[Conway,_Doyle,_Gilman,_Thurston.]_Geometry_and_the Imagination书籍

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1、GeometryandtheImaginationBasedonmaterialsfromthecoursetaughtattheUniversityofMinnesotaGeometryCenterinJune1991byJohnConway,PeterDoyle,JaneGilman,andBillThurstonVersion0.93,Fall1999DerivedfromworksCopyright(C)1991JohnConway,PeterDoyle,JaneGilman,BillThurstonContents1Bicycletracks32Pullingba

2、ckonapedal63Bicyclepedals74Bicyclechains95Pushleft,goleft136Knots137Reidemeistermoves158Notationforsomeknots159Knotsdiagramsandmaps15110Unicursalcurvesandknotdiagrams1811Exercisesinimagining1912Pizza2113Ideasforprojects2214Polyhedra2415Maps2616Eulernumbers2617Gas,water,electricity2918Topol

3、ogy3018.1Letters...............................3118.2Surfaces..............................3119Surfaces3120HowtoknitaM¨obiusBand3321Classicationofsurfaces3422Mirrors3523Morepaper-cuttingpatterns3524Symmetryandorbifolds3625Namesforfeaturesofsymmetricalpatterns3725.1Mirrorsandmirrorstrings.

4、...................3725.2Mirrorboundaries.........................4725.3Gyrationpoints..........................4725.4Conepoints............................4726Namesforsymmetrygroupsandorbifolds47227Theorbifoldshop4828TheEulercharacteristicofanorbifold4929PositiveandnegativeEulercharacteri

5、stic5330Aeldguidetotheorbifolds5430.1Conway'snames..........................5530.1.1Theprex.........................5530.1.2Thedescriptor.......................5630.2Howtolearntorecognizethepatterns.............5730.3Themanuscript..........................5831Geometryonthesphere5831.1Dis

6、cussion.............................5832Theangledefectofapolyhedron6433Descartes'sFormula.6433.1Firstproof.............................6433.2Secondproof...........................6534Thecelestialimageofapolyhedron6635Curvatureofsurfaces6736Clocksandcurvature7036.1Clocks....................

7、...........7136.2Curvature.............................7136.3Where'sthebeef?.........................731BicycletracksC.DennisThronhascalledattentiontothefollowingpassagefromTheAdventureofthePriorySchool,bySirArthurConanDoyle:`Thistrack,asyouperceive,wasmadebya