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

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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.
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Editorial Reviews

Stephen Jay Gould
“For more than half a century, Martin Gardner has been the single brightest beacon defending rationality and good science. . . . He is also one of the most brilliant men and gracious writers I have known.”
Douglas Hofstadter
Martin Gardner is one of the great intellects produced in this country in this century.
Dennis Shasha
Martin Gardner's puzzles share much with the greatest works of surrealist art: surprising, provocative, and influential for generations to come.
John Allen Paulos
[A] remarkable retrospective of his astonishingly influential career as an expositor extraordinaire.
Publishers Weekly
This weighty collection, containing 50 of what the Annotated Alice annotator and popular science journalist considers his best Scientific American "Mathematical Games" columns, is sure to please the relatively small but intensely loyal coterie of Gardner fans. Arranged in 12 broad categories (arithmetic and algebra, plane geometry, topology, infinity, etc.), these pieces cover subjects that will delight recreational math buffs, such as Penrose tiles, hypercubes, Klein bottles and fractal music. In addition to an up-to-date bibliography, each section includes a new, sometimes lengthy addendum, which should be the main hook for those who already own the 15 volumes of Gardner's complete Scientific American columns. While books on math for general audiences by authors such as Amir Aczel have been in vogue of late, they've tended to focus on personalities and to avoid equations. Since this collection is filled with problems and expressions (illustrated with 320 line drawings) that require solving with pencil and paper, its appeal should be mainly limited to puzzle nuts, but Gardner's elegant style could draw in new aficionados. An enemy of charlatanry and pretension, who appreciates the beauty and complexity of language as well as numbers (and still actively writing at age 86), Gardner remains a model of clear prose, understated wit and intellectual honesty. (Aug.) Copyright 2001 Cahners Business Information.
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Product Details

  • ISBN-13: 9780393020236
  • Publisher: Norton, W. W. & Company, Inc.
  • Publication date: 9/28/2001
  • Edition description: 1 ED
  • Edition number: 1
  • Pages: 704
  • Sales rank: 235,223
  • Product dimensions: 7.50 (w) x 9.50 (h) x 1.80 (d)

Meet the Author

Martin Gardner (1914-2010) is the author of more than seventy books, including Fads and Fallacies in the Name of Science, The Annotated Alice, The Annotated Hunting of the Snark, and The Colossal Book of Mathematics.
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Table of Contents

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