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1、FractalMusic,~~~ercardsandMore...MathematicalRecreationsfromSCIENTIFICAMERICANMagazineFractalMusic,MathematicalRecreationsfromSCIENTIFICAMERICANMagazineMartinGardnerW.H.FreemanandCompanyNewYorkLibraryofCongressCataloging-in-PublicationDataGardner,Martin,1914-Fractalmusic,hypercardsandmore:m
2、athematicalrecreationsfromScientific:AmericanIbyMartinGardner.p.cn1.Includesindex.ISBN0-7167-2188-0.-ISBN0-7167-2189-9(pbk.)1.Mathematicalrecreations.I.ScientificAmerican.11.Title.QA95.Gi161991793.8-dc2091-17066CIPCopyrightO1992byW.H.FreemanandCompanyNopartofthisbookmaybereproducedbyanymech
3、anical,photographicorelectronicprocess,orintheformofaphonographicrecording,normayitbestoredinaretrievalsystem,transmittedorotherwisecopiedforpublicorprivateuse,withoutwrittenpermissionfromthepublisher.PrintedintheUnitedStatesofAmericaToDouglasHofstadterForopeningoureyestothe"strangeloops"in
4、sideourheads,tothedeepmysteriesofmemory,intelligence,andself-awareness,andfortheincomparableinsights,humor,andwordplayinhiswrit-ings.PrefaceixChapterOneWhite,Brown,andFractalMusic1ChapterTwoTheTinklyTempleBells24ChapterThreeMathematicalZoo39ChapterFourCharlesSandersPeirce61ChapterFiveTwiste
5、dPrismaticRings76ChapterSixTheThirtyColorCubes88ChapterSevenEgyptianFractions100ChapterEightMinimalSculpture110ChapterNineMinimalSculptureI1133ChapterTenTangentCircles149ChapterElevenTheRotatingTableandOtherProblems167ChapterTwelveDoesTimeEverStop?CanthePastB;eAltered?191ChapterThirteenGene
6、ralizedTicktacktoe202ChapterFourteenPsychicWondersandProbability2I14ChapterFifteenMathematicalChessProblems228ChapterSixteenDouglasHofstadter'sadel,Escher,Bach243ChapterSenenteenImaginaryNumbers257ChapterEighteenPiandPoetry:SomeAccidentalPatterns271ChapterNineteenMoreonPoetry281ChapterTwent
7、yPackingSquares289ChapterTwenty-oneChaitin'sOmega307NameIndex321hisbookreprintsmyMathematicalGamescolumnsfromtheT1978and1979issuesofScientificAmericanMagazine.Itisthefourteenthsuchcollection,andIhaveonemoretogobe-forerunningoutofcolumns.Asinpreviousantho
