Workbook-ReadingSpeakingandWriting

Readingtask FINDINGTHESOLUTION Unit1Workbook Tryyourbesttogooverthewholepointsofeachpicturewithoutliftingyourpencilfromthepaperorgoingoveranylinetwice A A D D B B C C Topology Eulerpath Euler What sEuler spuzzle Konigsbergisanislandandthereisariverbreakinghereintotwoparts SevenBridgesofKonigsberg andthefamous Eulerpath Peoplewonderediftheycouldwalkaroundthecitybycrossingthesevenbridgeswithoutgoingoveranyofthemtwiceorgoingbackonhimself butEulerfoundhecouldn tcrossallthesevenones ThisisEuler spuzzle Thefirststageinhisresearchistofindtheproblemthathecouldcrosssixofthebridgeswithoutgoingoveranyofthemtwiceorgoingbackonhimself buthecouldn tcrossallseven HowdidEulerprepareforhisresearch Thesecondstageistothinkofamethod Hedrewamapanduseddotsandlinestosimplifyhisanalysis Tryingandobservingoverandoveragain hefoundageneralrule Itistopology Euler stheoryiscalled TheEulerpath whichisexpressedlikethis Ifafigurehasmorethantwooddpoints youcan tgooveritwithoutliftingyourpencilfromthepageorgoingoveralinetwice SothegeneralrulethatEulerfoundistheevenpointsandtheoddpoints Whatarethetheories ConclusionEuler stheory 一笔画 可以一笔画只有两种情况 1 没有奇数顶点 2 只有两个奇数顶点 同学们如果对此类问题感兴趣 可登录 http www e Readthetextandfindouttheanswerstothefollowingquestions HowdidEulerfindaproblem What sthegeneralruletothepuzzle WhatbranchofmathematicsdidEulerstart WhenhewalkedaroundthetownandoverthebridgesofKonigsberg hewassurprisedtofindthathecouldcrosssixofthebridgeswithoutgoingoveranyofthemtwiceorgoingbackonhimself buthecouldn tcrossallseven HowdidEulerfindaproblem What sthegeneralruletothepuzzle WhatbranchofmathematicsdidEulerstart Ifafigurehasmorethantwooddpoints youcan tgooveritwithoutliftingyourpencilfromthepageorgoingoveralinetwice Hestartedawholenewbranchofmathematicscalled topology Fillinthechartafterreadingthetext Byturningthemapintoadiagram Onewhichhasanoddnumberoflinesgoingtoit Four Two Ifafigurehasmorethantwooddpoints youcannotgooveritwithoutliftingyourpencilfromthepageorwithoutgoingoveralinetwice Yes Lookatthefollowingpictures Checktoseeifyouarerightbyusingapenciltogooverthediagram Remembernottomissanypointsorgooveranylinetwice Giveareasonifthereisnopath Inpairsdiscussthelifeandworkofanyscientistthatyouknow Explaintheirachievementsandrecountstoriesthatshowinterestingaspectsoftheircharacterandtheirwork Talkabouthowtheyachievedtheirsuccess Wasitbecauseofhis hertalent intelligence hardwork persistence confidence curiosity enthusiasmorluck Preparetogiveatalkonyourchosenscientisttotheclass Thefollowingquestionsmayhelpyouwithyourdiscussion 1 Whoisthescientistyouadmiremost 2 Whatnationalityisthisscientist 3 Whatkindoffamilydidhe shecomefrom 4 Whatkindofeducationdidhe shereceive 5 Whatdidhe sheachieveinhis herscientificwork 6 Whydidhe sheachievegreatsuccess Nowwriteareportaboutyourscientist his herlife achievementsandthekeytohis hersuccess Beforeyoubegintowrite remembertoputyourinformationunderthreeheadings LifeAchievementsKeytosuccess Pleaseplanyourreportaccordingtothesesteps Introductiontothescientist includingdates wherehe shelivedandworkedandwhichb