The Colossal Book of Mathematics Classic Puzzles, Paradoxes, and Problems

by Gardner, Martin

• ISBN13: 9780393020236
• ISBN10: 0393020231
• Edition: 00
• Format: Hardcover
• Copyright: 2001-09-17
• Publisher: W. W. Norton & Company

Summary

Whether discussing hexaflexagons or number theory, Klein bottles or the essence of "nothing," Martin Gardner has single-handedly created the field of "recreational mathematics." The Colossal Book of Mathematics collects together Gardner's most popular pieces from his legendary "Mathematical Games" column, which ran in Scientific American for twenty-five years. Gardner's array of absorbing puzzles and mind-twisting paradoxes opens mathematics up to the world at large, inspiring people to see past numbers and formulas and experience the application of mathematical principles to the mysterious world around them. With articles on topics ranging from simple algebra to the twisting surfaces of Mobius strips, from an endless game of Bulgarian solitaire to the unreachable dream of time travel, this volume comprises a substantial and definitive monument to Gardner's influence on mathematics, science, and culture. In its twelve sections, The Colossal Book of Math explores a wide range of areas, each startlingly illuminated by Gardner's incisive expertise. Beginning with seemingly simple topics, Gardner expertly guides us through complicated and wondrous worlds: by way of basic algebra we contemplate the mesmerizing, often hilarious, linguistic and numerical possibilities of palindromes; using simple geometry, he dissects the principles of symmetry upon which the renowned mathematical artist M. C. Escher constructs his unique, dizzying universe. Gardner, like few thinkers today, melds a rigorous scientific skepticism with a profound artistic and imaginative impulse. His stunning exploration of "The Church of the Fourth Dimension," for example, bridges the disparate worlds of religion and science by brilliantly imagining the spatial possibility of God's presence in the world as a fourth dimension, at once "everywhere and nowhere." With boundless wisdom and his trademark wit, Gardner allows the reader to further engage challenging topics like probability and game theory which have plagued clever gamblers, and famous mathematicians, for centuries. Whether debunking Pascal's wager with basic probability, making visual music with fractals, or uncoiling a "knotted doughnut" with introductory topology, Gardner continuously displays his fierce intelligence and gentle humor. His articles confront both the comfortingly mundane'”"Generalized Ticktacktoe" and "Sprouts and Brussel Sprouts"'”and the quakingly abstract'”"Hexaflexagons," "Nothing," and "Everything." He navigates these staggeringly obscure topics with a deft intelligence and, with addendums and suggested reading lists, he informs these classic articles with new insight. Admired by scientists and mathematicians, writers and readers alike, Gardner's vast knowledge and burning curiosity reveal themselves on every page. The culmination of a lifelong devotion to the wonders of mathematics, The Colossal Book of Mathematics is the largest and most comprehensive math book ever assembled by Gardner and remains an indispensable volume for the amateur and expert alike.

Author Biography

Martin Gardner is the author of more than seventy books on a vast range of topics. He wrote the "Mathematical Games" column for Scientific American for more than twenty-five years and is a regular columnist for The Skeptical Enquirer. He lives in Hendersonville, North Carolina.

Table of Contents

Preface	xi
I Arithmetic and Algebra
The Monkey and the Coconuts	3	(7)
The Calculus of Finite Differences	10	(13)
Palindromes: Words and Numbers	23	(12)
II Plane Geometry
Curves of Constant Width	35	(11)
Rep-Tiles	46	(13)
Piet Hein's Superellipse	59	(14)
Penrose Tiles	73	(21)
The Wonders of a Planiverse	94	(23)
III Solid Geometry and Higher Dimensions
The Helix	117	(11)
Packing Spheres	128	(9)
Spheres and Hyperspheres	137	(13)
The Church of the Fourth Dimension	150	(12)
Hypercubes	162	(13)
Non-Euclidean Geometry	175	(14)
IV Symmetry
Rotations and Reflections	189	(9)
The Amazing Creations of Scott Kim	198	(14)
The Art of M. C. Escher	212	(15)
V Topology
Klein Bottles and Other Surfaces	227	(12)
Knots	239	(15)
Doughnuts: Linked and Knotted	254	(19)
VI Probability
Probability and Ambiguity	273	(13)
Nontransitive Dice and Other Paradoxes	286	(11)
More Nontransitive Paradoxes	297	(18)
VII Infinity
Infinite Regress	315	(12)
Aleph-Null and Aleph-One	327	(13)
Supertasks	340	(10)
Fractal Music	350	(19)
Surreal Numbers	369	(16)
VIII Combinatorics
Hexaflexagons	385	(13)
The Soma Cube	398	(11)
The Game of Life	409	(14)
Paper Folding	423	(14)
Ramsey Theory	437	(18)
Bulgarian Solitaire and Other Seemingly Endless Tasks	455	(16)
IX Games and Decision Theory
A Matchbox Game-Learning Machine	471	(14)
Sprouts and Brussels Sprouts	485	(8)
Harary's Generalized Ticktacktoe	493	(11)
The New Eleusis	504	(13)
X Physics
Time Travel	517	(14)
Does Time Ever Stop?	531	(10)
Induction and Probability	541	(12)
Simplicity	553	(14)
XI Logic and Philosophy
The Unexpected Hanging	567	(13)
Newcomb's Paradox	580	(12)
Nothing	592	(18)
Everything	610	(17)
XII Miscellaneous
Melody-Making Machines	627	(13)
Mathematical Zoo	640	(20)
Godel, Escher, Bach	660	(14)
Six Sensational Discoveries	674	(21)
Selected Titles by the Author on Mathematics	695	(2)
Index	697