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1、TheBeautyofEverydayMathematicsNorbertHerrmannTheBeautyofEverydayMathematicsCopernicusBooksAnImprintofSpringerScienceþBusinessMediaDr.Dr.h.c.NorbertHerrmannUniversitätHannoverInstitutfürAngewandteMathematikWelfengarten130167HannoverGermanyDr.Dr.Herrmann@googlemail.comTranslatedfromGermanbyMartina
2、Lohmann-Hinner,mlh.communications©Springer-VerlagBerlinHeidelberg2012Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.Publi
3、shedintheUnitedStatesbyCopernicusBooks,animprintofSpringerScience+BusinessMedia.CopernicusBooksSpringerScience+BusinessMedia233SpringStreetNewYork,NY10013www.springer.comLibraryofCongressControlNumber:2011940689MathematicsSubjectClassification(2010):00A09Translationfromthe3rdGermaneditionMathema
4、tikistüberallbyNorbertHerrmann,withkindpermissionofOldenbourgVerlagGermany.Copyright©byOldenbourgVerlagGermany.Allrightsreserved.Printedonacid-freepaperISBN978-3-642-22103-3e-ISBN978-3-642-22104-0DOI10.1007/978-3-642-22104-0PrefaceOnceuponatime,therewasagroupofrepresentativesfromtheStateofUtahin
5、theUnitedStatesofAmericaaroundtheyear1875.OneofthemwasJamesA.Garfield.Duringabreak,theyweresittinginthecongressionalcafeteria.Topassthetime,oneofthem,namelyMr.Garfield,suggestedthattheytakealookatthePythagoreanTheorem.Eventhoughthisfamoustheoremhadalreadybeenstudiedandproven2000yearsago,hewantedto
6、comeupwithanewproof.Togetherwithhiscolleagues,heworkedforalittlewhile,anddiscoveredthefollowingconstruction:CB•βαA•β•αDEFig.0.1SketchprovingthePythagoreanTheorem.vviPrefaceHere,weavethecrosshatchedrighttriangleABC.Wesketchthistriangleoncemorebelowit,thoughthistimeturnedslightlysothatsideADliese
7、xactlyontheextensionofsideAC.TheconnectinglineEBcompletesthefigure,turningitintoatrapezoidbecausethebot-tomsideisparalleltothetopsidethankstotherightangles.Thetwotrianglesmeet,withtheiranglesαandβ,atA.Becausethetrianglesareri
