Sherman Stein, Sandor Szabó's Algebra and Tiling: Homomorphisms in the Service of Geometry PDF

By Sherman Stein, Sandor Szabó

ISBN-10: 0883850281

ISBN-13: 9780883850282

Usually questions on tiling area or a polygon result in questions referring to algebra. for example, tiling through cubes increases questions on finite abelian teams. Tiling by means of triangles of equivalent parts quickly includes Sperner's lemma from topology and valuations from algebra. the 1st six chapters of Algebra and Tiling shape a self-contained remedy of those subject matters, starting with Minkowski's conjecture approximately lattice tiling of Euclidean area by means of unit cubes, and concluding with Laczkowicz's fresh paintings on tiling via comparable triangles. The concluding bankruptcy provides a simplified model of Rédei's theorem on finite abelian teams. Algebra and Tiling is obtainable to undergraduate arithmetic majors, as lots of the instruments essential to learn the booklet are present in usual top point algebra classes, yet academics, researchers mathematicians will locate the booklet both attractive.

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Extra info for Algebra and Tiling: Homomorphisms in the Service of Geometry

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Lagarias and P. W. Shor, Keller's cube-tiling conjecture is false in high dimensions, Bull. Amer. Math. Soc. 27 (1992), 279-283. 10. A. K. Lenstra, H. W. Lenstra, and L. Loväsz, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534. 11. H. Minkowski, Geometrie der Zahlen, Teubner, Leipzig, 1896. 12. ,DiophantischeApproximationen, Teubner, Leipzig, 1907 (reprint: Physica- Verlag, Würzberg, 1961). 13. , Gesammelte Abhandlungen von Hermann Minkowski, Chelsea, New York, 1967.

U. Inst, angew. Math. Univ. Berlin 1 (1933), 186-212. 20. S. K. Stein, Algebraic tiling, Amer. Math. Monthly 81 (1974), 445-462. 21. S. Szabo, A reduction of Keller's conjecture, Periodica Math. Hung. 17 (1986), 265-277. 22. M. F. Woepcke, Recherches sur plusieurs ouvrages de Leonard de Pise decouverts et publies par Μ. le prince Balthasar Boncompagni et sur les rapports que existent entre les ouvrages et les travaux mathematiques des Arabes, Atti della Academia dei Lincei 14 (1861), 301-324. Chapter 2 Cubical Clusters In Chapter 1 we were concerned with the way translates of a single cube fit together to tile space.

166 (1979), 225-264. 34 ALGEBRA AND TILING 19. T. Schmidt, Uber die Zerlegung des n-dimensionalen Raumes in gitterformig angeordnete Würfeln, Sehr. math. Semin. u. Inst, angew. Math. Univ. Berlin 1 (1933), 186-212. 20. S. K. Stein, Algebraic tiling, Amer. Math. Monthly 81 (1974), 445-462. 21. S. Szabo, A reduction of Keller's conjecture, Periodica Math. Hung. 17 (1986), 265-277. 22. M. F. Woepcke, Recherches sur plusieurs ouvrages de Leonard de Pise decouverts et publies par Μ. le prince Balthasar Boncompagni et sur les rapports que existent entre les ouvrages et les travaux mathematiques des Arabes, Atti della Academia dei Lincei 14 (1861), 301-324.

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Algebra and Tiling: Homomorphisms in the Service of Geometry by Sherman Stein, Sandor Szabó


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