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1、SYMMETRYBYHERMANNWEYLPRINCETONUNIVERSITYPRESS,PRINCETON,NEWJERSEYPREFACEANDBlBLlOGRAPHlCALREMARKSSTARTINGfromthesomewhatvaguenotionofsymmetry=harmonyofproportions,thesefourlecturesgraduallydevelopfirstthegeometricconceptofsymmetryinitsseveralforms,as
2、bilateral,translatory,rotational,ornamentalandcrystallographicsymmetry,etc.,andfinallyrisetothegeneralideaunder-Copyright1952byPrincetonUniversityPresslyingallthesespecialforms,namelythatofCopyrightOrenewed1980byPrincetoninvarianceofaconfigurationofe
3、lementsUniversityPressunderagroupofautomorphictransforma-tions.Iaimattwothings:ontheonehandPublishedbyPrincetonUniversityPress,41WilliamStreet,todisplaythegreatvarietyofapplicationsPrinceton,NewJersey08540oftheprincipleofsymmetryinthearts,ininorganic
4、andorganicnature,onthe'otherALLRIGHTSRESERVEDhandtoclarifystepbystepthephilosophico-LCC52-5830mathematicalsignificanceoftheideaofsym-ISBN0-691-08045-3metry.Thelatterpurposemakesitneces-sarytoconfrontthenotionsandtheoriesofISBN0-691-02374-3,PSLpbk.sym
5、metryandrelativity,whilenumerousillustrationssupportingthetexthelptoPrintedintheUnitedStatesofAmericaaccomplishtheformer.byPrincetonUniversityPress,Princeton,NewJerseyAsreadersofthisbookIhadawidercircleinmindthanthatoflearnedspecialists.ItFirstPrince
6、tonPaperbackprinting,1982doesnotshunmathematics(thatwoulddefeatFirstPrincetonScienceLibraryprinting,1989itspurpose),butdetailedtreatmentofmostoftheproblemsitdealswith,inparticularcompletemathematicaltreatment,isbeyonditsscope.Tothelectures,whichrepro
7、duceinslightlymodifiedversiontheLouisClarkVanuxemLecturesgivenbytheauthoratPrincetonUniversityinFebruary1951,twoappendicescontainingmathematicalproofshavebeenadded.Otherbooksinthefield,asforinstanceF.M.Jaeger'sclassicalLecturesontheprincipleofsymmetr
8、yanditsapplicationsinnaturalscience(AmsterdamandLondon,1917)'orthemuchsmallerandmorerecentbookletbyJacqueNicolle,Lasymitrieetsesapplications(Paris,AlbinMichel,1950)coveronlypartofthematerial,thoughinamoredetailedBilateralsymmetryfashion.Symmetryisbut
