Subject(s) 
Mathematics


Geometry


Mathematical recreations

Physical Description 
xv, 290 p. : ill. ; 25 cm 
Summary 
"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 
Note 
Includes bibliographical references (p. 282285) and index 

Machine generated contents note: Preface; 1. Flexagons  a beginning thread; 2. Another thread  1period paper folding; 3. More paper folding threads  2period paperfolding; 4. A numbertheory thread  folding numbers, a number trick, and some tidbits; 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 paperfolding 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 trihexaflexagon; 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 Pólya's dream; 16. Tying some loose ends together  symmetry, group theory, homologues, and the Pólya enumeration theorem; 17. Returning to the number theory thread  generalized quasiorder and coach theorems; References; Index 
Alternate Author 
Pedersen, Jean

