Algebra and Tiling
Homomorphisms in the Service of Geometry
Series: Carus Mathematical Monographs; 25;
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Product details:
- Publisher The Mathematical Association of America
- Date of Publication 15 July 2010
- ISBN 9780883850411
- Binding Paperback
- No. of pages222 pages
- Size 210x142x10 mm
- Weight 260 g
- Language English 0
Categories
Short description:
A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
MoreLong description:
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&&&233;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.
'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
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. R&&&233;dei's theorem; 8. Epilogue; Appendices; References.
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