03118cam a22002774a 4500 100309s2010 nyua b 001 0 eng 9780521764100 0521764106 9780521128216 0521128218 SDU QA36 H641 M 2010 Hilton, Peter John. 219342 A mathematical tapestry : demonstrating the beautiful unity of mathematics / Peter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer. New York : Cambridge University Press, 2010. 290 p. : ill. Machine generated contents note: 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. HKBU library YT2025 M10 "This easy-to-read 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"-- Mathematics. Pedersen, Jean. 219343 Donmoyer, Sylvie. 219344 = C.1 SDU GBE lcc 112437 112437 0 0 lcc 0 QA0036 H641 M2010 0 CGB 284406 SDU SDU GEN3 2025-10-09 2 0 QA36 H641 M 2010 1000377847 2025-10-09 00:00:00 C.1 2025-10-09 GBE