK[case2]thefollowingfourfig

8、uresareequilateraltrianglesSquareFive-pointedstarRegularhexagonAfterpointingouthowmanydegreestheyrotateatleast,theycancoincidewiththemselvesABCDFigure2Thusweobtainthepropertiesofthegraphbeforeandaftertherotat