应用数学专业外文翻译

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1、本科毕业论文外文翻译外文译文题目（中文）：具体数学：汉诺塔问题学院:专业:学号:学生姓名:指导教师:日期:二○一二年六月武汉科技大学本科毕业论文外文翻译1RecurrentProblemsTHISCHAPTEREXPLORESthreesampleproblemsthatgiveafeelforwhat’stocome.Theyhavetwotraitsincommon:They’veallbeeninvestigatedrepeatedlybymathematicians;andtheirsolutio

2、nsallusetheideaofrecurrence,inwhichthesolutiontoeachproblemdependsonthesolutionstosmallerinstancesofthesameproblem.1.1THETOWEROFHANOILet’slookfirstataneatlittlepuzzlecalledtheTowerofHanoi,inventedbytheFrenchmathematicianEdouardLucasin1883.Wearegivenatower

3、ofeightdisks,initiallystackedindecreasingsizeononeofthreepegs:Theobjectiveistotransfertheentiretowertooneoftheotherpegs,movingonlyonediskatatimeandnevermovingalargeroneontoasmaller.LucasfurnishedhistoywitharomanticlegendaboutamuchlargerTowerofBrahma,which

4、supposedlyhas64disksofpuregoldrestingonthreediamondneedles.Atthebeginningoftime,hesaid,Godplacedthesegoldendisksonthefirstneedleandordainedthatagroupofpriestsshouldtransferthemtothethird,accordingtotherulesabove.Thepriestsreportedlyworkdayandnightattheirt

5、ask.Whentheyfinish,theTowerwillcrumbleandtheworldwillend.5武汉科技大学本科毕业论文外文翻译It'snotimmediatelyobviousthatthepuzzlehasasolution,butalittlethought(orhavingseentheproblembefore)convincesusthatitdoes.Nowthequestionarises：What'sthebestwecando？Thatis，howmanymoves

6、arenecessaryandsufficienttoperformthetask?Thebestwaytotackleaquestionlikethisistogeneralizeitabit.TheTowerofBrahmahas64disksandtheTowerofHanoihas8；let'sconsiderwhathappensifthereareTLdisks.Oneadvantageofthisgeneralizationisthatwecanscaletheproblemdowneven

7、more.Infact,we'llseerepeatedlyinthisbookthatit'sadvantageoustoLOOKATSMALLCASESfirst.It'seasytoseehowtotransferatowerthatcontainsonlyoneortwodisks.Andasmallamountofexperimentationshowshowtotransferatowerofthree.Thenextstepinsolvingtheproblemistointroduceap

8、propriatenotation：NAMEANOCONQUER.Let'ssaythatTnistheminimumnumberofmovesthatwilltransferndisksfromonepegtoanotherunderLucas'srules.ThenT1isobviously1,andT2=3.Wecanalsogetanotherpieceofdataforfree,byconsideringthesma