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Mathematics of the Rubik's cube



EBook NameMathematics of the Rubik's cube
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EBook Description: Groups measure symmetry. No where is this more evident than in the study of symmetry in 2- and 3-dimensional geometric figures. Symmetry, and hence groups, play a key role in the study of crystallography, elementary particle physics, coding theory, and the Rubik' s cube, to name just a few. This is a book biased towards group theory not the 'the cube'. To paraphrase the German mathematician David Hilbert, the art of doing group theory is to pick a good example to learn from. The Rubik's cube will be our example. We motivate the study of groups by creating a group-theoretical model of Rubik's cube-like puzzles. Although some solution strategies are discussed (for the Rubik's cube - the 3 x 3 x 3 and 4 x 4 x 4 versions, the 'Rubik tetrahedron' or pyraminx, the the 'Rubik dodecahedron', or megaminx, the skewb, square 1, the masterball, and the equator puzzle), these are viewed more abstractly than most other books on the subject. We regard a solution strategy merely as a not-too-inefficient algorithm for producing all the elements in the associated group of moves.


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