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1、FelixKleinandSophusLieI.M.YaglomFelixKleinandSophusLieEvolutionoftheIdeaofSymmetryintheNineteenthCenturyTranslatedbySergeiSossinskyEditedbyHardyGrantandAbeShenitzerWith35Illustrationsand18PhotographsBirkhauserBoston·BaselI.M.YaglomAcademyofPedagogicalSciences"NIISHOTSOMoscow119905U.S.S.
2、R.LibraryofCongressCataloging-in-PublicationDataIAglom,I.M.(IsaakMoiseevich),1921-FelixKleinandSophusLie.1.Geometry-History.2.Symmetry-History.3.Klein,Felix,1849-1925.4.Lie,Sophus,1842-1899.5.Mathematicians-Biography.I.Title.QA443.5.118131988510'.92'2[B]85-13336CIP-KurztitelaufnahmederD
3、eutschenBibliothekYaglom,IsaakM.:FelixKleinandSophusLie/I.M.Yaglom.Boston;Basel:Birkhiiuser,1988.ISBN3-7643-3316-2(Basel)ISBN0-8176-3316-2(Boston)©BirkhiiuserBoston,1988Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,
4、electronic,mechanical,photocopying,recordingorotherwise,withoutpriorpermissionofthecopyrightowner.ISBN0-8176-3316-2ISBN3-7643-3316-2TypesetbyASCOTradeTypesettingLtd.,HongKong.PrintedandboundbyR.R.Donnelley&Sons,Harrisonburg,Virginia.PrintedintheU.S.A.987654321ForewordThisbookonthehistor
5、yofmathematicsmay,toacertainextent,beregardedasabiography.However,itdoesnottellthestoryofthelifeofaspecificperson(orthestoriesoftwopeople,asthetitlemayleadonetothink),butthestoryoftheevolutionofarathergeneralconcept,thatofsymmetry.Itismyfirmbeliefthatofallthegeneralscientificideaswhicha
6、roseinthenineteenthcenturyandwereinheritedbyourcentury,nonecontributedsomuchtotheintellectualatmosphereofourtimeastheideaofsymmetry.Thisisconfirmedbytheabundanceofbooksindifferentcategoriesandgenresdevotedtosymmetryinphysics,tosymmetryinchemistry,tosymmetryinbiologyandsoon,ortothegenera
7、l(occasionallyphilosophical)conceptofsymmetry.Themajorroleplayedbysymmetrynotionsinmoderneducationisattestedevenbythecoverdesignsofmanytextbooks,forinstanceH.R.Jacobs'sGeometry(Freeman,1974).Symmetryalsoplaysaroleinart,asevidencedby,say,theinterestshownfortheworksofthewell-know
