book - adventures in group theory - rubiks cu

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1、AdventuresinGroupTheory:Rubik’sCube,Merlin’sMachine,andOtherMathematicalToysDavidJoyner8-30-2007Inmathematicsyoudon’tunderstandthings.Youjustgetusedtothem.JohannvonNeumannvContentsviiviiiContents1Elementary,mydearWatson11.1Youhavealogicalmindif........................1

2、1.1.1‘Youtalkingtome?’.....................61.2Elements,mydearWatson.....................72‘Andyoudoaddition?’132.1Functions...............................132.2Functionsonvectors.........................202.2.1History............................202.2.23×3matrices......

3、..................202.2.3m×nmatrices........................222.2.4Multiplicationandinverses.................232.2.5Determinants.........................242.3Relations...............................262.4Countingandmathematicalinduction...............293Bellringingandot

4、herpermutations353.1Definitions...............................353.2Inverses................................413.3Cyclenotation............................463.4Analgorithmtolistallthepermutations.............513.4.1WhySteinhaus’algorithmworks..............533.4.2Asideorde

5、rofdessert:cakecutting............543.5Permutationsandbellringing....................544Aprocessionofpermutationpuzzles594.115Puzzle...............................604.2TheHockeypuckpuzzle.......................614.3RainbowMasterball.........................624.4Pyramin

6、x...............................664.5Rubik’sCubes............................674.5.12×2×2Rubik’sCube...................674.5.23×3×3Rubik’sCube...................694.5.3Sometwo-playerRubik’sCubegames...........72ixCONTENTS4.6Skewb.................................734.7Me

7、gaminx...............................754.8Otherpermutationpuzzles......................785What’scommutativeandpurple?795.1Theunitquaternions.........................805.2Finitecyclicgroups..........................815.3Thedihedralgroup..........................825.4The

8、symmetricgroup........................835.5Generaldefinitions..........................845.5.1TheGordongame...........