The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational MathematicsWhether discussing hexaflexagons or number theory, Klein bottles or the essence of "nothing," Martin Gardner has singlehandedly 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 twentyfive years. Gardner's array of absorbing puzzles and mindtwisting 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. 
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Review: The Colossal Book of Mathematics
User Review  Brett  GoodreadsThis is a treasure of recreational mathematics. Fascinating illustrations and Gardner's easy to read prose make this a great read. Read full review
Review: The Colossal Book of Mathematics
User Review  Slickmez  GoodreadsOnly skimmed it. Has some interesting problems and concepts. Read full review
Contents
The Monkey and the Coconuts  3 
The Calculus of Finite Differences  10 
Infinity  13 
Words and Numbers  23 
Plane Qeometry 4 Curves of Constant Width  35 
RepTiles  46 
Piet Heins Superellipse  59 
Penrose Tiles  73 
Surreal Numbers  369 
Combinatorics  380 
Hexaflexagons  385 
The Soma Cube  398 
The Game of Life  409 
Paper Folding  423 
Ramsey Theory  437 
Bulgarian Solitaire and Other Seemingly Endless Tasks  455 
The Wonders of a Planiverse  94 
Solid Qeometry and Higher Dimensions 9 The Helix  117 
Packing Spheres  128 
Spheres and Hyperspheres  137 
The Church of the Fourth Dimension  150 
Hypercubes  162 
14 NonEuclidean Geometry  175 
Symmetry  181 
Rotations and Reflections  189 
The Amazing Creations of Scott Kim  198 
The Art of M C Escher  212 
Topology  221 
Klein Bottles and Other Surfaces  227 
Knots  239 
Linked and Knotted  254 
Probability  271 
Probability and Ambiguity  273 
Nontransitive Dice and Other Paradoxes  286 
More Nontransitive Paradoxes  297 
Infinite Regress  315 
AlephNull and AlephOne  327 
Supertasks  340 
Fractal Music  350 
Qames and Decision Theory  469 
A Matchbox GameLearning Machine  471 
Sprouts and Brussels Sprouts  485 
Hararys Generalized Ticktacktoe  493 
The New Eleusis  504 
514  
Time Travel  517 
Does Time Ever Stop?  531 
Induction and Probability  541 
Simplicity  553 
Logic and Philosophy  565 
The Unexpected Hanging  567 
44 Newcombs Paradox  580 
Nothing  592 
Everything  610 
Miscellaneous  625 
MelodyMaking Machines  627 
Mathematical Zoo  640 
Godel Escher Bach  660 
Six Sensational Discoveries  674 
Selected Titles by the Author on Mathematics  695 
Common terms and phrases
3space Addendum alephnull American Mathematical answer balls Bibliography called cards cells Chapter circle color complete graph conjecture constant width Conway Conway's corners cross cube curve Dewdney dice digits dimensions edges Escher example face finite number flexagons folded formula four geometry graph helical hexagon hole hypercube infinite infinity inside integers John Horton Conway Journal Klein bottle knot knot theory letter loop math mathematician move nonEuclidean nonperiodic packing pair palindrome paper paradox pattern Penrose Penrose Tiles physicist pieces Piet Hein plane planiverse play polycube polygons possible probability problem proof proved puzzle Quasicrystals Ramsey random readers Recreational Mathematics Reuleaux triangle rotated Science Scientific American second player shape shown in Figure shows side solid space sphere square strip superegg superellipse surface symmetry tesseract theorem theory tiles tion topologically torus turn University