Time Travel and Other Mathematical Bewilderments

298 Pages·1987·15.3 MB·English

by  Martin Gardner

T I M E TRAVEL
AND OTHER MATHEMATICAL BEWILDERMENTS
TIME TRAVEL
AND OTHER MATHEMATICAL BEWILDERMENTS
MARTIN GARDNER
me
W. H. FREEMAN AND COMPANY N E W Y O R K
Library of'C ongress Cataloguing-in-Publication Data
Gardner, Martin, 1914-
Time travel and other mathematical bewilderments.
1nclud~:s index.
1. Mathematical recreations. I. Title.
QA95.G325 1987 793.7'4 87-11849
ISBN 0-7167-1924-X
ISBN 0-7167-1925-8 @bk.)
Copyright la1988 by W. H. Freeman and Company
No part of this book may be reproduced by any mechanical,
photographic, or electronic process, or in the form of a photographic
recording, nor may it be stored in a retrieval system, transmitted, or
otherwise copied for public or private use, without written permission
from the publisher.
Printed in the United States of America
3 4 5 6 7 8 9 0 VB 6 5 4 3 2 1 0 8 9
To David A. Klarner
for his many splendid contributions
to recreational mathematics,
for his friendship over the years,
and in !gratitude for many other things.
C O N T E N T S
CHAPTER ONE
Time Travel 1
CHAPTER TWO
Hexes and Stars 15
.
CHAPTER THREE
Tangrams, Part 1 27
CHAPTER FOUR
Tangrams, Part 2 39
CHAPTER FIVE
Nontransitive Paradoxes 55
CHAPTER SIX
Combinatorial Card Problems 71
CHAPTER SEVEN
Melody-Making Machines 85
CHAPTER EIGHT
.
Anamorphic Art 97
CHAPTER NINE
The Rubber Rope and Other Problems 11 1
viii CONTENTS
CHAPTER TEN
Six Sensational Discoveries 125
CHAPTER ELEVEN
The Csaszar Polyhedron 139
CHAPTER TWELVE
Dodgem and Other Simple Games 153
CHAPTER THIRTEEN
Tiling with Convex Polygons 163
CHAPTER FOURTEEN
Tiling with Polyominoes, Polyiamonds, and Polyhexes 177
CHAPTER FIFTEEN
Curious Maps 189
CHAPTER SIXTEEN
The Sixth Symbol and Other Problems 205
CHAPTER SEVENTEEN
Magic Squares and Cubes 213
CHAPTER EIGHTEEN
Block Packing 227
CHAPTER NINETEEN
Induction and ~robabilit~ 24 1
CONTENTS ix
CHAPTER TWENTY
Catalan Numbers 253
CHAPTER TWENTY-ONE
Fun with a Pocket Calculator 267
CHAPTER TWENTY-TWO
Tree-Plant Problems 22 7
INDEX OF NAMES 291
Herewith the twelfth collection of my columns from Scientijic American.
As usual, they have been corrected, updated, and expanded, mostly on the
basis of letters from knowledgeable and alert readers.
T I M E TRAVEL
AND OTHER MATHEMATICAL BEWILDERMENTS