Home » Algebra and Tiling: Homomorphisms in the Service of Geometry by Sherman Stein
Algebra and Tiling: Homomorphisms in the Service of Geometry Sherman Stein

Algebra and Tiling: Homomorphisms in the Service of Geometry

Sherman Stein

Published September 5th 1996
ISBN : 9780883850282
Hardcover
218 pages
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 About the Book 

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 Sperners lemma from topology andMoreOften 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 Sperners 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 Minkowskis conjecture about lattice tiling of Euclidean space by unit cubes, and concluding with Laczkowiczs recent work on tiling by similar triangles. The concluding chapter presents a simplified version of Redeis 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.