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人教课标高二必修5 Unit1,ReadingtaskonPage44Unit1Greatscientists,What’sEuler’spuzzle?Koningsbergisanislandandthereisariverbreakingitintotwoparts.“SevenBridgesofKonigsberg”andthefamous“Eulerpath”.,Peoplewonderediftheycouldwalkaroundthecitybycrossingthesevenbridgeswithoutgoingoveranyofthemtwiceorgoingbackonhimself,butEulerfoundhecouldn’tcrossallthesevenones.ThisisEuler’spuzzle.,Thefirststageinhisresearchistofindtheproblemthathecouldcrosssixofthebridgeswithoutgoingoveranyofthemtwiceorgoingbackonhimself,buthecouldn’tcrossallseven.HowdidEulerprepareforhisresearch?,Thesecondstageistothinkofamethod:Hedrewamapanduseddotsandlinestosimplifyhisanalysis.Tryingandobservingoverandoveragain,hefoundageneralrule.,Itistopology.Euler’stheoryiscalled“TheEulerpath”,whichisexpressedlikethis:Ifafigurehasmorethantwooddpoints,youcannotgooveritwithoutliftingyourpencilfromthepageorgoingoveralinetwice.Whatarethetheories?,SothegeneralrulethatEulerfoundistheevenpointsandtheoddpoints.Lookatthefollowingpictures:,,,,,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。,
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