KNOTS AND BORROMEAN RINGS, REP-TILES, AND EIGHT QUEENS Martin Gardner s Unexpected Hanging
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1 's Unexpected Hanging KNOTS AND BORROMEAN RINGS, REP-TILES, AND EIGHT QUEENS s Unexpected Hanging For 25 years, ( ) wrote Mathematical Games and Recreations, a monthly column for Scientific American magazine. These columns have inspired hundreds of thousands of readers to delve more deeply into the large world of mathematics. He also made significant contributions to magic, philosophy, debunking pseudoscience, and children s literature. He produced more than 60 books, including many bestsellers, most of which are still in print, and wrote a regular column for the Skeptical Inquirer magazine from 1983 to His Annotated Alice has sold more than a million copies. (The photograph is of the author at the time of the first edition.)
2 's Unexpected Hanging
3 's Unexpected Hanging THE NEW MARTIN GARDNER MATHEMATICAL LIBRARY From 1957 through 1986 wrote the Mathematical Games and Recreations columns for Scientific American that are the basis for these books. Scientific American editor Dennis Flanagan noted that this column contributed substantially to the success of the magazine. The exchanges between and his readers gave life to these columns and books. These exchanges have continued, and the impact of the columns and books has grown. These new editions give the chance to bring readers up to date on newer twists on old puzzles and games, on new explanations and proofs, and on links to recent developments and discoveries. Illustrations have been added and existing ones improved, and the bibliographies have been greatly expanded throughout. 1. Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: s First Book of Mathematical Puzzles and Games 2. Origami, Eleusis, and the Soma Cube: s Mathematical Diversions 3. Sphere Packing, Lewis Carroll, and Reversi: s New Mathematical Diversions 4. Knots and Borromean Rings, Rep-Tiles, and Eight Queens: Martin Gardner s Unexpected Hanging 5. Klein Bottles, Op-Art, and Sliding-Block Puzzles: More of Martin Gardner s Mathematical Games 6. Sprouts, Hypercubes, and Superellipses: s Mathematical Carnival 7. Nothing and Everything, Polyominoes and Game Theory: Martin Gardner s Mathematical Magic Show 8. Random Walks, Hyperspheres, and Palindromes: s Mathematical Circus 9. Words, Numbers, and Combinatorics: on the Trail of Dr. Matrix 10. Wheels, Life, and Knotted Molecules: s Mathematical Musements 11. Knotted Doughnuts, Napier s Bones, and Gray Codes: Martin Gardner s Mathematical Entertainments 12. Tangrams, Tilings, and Time Travel: s Mathematical Bewilderments
4 's Unexpected Hanging 13. Penrose Tiles, Trapdoor Ciphers, and The Oulipo: s Mathematical Tour 14. Fractal Music, Hypercards, and Chaitin s Omega: s Mathematical Recreations 15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications: s Last Mathematical Recreations
5 's Unexpected Hanging Knots and Borromean Rings, Rep-Tiles, and Eight Queens MARTIN GARDNER S UNEXPECTED HANGING MATHEMATICAL ASSOCIATION OF AMERICA
6 's Unexpected Hanging 32 Avenue of the Americas, New York, NY , USA Cambridge University Press is part of the University of Cambridge. It furthers the University s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. Information on this title: / Mathematical Association of America th St. NW, Washington, DC C Mathematical Association of America 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of the Mathematical Association of America. First published as Unexpected Hangings, and Other Mathematical Diversions by Simon & Schuster 1968 New edition published 2014 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Gardner, Martin, , author. [Magazine columns. Selections] Knots and borromean rings, rep-tiles, and eight queens : s unexpected hanging /. pages cm. (The new mathematical library ; 4) Includes bibliographical references and index. ISBN (hardback) ISBN (paperback) 1. Mathematical recreations. I. Title. QA95.G dc ISBN Hardback ISBN Paperback Cambridge University Press and the Mathematical Association of America have no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and do not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.
7 's Unexpected Hanging For My Niece Dorothy Elise Weaver
8 's Unexpected Hanging
9 's Unexpected Hanging Contents Acknowledgments page xi 1 The Paradox of the Unexpected Hanging 1 2 Knots and Borromean Rings 16 3 The Transcendental Number e 28 4 Geometric Dissections 38 5 Scarne on Gambling 50 6 The Church of the Fourth Dimension 62 7 Eight Problems 75 8 A Matchbox Game-Learning Machine 91 9 Spirals Rotations and Reflections Peg Solitaire Flatlands Chicago Magic Convention Tests of Divisibility Nine Problems The Eight Queens and Other Chessboard Diversions A Loop of String Curves of Constant Width Rep-Tiles: Replicating Figures on the Plane Thirty-Six Catch Questions 259 Index 271 ix
10 's Unexpected Hanging
11 's Unexpected Hanging Acknowledgments thanks Scientific American for allowing reuse of material from his columns in that magazine, material copyright 1961 (Chapter 2 5), 1962 (Chapters 6 17), and 1963 (Chapters 1 and 18 20) by Scientific American, Inc. He also thanks the artists who contributed to the success of these columns and books for allowing reuse of their work: Allen Beechel, James D. Egleson (via heirs Jane and Nicholas Egleson), Harold Jacobs, John Johnson, Joe Kaufman, John McClellan, Patra McElwee, Manfred Mornhinweg, Thomas Prentiss, George T. Rab, Peter Renz, Alex Semenoick, Chris Sangwin, Joan Starwood, Bunji Tagawa (via Donald Garber for the Tagawa Estate), and Dan Todd. Artists names are cited where these were known. Figure 58 is used with permission, copyright 2014 Artists Rights Society (ARS), New York / DACS, London. xi
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