A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics

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Cambridge University Press, Jul 22, 2010 - Mathematics
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This easy-to-read 2010 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.
 

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LibraryThing Review

User Review  - themulhern - LibraryThing

A book of demanding recreational mathematics about flexagons. Full of detailed instructions for the construction of flexagons. This book must have taken as much or more effort as any well written mathematical textbook. If only I had the hours and the energy to dig into it now. Read full review

Contents

1 Flexagons
1
2 Another thread
17
3 More paperfolding threads
39
4 A numbertheory thread
52
5 The polyhedron thread
71
6 Constructing dipyramids and rotating rings
86
7 Continuing the paperfolding and numbertheory threads
96
8 A geometry and algebra thread
110
11 Some golden threads
163
12 More combinatorial threads
175
13 Group theory
195
14 Combinatorial and grouptheoretical threads
206
15 A historical thread
223
16 Tying some loose ends together
236
17 Returning to the numbertheory thread
260
References
282

9 A polyhedral geometry thread
123
10 Combinatorial and symmetry threads
145

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About the author (2010)

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.

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