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The Beauty of Geometry: Twelve Essays

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The Beauty of Geometry: Twelve Essays Cover

 

Synopses & Reviews

Publisher Comments:

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.

Book News Annotation:

Discusses geometry's applications to number theory, group theory, graph theory, communication theory, and relativity theory. Originally published as Twelve Geometric Essays in 1968 by SIU Press.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Absorbing essays demonstrate the charms of mathematics. Stimulating and thought-provoking treatment of geometry's crucial role in a wide range of mathematical applications, for students and mathematicians.

Synopsis:

These absorbing essays by a distinguished mathematician provide a compelling demonstration of the charms of mathematics. 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 plays in a wide range of mathematical applications.

Table of Contents

Preface

1 The Functions of Schläfli and Lobatschefsky

2 Integral Cayley Numbers

3 Wythoff's Construction for Uniform Polytopes

4 The Classification of Zonohedra by Means of Projective Diagrams

5 "Regular Skew polyhedra in Three and Four Dimensions, and Their Topological Analogues "

6 Self-dual Configurations and Regular Graphs

7 "Twelve Points in PG(5, 3) with 95040 Self-transformations "

8 Arrangements of Equal Spheres in Non-Euclidean Spaces

9 An Upper Bound for the Number of Equal Nonoverlapping Spheres That Can Touch Another of the Same Size

10 Regular Honeycombs in Hyperbolic Space

11 Reflected Light Signals

12 Geometry

Index

Product Details

ISBN:
9780486409191
Author:
Coxeter, H. S. M.
Publisher:
Dover Publications
Author:
Mathematics
Author:
Coxeter
Location:
Mineola, NY
Subject:
Geometry - General
Subject:
Geometry
Subject:
General Mathematics
Subject:
Mathematics-Geometry and Trigonometry
Edition Number:
Dover ed.
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
1235
Publication Date:
19990731
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
288
Dimensions:
8.5 x 5.38 in 0.53 lb

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Related Subjects

History and Social Science » World History » General
Science and Mathematics » Mathematics » Geometry » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
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The Beauty of Geometry: Twelve Essays New Trade Paper
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Product details 288 pages Dover Publications - English 9780486409191 Reviews:
"Synopsis" by ,
Absorbing essays demonstrate the charms of mathematics. Stimulating and thought-provoking treatment of geometry's crucial role in a wide range of mathematical applications, for students and mathematicians.

"Synopsis" by ,
These absorbing essays by a distinguished mathematician provide a compelling demonstration of the charms of mathematics. 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 plays in a wide range of mathematical applications.

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