Descript 
xv, 290 pages : illustrations ; 25 cm 

text rdacontent 

unmediated rdamedia 

volume rdacarrier 
Note 
Includes bibliographical references (p. 282285) and index 
Contents 
Flexagons  a beginning thread  Another thread  1period paper folding  More paper folding threads  2period paperfolding  A numbertheory thread  folding numbers, a number trick, and some titbits  The polyhedron thread  building some polyhedra and defining a regular polyhedron  Constructing dipyramids and rotating rings from straight strips of triangles  Continuing the paperfolding and numbertheory threads  A geometry and algebra thread  constructing, and using, Jennifer's puzzle  A polyhedral geometry thread  constructing braided Platonic solids and other woven polyhedra  Combinatorial and symmetry threads  Some golden threads  constructing more dodecahedra  More combinatorial threads  Collapsoids  Group theory  the faces of the trihexaflexagon  Combinatorial and grouptheoretical threads  extended face planes of the Platonic solids  A historical thread  Involving the Euler characteristic, Descartes' total angular defect, and Pólya's dream  Tying some loose ends together  Symmetry, group theory, homologues, and the Pólya enumeration theorem  Returning to the numbertheory thread  Generalized quasiorder and coach theorems 
Note 
"This easytoread 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 paperfolding 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 handson experience constructing these models and to discover for themselves the patterns and relationships they unearth" Provided by publisher 
LC subject 
Mathematics

Add Author 
Pedersen, Jean


Donmoyer, Sylvie

ISBN 
9780521128216 (pbk.) 

0521128218 (pbk.) 

9780521764100 (hbk.) 

0521764106 (hbk.) 
