Title: Algebra and Tiling: Homomorphisms in the Service of Geometry (Carus Mathematical Monographs, Series Number 25)
Publisher: The Mathematical Association of America
Publication Date: 1996
Language: English
ISBN 10: 0883850281
ISBN 13: 9780883850282
Binding: hardcover
Condition: New
Weight: 14 ounces

About this title

Synopsis

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 R�dei'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.

About the Authors

Sherman Stein received his PhD from Columbia University. His research interests are primarily algebra and combinatorics. He has received the Lester R. Ford prize for exposition. He is now retired from teaching at the University of California, Davis.

Sandor Szab� received his PhD from E�tv�s University. He currently teaches in the Institute of Mathematics and Informatics at the University of P�cs, in Hungary.

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