Penrose Tiles To Trapdoor Ciphers

325 Pages·2003·11.45 MB·English

Martin Gardner
PENROSE TILES
TO TRHPDOOR
CIPHERS
...
OF DR. MATRIX
The Mathematical Association of America
Washington, D.C.
Cover design by John Johnson, Teapot Graphics
@ 1989 by W. H. Freeman
This book was updated and revised from the 1989
edition published by W. H. Freeman, New York
@ 1997 by
The Mathematical Association of America (Incorporated)
Library of Congress Catalog Card Number 97-70505
ISBN 0-88385-521-6
Printed in the United States ofAmerica
Current Printing (last digit):
1 0 9 8 7 6 5 4 3 2 1
PENROSE TILES
to Trapdoor Ciphers
...
and the return of Dr. Matrix
SPECTRUM SERIES
Published by
THE MATHEMATICAL ASSOCIATION OF AMERICA
Committee on Publications
JAMES W. DANIEL, Chair
Spectrum Editorial Board
ARTHUR T. BENJAMIN, Editor
DANIEL ASIMOV
KATHLEEN BERVER
DIPA CHOUDHURY
RICHARD K. GUY
JEFFREY NUNEMACHER
ELLEN MAYCOCK PARKER
JENNIFER J. QUINN
EDWARD R. SCHEINERMAN
SANFORD L. SEGAL
To Roger Penrose
For his beautiful, surprising discoveries in mathematics,
physics and cosmology; for his deep creative insight
into how the universe operates; and for his humility in
not supposing that he is exploring only the PI-oducts of
human minds.
SPECTRUM SERIES
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All the Math That's Fit to Print, by Keith Devlin
Circles: A Mathematical View, by Dan Pedoe
Complex Numbers and Geometry, by Liang-shin Hahn
Cryptology, by Albrecht Beutelspacher
Five Hundred Mathematical Challenges, Edward J. Barbeau, Murray S. Klamkin,
and William 0. J. Moser
From Zero to Infinity, by Constance Reid
I Want to be a Mathematician, by Paul R. Halmos
Journey into Geometries, by Marta Sved
JULIA: a life in mathematics, by Constance Reid
The Last Problem, by E. T. Bell (revised and updated by Underwood Dudley)
The Lighter Side of Mathematics: Proceedings of the Eugkne Strens Memorial Confer-
ence on Recreational Mathematics & its History, edited by Richard K. Guy and
Robert E. Woodrow
Lure of the Integers, by Joe Roberts
Mathematical Carnival, by Martin Gardner
Mathematical Circus, by Martin Gardner
Mathematical Cranks, by Underwood Dudley
Mathematical Magic Show, by Martin Gardner
Mathematics: Queen and Sewant of Science, by E. T. Bell
Memorabilia Mathematica, by Robert Edouard Moritz
New Mathenutical Diversions, by Martin Gardner
Numerical Methods that Work, by Forman Acton
Out of the Mouths of Mathematicians, by Rosemary Schmalz
Penrose Eles to Trapdoor Ciphers . . . and the Return of Dr. Matrix, by Martin Gardner
Polyominoes, by George Martin
The Search for E. T. Bell, also known as John Taine, by Constance Reid
Shaping Space, edited by Marjorie Senechal and George Fleck
Student Research Projects in Calculus, by Marcus Cohen, Edward D. Gaughan,
Arthur Knoebel, Douglas S. Kurtz, and David Pengelley
The Trisectors, by Underwood Dudley
The Words of Mathematics, by Steven Schwartzman
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Prefuce ix
1
CHAPTER Penruse ~bng I
2
CHAPTER Penrose Zbng 11 19
3
CHAPTER MundehoJs fractuh 31
4
CHAPTER Conwa/s Surreul lumbers 49
5
CHAPTER Back fiom the Nondike and Other Problems 63
6
CHAPTER The oulipo 79
7
CHAPTER The Oulipo I/ 95
8
CHAPTER ~ytlro~Ksm 103
9
CHAPTER Pool-Bai7 Triungles und Other Problems 119
10
CHAPTER Muthemutjml Induction und Colored Huts 137
11
CHAPTER Negative Numbers I51
12
c HAPTER Cuffing Shapes into N Congruent Putts 165
13
CHAPTER liopdoor fiphers 183
14
CHAPTER liapdoor fipherr 11 195
15
CHAPTER Hyperbolas 205
16
CHAPTER The New Eleusis 219
17
CHAPTER Ramsey Theory 231
1 8
CHAPTER from Burrs to ~erroca~ 249
19
CHAPTER Sicherman Dice, the Kruskol Count ond Other Curiosities 265
20
CHAPTER Raymond SmuNyannj- logic Puzzles 281
2 1
CHAPTER The Return of Dr. Matuk 293
Postscript 307
Name Index 315
Preface
This book is a collection of Scientific American columns that I wrote
over a period of 25 years. It is the thirteenth such collection.. The unify-
ing theme, if there must be one, is recreational mathematics; that is,
mathematics presented in a spirit of play. As with earlier books, the
columns have been corrected and expanded with addendums based on
current feedback from readers. So much has happened since to Penrose
tilings (especially their unexpected applications to crystal theory), to
public key cryptosystems and to the French Oulipo, that I have written
brand new chapters for each of these topics. Also published lhere for the
first time is astonishing news concerning my old and dear friend Dr.
Matrix. I report my discovery that Dr. Matrix had not been killed by a
Russian KGB agent, as supposed, but is alive and well in Casablanca.
Martin Gardner