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 Polya's dream; 16. Tying some loose ends together - symmetry, group theory, homologues, and the Polya enumeration theorem; 17. Returning to the number theory thread - generalized quasi-order and coach theorems; References; Index.
Build paper polygons and discover how systematic paper folding reveals exciting patterns and relationships between seemingly unconnected branches of mathematics.
Peter 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.
'For some 30 years Peter Hilton and Jean Pedersen have written
papers and books on mathematics, both recreational and advanced.
Now they have pulled it all together in one exciting and handsome
volume. It opens with detailed instructions on how to fold paper
flexagons (there are now dozens of websites on these bewildering
paper toys), followed by paper models of polygons and curious
polyhedra, then on to other fascinating topics. The emphasis
throughout is on symmetry and elegance. The writing is clear and
informal, and the authors do not hesitate to include lovely proofs
in number theory, algebra, geometry, and group theory. The book is
a rich 'tapestry, as the authors call it, from first page to last.'
'The book demonstrates the great unity of mathematics. This is supported by a wealth of instructive illustrations ...' Zentralblatt MATH