A Mathematical Tapestry: Demonstrating the Beautiful Unity of MathematicsCambridge University Press, 2010年7月22日 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. |
內容
| 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 |
| 282 | |
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常見字詞
6-flexagons angle angular deficiency braided model cells Chapter coach theorem complete symbol configuration construct coprime coset crease line cycle index defined definition deltahedra diagonal cube elements equilateral triangles Euclidean Euler characteristic example fact FAT algorithm figure find finished model finite first fit flaps flat flex flexagon fold lines folding number folding procedure formula geometry glue gluing golden dodecahedron homologues icosahedron integer look mathematics N-gon Notice number of faces number theory obtain octahedron odd permutations orientation P´olya paper clip paper-folding pattern piece pentagonal dipyramid permutation Platonic solids polygon polyhedra polyhedron position produce proof pyramid quasi-order theorem regular convex regular octahedron regular tetrahedron result rotating ring Section sequence shown in Figure sides small stellated dodecahedron star polygons stella octangula stellated dodecahedron straight strips surface symmetry group Table tabs top edge triangular triangular dipyramid unbounded regions vertex vertices zone