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Algebra and Tiling: Homomorphisms in the Service of Geometry (Carus Mathematical Monographs)
Sherman Stein
Paperback. The Mathematical Association of America 2010-06-30.
ISBN 9780883850411
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Förlagets beskrivning
Often questions about tiling space or a polygon lead to questions concerning algebra. For instance, tiling by cubes raises questions about finite abelian groups. Tiling by triangles of equal areas soon involves Sperner's lemma from topology and valuations from algebra. The first six chapters of Algebra and Tiling form a self-contained treatment of these topics, beginning with Minkowski's conjecture about lattice tiling of Euclidean space by unit cubes, and concluding with Laczkowicz's recent work on tiling by similar triangles. The concluding chapter presents a simplified version of Rédei's theorem on finite abelian groups. Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper level algebra courses, but teachers, researchers and professional mathematicians will find the book equally appealing
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Algebra and Tiling: Homomorphisms in the Service of Geometry
Bokrecensioner » Algebra and Tiling: Homomorphisms in the Service of Geometry (Carus Mathematical Monographs)
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