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More copies of this ISBNThis title in other editionsA Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematicsby Peter Hilton
Synopses & ReviewsPublisher Comments:This easytoread 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 paperfolding 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 handson experience constructing these models and to discover for themselves the patterns and relationships they unearth.
Book News Annotation:Each of the 17 chapters provides some arithmetic, some geometry, or some algebra, say Hilton (mathematical sciences, State U. of New YorkBinghamton) and Pedersen (mathematics and computer science, Santa Clara U., California), and are laced together with at least nine threads, such as paperfolding, numbertheory, polyhedral, geometry, algebra, combinatorial, symmetry, grouptheory, and historical. It is possible to follow a single thread through the entire book, though they do not recommend it, noting that the chapters demonstrate how a single idea in mathematics can lead in many different directions. Anyone with a knowledge of high school algebra and plane geometry should be able to follow the argument, even if they do not want to fold up the paper models. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)
Synopsis:Build paper polygons and discover how systematic paper folding reveals exciting patterns and relationships between seemingly unconnected branches of mathematics.
Synopsis:Using the simple geometric idea of systematic paper folding, the authors demonstrate the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions show how to build threedimensional polygons that help the reader unearth some surprising and delightful results.
About the AuthorPeter Hilton is Distinguished Professor Emeritus in the Department of Mathematical Sciences at the State University of New York (SUNY), Binghamton.Jean Pedersen is Professor of Mathematics and Computer Science at Santa Clara University, California.Sylvie Donmoyer is a professional artist and freelance illustrator.
Table of ContentsPreface; 1. Flexagons  a beginning thread; 2. Another thread  1period paper folding; 3. More paper folding threads  2period paperfolding; 4. A numbertheory 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 paperfolding 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 trihexaflexagon; 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 quasiorder and coach theorems; References; Index.
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Related SubjectsScience and Mathematics » Mathematics » General Science and Mathematics » Mathematics » Geometry » General Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry Science and Mathematics » Mathematics » Group Theory Science and Mathematics » Mathematics » Number Theory 

