1622

demonstrating the beautiful unity of mathematics

Peter Hilton, Jean Pedersen ; with illustrations by Sylvie Donmoyer

Cambridge University Press

2010

xv, 290 p. ill. 25 cm

Includes bibliographical references and index , 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 Plya's dream; 16. Tying some loose ends together - symmetry, group theory, homologues, and the Plya enumeration theorem; 17. Returning to the number theory thread - generalized quasi-order and coach theorems; References; Index.

Pedersen, Jean , Donmoyer, Sylvie ,

QA

36

.H53

2010