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A Mathematical Tapestry
Demonstrating the Beautiful Unity of Mathematics

$123.95

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  • Date Published: July 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521764100

$ 123.95
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About the Authors
  • This easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth.

    • Accessible to anyone interested in symmetry, numbers and patterns
    • Assumes no mathematical knowledge beyond school level
    • Open questions encourage the reader to pursue the subject further on their own
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    Awards

    • A Choice Outstanding Academic Title, 2011

    Reviews & endorsements

    'For some 30 years Peter Hilton and Jean Pedersen have written papers and books on mathematics, both recreational and advanced. Now they have pulled it all together in one exciting and handsome volume. It opens with detailed instructions on how to fold paper flexagons (there are now dozens of websites on these bewildering paper toys), followed by paper models of polygons and curious polyhedra, then on to other fascinating topics. The emphasis throughout is on symmetry and elegance. The writing is clear and informal, and the authors do not hesitate to include lovely proofs in number theory, algebra, geometry, and group theory. The book is a rich 'tapestry, as the authors call it, from first page to last.' Martin Gardner

    'The book demonstrates the great unity of mathematics. This is supported by a wealth of instructive illustrations …' Zentralblatt MATH

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    Product details

    • Date Published: July 2010
    • format: Hardback
    • isbn: 9780521764100
    • length: 308 pages
    • dimensions: 244 x 170 x 19 mm
    • weight: 0.69kg
    • contains: 175 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    1. Flexagons - a beginning thread
    2. Another thread - 1-period paper folding
    3. More paper folding threads - 2-period paper-folding
    4. A number-theory thread - folding numbers, a number trick, and some titbits
    5. The polyhedron thread - building some polyhedra and defining a regular polyhedron
    6. Constructing dipyramids and rotating rings from straight strips of triangles
    7. Continuing the paper-folding and number theory threads
    8. A geometry and algebra thread - constructing, and using, Jennifer's puzzle
    9. A polyhedral geometry thread - constructing braided platonic solids and other woven polyhedra
    10. Combinatorial and symmetry threads
    11. Some golden threads - constructing more dodecahedra
    12. More combinatorial threads - collapsoids
    13. Group theory - the faces of the tri-hexaflexagon
    14. Combinatorial and group theory threads - extended face planes of the platonic solids
    15. A historical thread - involving the Euler characteristic, Descartes' total angular defect, and Pólya's dream
    16. Tying some loose ends together - symmetry, group theory, homologues, and the Pólya enumeration theorem
    17. Returning to the number theory thread - generalized quasi-order and coach theorems
    References
    Index.

  • Authors

    Peter Hilton, State University of New York, Binghamton
    Peter Hilton is Distinguished Professor Emeritus in the Department of Mathematical Sciences at the State University of New York (SUNY), Binghamton.

    Jean Pedersen, Santa Clara University, California
    Jean Pedersen is Professor of Mathematics and Computer Science at Santa Clara University, California.

    Illustrated by

    Sylvie Donmoyer
    Sylvie Donmoyer is a professional artist and freelance illustrator.

    Awards

    • A Choice Outstanding Academic Title, 2011

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