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Algebra and Tiling

Algebra and Tiling
Homomorphisms in the Service of Geometry

$42.00 (P)

Part of Carus Mathematical Monographs

  • Date Published: July 2010
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Paperback
  • isbn: 9780883850411

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About the Authors
  • 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.

    • Self-contained explanation of the requisite algebra
    • Tiling problems are placed in their historical background to help focus the reader
    • Includes both worked exercises and unsolved problems, to invite further research
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    Reviews & endorsements

    'Algebra and Tiling is perfect for bringing alive an abstract algebra course. Intuitive but difficult problems of geometry are translated into algebraic problems more amenable to solution. Full of nice surprises, the book is a pleasure to read.' Choice

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    Product details

    • Date Published: July 2010
    • format: Paperback
    • isbn: 9780883850411
    • length: 222 pages
    • dimensions: 210 x 142 x 10 mm
    • weight: 0.26kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    1. Minkowski's conjecture
    2. Cubical clusters
    3. Tiling by the semicross and cross
    4. Packing and covering by the semicross and cross
    5. Tiling by triangles of equal areas
    6. Tiling by similar triangles
    7. Rédei's theorem
    8. Epilogue
    Appendices
    References.

  • Authors

    Sherman Stein
    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 Szabó, University of Bahrain
    Sandor Szabó received his PhD from Eötvös University. He currently teaches in the Institute of Mathematics and Informatics at the University of Pécs, in Hungary.

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