MARC Record from harvard_bibliographic_metadata

LEADER: 03693cam a2200433 a 4500
001 012564261-X
005 20140130021556.0
008 100309s2010 enka b 001 0 eng
010 $a 2010010230
020 $a9780521764100 (hardback)
020 $a0521764106 (hardback)
020 $a9780521128216 (pbk.)
020 $a0521128218 (pbk.)
035 0 $aocn564132786
040 $aDLC$cDLC$dYDX$dYDXCP$dBWK$dCDX
042 $apcc
050 00 $aQA36$b.H53 2010
082 00 $a510$222
100 1 $aHilton, Peter John.
245 12 $aA mathematical tapestry :$bdemonstrating the beautiful unity of mathematics /$cPeter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer.
260 $aCambridge, UK ;$aNew York :$bCambridge University Press,$cc2010.
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 (p. 282-285) 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 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.
650 0 $aMathematics.
650 0 $aPaper work.
650 0 $aGeometrical models.
650 0 $aPolyhedra$xModels.
650 0 $aMathematics$xStudy and teaching.
650 0 $aGeometry$xStudy and teaching.
650 0 $aCombinatorial geometry$xStudy and teaching.
650 0 $aMathematical recreations.
700 1 $aPedersen, Jean.
700 1 $aDonmoyer, Sylvie.
899 $a415_356033
988 $a20100907
049 $aCLSL
906 $0DLC