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The Beauty of Geometry: Twelve Essays (Dover Books on Mathematics), by H. S. M. Coxeter
PDF Download The Beauty of Geometry: Twelve Essays (Dover Books on Mathematics), by H. S. M. Coxeter
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Written by a distinguished mathematician, the dozen absorbing essays in this versatile volume offer both supplementary classroom material and pleasurable reading for the mathematically inclined.
The essays promise to encourage readers in the further study of elementary geometry, not just for its own sake, but also for its broader applications, which receive a full and engaging treatment. Beginning with an analytic approach, the author reviews the functions of Schlafli and Lobatschefsky and discusses number theory in a dissertation on integral Cayley numbers. A detailed examination of group theory includes discussion of Wythoff's construction for uniform polytopes, as well as a chapter on regular skew polyhedra in three and four dimensions and their topological analogues. A profile of self-dual configurations and regular graphs introduces elements of graph theory, followed up with a chapter on twelve points in PG (5, 3) with 95040 self-transformations. Discussion of an upper bound for the number of equal nonoverlapping spheres that can touch another same-sized sphere develops aspects of communication theory, while relativity theory is explored in a chapter on reflected light signals.
Additional topics include the classification of zonohedra by means of projective diagrams, arrangements of equal spheres in non-Euclidean spaces, and regular honeycombs in hyperbolic space. Stimulating and thought-provoking, this collection is sure to interest students, mathematicians, and any math buff with its lucid treatment of geometry and the crucial role geometry can play in a wide range of mathematical applications.
- Sales Rank: #1093965 in Books
- Published on: 1999-07-02
- Released on: 1999-07-02
- Original language: English
- Number of items: 1
- Dimensions: 8.46" h x .59" w x 5.41" l, .66 pounds
- Binding: Paperback
- 288 pages
Most helpful customer reviews
35 of 38 people found the following review helpful.
A splendid legacy of 20th century mathematics
By mathatout
This book collects 12 articles by Coxeter, already published in various mathematics technical journal but would be quite tedious to collect for one's pleasure. Each explains fascinating connections between exceptional discrete groups, polyhedra, graphs, sphere packings, projective spaces. All carry the particular favour of HSM Coxeter mathematics with his love of polyhedra and of their geometry. Starting points are often elementary but conclusions and connections are worthwile aven for today mathematics. I recommend it for graduates in mathematics, especially those interested in group theory, discrete/finite geometry, non-euclidean geometry as a very inspiring book giving a sense of unity in those parts of mathematics.
0 of 0 people found the following review helpful.
It is what I wanted and was delivered on time.
By OldFish
It is what I wanted and was delivered on time.
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