The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems / Edition 1
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The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems / Edition 1

by Martin Gardner
     
 

ISBN-10: 0393020231

ISBN-13: 9780393020236

Pub. Date: 09/28/2001

Publisher: Norton, W. W. & Company, Inc.

No amateur or math authority can be without this ultimate compendium from America's best-loved mathematical expert.
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

Overview

No amateur or math authority can be without this ultimate compendium from America's best-loved mathematical expert.
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.

Product Details

ISBN-13:
9780393020236
Publisher:
Norton, W. W. & Company, Inc.
Publication date:
09/28/2001
Edition description:
1 ED
Pages:
704
Sales rank:
384,080
Product dimensions:
7.50(w) x 9.60(h) x 1.80(d)

Table of Contents

Prefacexi
IArithmetic and Algebra
1.The Monkey and the Coconuts3
2.The Calculus of Finite Differences10
3.Palindromes: Words and Numbers23
IIPlane Geometry
4.Curves of Constant Width35
5.Rep-Tiles46
6.Piet Hein's Superellipse59
7.Penrose Tiles73
8.The Wonders of a Planiverse94
IIISolid Geometry and Higher Dimensions
9.The Helix117
10.Packing Spheres128
11.Spheres and Hyperspheres137
12.The Church of the Fourth Dimension150
13.Hypercubes162
14.Non-Euclidean Geometry175
IVSymmetry
15.Rotations and Reflections189
16.The Amazing Creations of Scott Kim198
17.The Art of M. C. Escher212
VTopology
18.Klein Bottles and Other Surfaces227
19.Knots239
20.Doughnuts: Linked and Knotted254
VIProbability
21.Probability and Ambiguity273
22.Nontransitive Dice and Other Paradoxes286
23.More Nontransitive Paradoxes297
VIIInfinity
24.Infinite Regress315
25.Aleph-Null and Aleph-One327
26.Supertasks340
27.Fractal Music350
28.Surreal Numbers369
VIIICombinatorics
29.Hexaflexagons385
30.The Soma Cube398
31.The Game of Life409
32.Paper Folding423
33.Ramsey Theory437
34.Bulgarian Solitaire and Other Seemingly Endless Tasks455
IXGames and Decision Theory
35.A Matchbox Game-Learning Machine471
36.Sprouts and Brussels Sprouts485
37.Harary's Generalized Ticktacktoe493
38.The New Eleusis504
XPhysics
39.Time Travel517
40.Does Time Ever Stop?531
41.Induction and Probability541
42.Simplicity553
XILogic and Philosophy
43.The Unexpected Hanging567
44.Newcomb's Paradox580
45.Nothing592
46.Everything610
XIIMiscellaneous
47.Melody-Making Machines627
48.Mathematical Zoo640
49.Godel, Escher, Bach660
50.Six Sensational Discoveries674
Selected Titles by the Author on Mathematics695
Index697

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