The Beauty of Geometry Twelve Essays

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.

Contents

Preface v

1 The Functions of Schlafli and Lobatschefsky 3
2 Integral Cayley Numbers 21
3 Wythoff's Construction for Uniform Polytopes 40
4 The Classification of Zonohedra by Means of Projective Diagrams 54
5 Regular Skew Polyhedra in Three and Four Dimensions, and Their Topological Analogues 75
6 Self-dual Configurations and Regular Graphs 106
7 Twelve Points in PG(5, 3) with 95040 Self-transformations 150
8 Arrangements of Equal Spheres in Non-Euclidean Spaces 166
9 An Upper Bound for the Number of Equal Nonoverlapping Spheres That Can Touch Another of the Same Size 179
10 Regular Honeycombs in Hyperbolic Space 199
11 Reflected Light Signals 215
12 Geometry 229

Index