A mathematical tapestry demonstrating the beautiful unity of mathematics
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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2010
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| Online-Zugang: | DE-12 DE-92 URL des Erstveröffentlichers |
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Inhaltsangabe:
- Flexagons : a beginning thread
- Another thread : 1-period paper folding
- More paper folding threads : 2-period paper-folding
- A number-theory 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 paper-folding and number-theory 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 group-theoretical 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 number-theory thread : generalized quasi-order and coach theorems