"It is a cross between providing mathematical challenge and a cultural placement of some famous problems. I hope it will persuade non-mathematicians that mathematics is worthwhile, and provide mathematicians with some background to the personalities and history of the main stream, and, equally as important, to the quiet little-visited back-waters of their subject." -Tony Crilly, The Mathematical Gazette , March 2002

Chapter 1 Euler's Formula for Polyhedra, and Related Topics --
Section 2 Regular Polyhedra 12 --
Section 3 Deltahedra 21 --
Section 4 Polyhedra without Diagonals 31 --
Section 5 The n-dimensional Cube and the Tower of Hanoi 40 --
Section 6 The Four-color Problem and the Five-color Theorem 55 --
Section 7 The Conquest of Saturn, the Scramble for Africa, and Other Problems 64 --
Chapter 2 The Search for Perfect Numbers --
Section 2 Prime Numbers and Factorization 84 --
Section 3 Euclidean Perfect Numbers 93 --
Section 4 Primes and Their Distribution 102 --
Section 5 Factorization Techniques 110 --
Section 6 Non-Euclidean Perfect Numbers 124 --
Section 7 Extensions and Generalizations 137 --
Chapter 3 What is Area? --
Section 2 Rectangles and Grid Figures 153 --
Section 3 Triangles 161 --
Section 4 Polygons 166 --
Section 5 Polygonal Regions 177 --
Section 6 Area in General 185 --
Section 7 Pathology 201 --
Chapter 4 Some Exotic Geometries --
Section 2 Spherical Geometry 217 --
Section 3 Absolute Geometry 221 --
Section 4 More History --
Saccheri, Bolyai, and Lobachevsky 226 --
Section 5 Hyperbolic Geometry 230 --
Section 7 Analytic Geometry --
A Reminder 248 --
Section 8 Finite Arithmetics 255 --
Section 9 Finite Geometries 262 --
Section 10 Application 273 --
Section 11 Circles and Quadratic Equations 279 --
Section 12 Finite Affine Planes 289 --
Section 13 Finite Projective Planes 292 --
Section 14 Ovals in a Finite Plane 296 --
Section 15 A Finite Version of Poincare's Universe 303 --
Appendix Excerpts from Euclid 308 --
Chapter 5 Games --
Section 2 Some Tree Games 318 --
Section 3 The Game of Hex 327 --
Section 4 The Game of Nim 340 --
Section 5 Games of Chance 359 --
Section 6 Matrix Games 365 --
Section 7 Applications of Matrix Games 378 --
Section 8 Positive-sum Games 381 --
Section 9 Sharing 383 --
Section 10 Cooperative Games 385 --
Chapter 6 What's in a Name? --
Section 3 Place Notation for the Base b 396 --
Section 4 Some Properties of Natural Numbers Related to Notation 402 --
Section 5 Fractions: First Comments 414 --
Section 6 Farey Fractions 416 --
Section 7 Egyptian Fractions 421 --
Section 8 The Euclidean Algorithm 435 --
Section 9 Continued Fractions 440 --
Section 10 Decimal Fractions 444.

"Since it was first published three decades ago, Excursions into mathematics has been one of the most popular mathematical books written for a general audience. Taking the reader for short "excursions" into several specific disciplines of mathematics, it makes mathematical concepts accessible to a wide audience. The Millennium Edition is updated with current research and new solutions to outstanding problems that have been discovered since the last edition was printed, such as the solution to the well-known "four-color problem." Excursions into mathematics: The Millennium edition is an exciting revision of the original, much-loved classic. Everyone with an interest in mathematics should read this book." --Publisher descriptio