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A Mathematical Tapestry


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Table of Contents

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.

Promotional Information

Build paper polygons and discover how systematic paper folding reveals exciting patterns and relationships between seemingly unconnected branches of mathematics.

About the Author

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.' Martin Gardner
'The book demonstrates the great unity of mathematics. This is supported by a wealth of instructive illustrations ...' Zentralblatt MATH
"There is something very pleasing about seeing paper figures that are visual displays about how math works in the world. The difference from seeing tall buildings or watching planes fly is that it is even possible for children to apply the mathematics to build something. In my opinion, origami and other constructions using paper are one of the best ways to train mathematicians that will be teaching mathematics and this is independent of the level of mathematics that will be taught. While the mathematics in this book is at the level of the college student, people that just want directions on how to make the figures can still use it." Charles Ashbacher, Journal of Recreational Mathematics
"... a triumph of embodied learning, which applies direct experience with the mathematics of objects. This book should be in every library where a chance meeting with a willing student will surely produce a new mathematician. Highly recommended." J. McCleary, Vassar College for Choice Magazine
"This culminating work of these two mathematicians is essential reading. A Mathematical Tapestry, which reveals how a seemingly simple paper-folding technique can lead to some of the most powerful ideas in mathematics. What I find most compelling about the book are its accessible tone and its mathematical complexity as well as the detailed connections made across so many different strands. Hilton and Pedersen present a rare opportunity to embark on a true mathematical exploration." Kasi C. Allen, Lewis and Clark College for Mathematics Teacher

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