## New MAA Book: Sphere Packing, Lewis Carroll, and Reversi

July 9, 2009

Sphere Packing, Lewis Carroll, and Reversi: Martin Gardner's New Mathematical Diversions
Martin Gardner
296 pp., paperbound, 2009. Series: The New Martin Gardner Mathematical Library (No. 3)
ISBN: 978-0-521-74701-1

Packed spheres, Reversi, braids, polyominoes, board games, puzzles of Lewis Carroll, and other mathematical diversions, originally published in 1959-61, now return with updates. Included are Gardner's accounts of new game variations, mathematical proofs, developments, and discoveries. Read about Don Knuth's word ladders program, the four-color map theorem, and the latest developments in the never-ending search for the digits of pi.

Martin Gardner's puzzles will charm readers while demonstrating principles of logic, probability, geometry, and other fields of mathematics.

Highlights:
• Timeless puzzles from the 25-year run of Scientific American's "Mathematical Games" columns.
• Part of the first complete collection of Martin Gardner’s Mathematical Library.

Excerpt:
Beer Signs on the Highway (p. 144)
Smith drove at a steady clip along the highway, his wife beside him. "Have you noticed," he said, "that those annoying signs for Flatz beer seem to be regularly spaced along the road? I wonder how far apart they are."
Mrs. Smith glanced at her wristwatch, then counted the number of Flatz beer signs they passed in 1 minute.
"What an odd coincidence!" exclaimed Smith. "When you multiply that number by 10, it exactly equals the speed of our car in miles per hour."
Assuming that the car's speed is constant, that the signs are equally spaced and that Mrs. Smith's minute began and ended with the car midway between two signs, how far is it between one sign and the next?

Contents:
Introduction. 1. The Binary System 2. Group Theory and Braids 3. Eight Problems 4. The Games and Puzzles of Lewis Carroll 5. Paper Cutting 6. Board Games 7. Packing Spheres 8. The Transcendental Number pi 9. Victor Eigen: Mathemagician 10. The Four-Color Map Theorem 11. Mr. Apollinax Visits New York 12. Nine Problems 13. Polyominoes and Fault-Free Rectangles 14. Euler's Spoilers: the Discovery of an Order-10 Graeco-Latin Square 15. The Ellipse 16. The 24 Color Squares and the 30 Color Cubes 17. H. S. M. Coxeter 18. Bridg-it and Other Games 19. Nine More Problems 20. The Calculus of Finite Differences. Index.

Order Sphere Packing, Lewis Carroll, and Reversi from the MAA Bookstore.
List: \$14.99

About the New Martin Gardner Mathematical Library:
Martin Gardner's "Mathematical Games" columns in Scientific American linked the world of professional mathematicians with that of recreational mathematics. Gardner's columns broke stories about knot theory, fractals, and Penrose tilings, among may other mathematical and scientific subjects. This series brings all his original books together for the first time, in revised and expanded editions for the twenty-first century.

Editorial Board: Donald J. Albers, Gerald L. Alexanderson, John H. Conway, Richard K. Guy, Harold R. Jacobs, Donald E. Knuth, and Peter L. Renz.

Other Books in the Series:
Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi
Origami, Eleusis, and the Soma Cube