000			03585cam a22003974a 4500
001			2010010230
003			DLC
005			20250203135600.0
008			100309s2010 nyua b 001 0 eng
010			_a 2010010230
020			_a9780521764100 (hardback)
020			_a0521764106 (hardback)
020			_a9780521128216 (pbk.)
020			_a0521128218 (pbk.)
035			_a(OCoLC)ocn564132786
040			_aDLC _cDLC _dYDX _dYDXCP _dBWK _dCDX _dBWX _dDLC
042			_apcc
049			_aEY8Z
050	0	0	_aQA36 _b.H53 2010
082	0	0	_a510 _222
100	1		_aHilton, Peter John.
245	1	2	_aA mathematical tapestry : _bdemonstrating the beautiful unity of mathematics / _cPeter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer.
260			_aNew York : _bCambridge University Press, _c2010.
300			_axv, 290 p. : _bill. ; _c25 cm.
520			_a"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"-- _cProvided by publisher.
504			_aIncludes bibliographical references and index.
505	8		_aMachine 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 PoÌlya's dream; 16. Tying some loose ends together - symmetry, group theory, homologues, and the PoÌlya enumeration theorem; 17. Returning to the number theory thread - generalized quasi-order and coach theorems; References; Index.
650		0	_aMathematics. _92885
700	1		_aPedersen, Jean.
700	1		_aDonmoyer, Sylvie.
856	4	2	_3Cover image _uhttp://assets.cambridge.org/97805217/64100/cover/9780521764100.jpg
948			_au330318
949			_aQA36 .H53 2010 _wLC _c1 _hEY8Z _i33039001177251
596			_a1
903			_a20196
999			_c20196 _d20196