A passion for mathematics: numbers, puzzles, madness, religion, and the quest for reality

411 Pages·2005·5.904 MB·English

by  Clifford A. Pickover

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AA PPaassssiioonn ffoorr
MMaatthheemmaattiiccss
Numbers, Puzzles, Madness, Religion,
and the Quest for Reality
CLIFFORD A. PICKOVER
John Wiley & Sons, Inc.
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AA PPaassssiioonn ffoorr
MMaatthheemmaattiiccss
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Works by Clifford A. Pickover
The Alien IQ Test
Black Holes: A Traveler’s Guide
Calculus and Pizza
Chaos and Fractals
Chaos in Wonderland
Computers, Pattern, Chaos, and Beauty
Computers and the Imagination
Cryptorunes: Codes and Secret Writing
Dreaming the Future
Egg Drop Soup
Future Health
Fractal Horizons: The Future Use of Fractals
Frontiers of Scientific Visualization
The Girl Who Gave Birth to Rabbits
Keys to Infinity
Liquid Earth
The Lobotomy Club
The Loom of God
The Mathematics of Oz
Mazes for the Mind: Computers and the Unexpected
Mind-Bending Visual Puzzles (calendars and card sets)
The Paradox of God and the Science of Omniscience
The Pattern Book: Fractals, Art, and Nature
The Science of Aliens
Sex, Drugs, Einstein, and Elves
Spider Legs (with Piers Anthony)
Spiral Symmetry (with Istvan Hargittai)
Strange Brains and Genius
Sushi Never Sleeps
The Stars of Heaven
Surfing through Hyperspace
Time: A Traveler’s Guide
Visions of the Future
Visualizing Biological Information
Wonders of Numbers
The Zen of Magic Squares, Circles, and Stars
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AA PPaassssiioonn ffoorr
MMaatthheemmaattiiccss
Numbers, Puzzles, Madness, Religion,
and the Quest for Reality
CLIFFORD A. PICKOVER
John Wiley & Sons, Inc.
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Copyright © 2005 by Clifford A. Pickover. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
Illustration credits: pages 91, 116, 137, 140, 142, 149, 150, 151, 157, 158, 159, 160, 162, 164, 167, 168,
169, 179, 199, 214, 215, 224, 225, 230, 274, 302, 336, 338, 341, 343, 345, and 348 by Brian C. Mans-
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Edit Hepp; 141 by Stewart Raphael, Audrey Raphael, and Richard King; 155 by Patrick Grimm and Paul
St. Denis; 165 and 166 from Magic Squares and Cubesby W. S. Andrews; 177 and 352 by Henry Ernest
Dudeney; 200 by Bruce Patterson; 204 by Bruce Rawles; 206 by Jürgen Schmidhuber; 253 by Abram
Hindle; 254, 255, 256, and 257 by Chris Coyne; 258 and 259 by Jock Cooper; 260 by Linda Bucklin; 261
by Sally Hunter; 262 and 263 by Jos Leys; 264 by Robert A. Johnston; and 266 by Cory and Catska Ench.
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Library of Congress Cataloging-in-Publication Data:
Pickover, Clifford A.
A passion for mathematics : numbers, puzzles, madness, religion, and the quest for reality
/ Clifford A. Pickover.
p. cm.
Includes bibliographical references and index.
ISBN-13 978-0-471-69098-6 (paper)
ISBN-10 0-471-69098-8 (paper)
1. Mathematics. I. Title
QA39.3.P53 2005
510—dc22 2004060622
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
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Ramanujan said that he received his formulas from
God. This book is dedicated to all those who find
Ramanujan’s πformulas beautiful to look at:
1 ∑∞ (1103+26390n)(2n−1)!!(4n−1)!!
= 8
π 994n+232n(n!)3
n=0
( )
n 0
π= 5 5 ∑∞ (11n+1)(21)Poch(n)(61)Poch(n)(65)Poch(n)  4 n−1
 
 
2 3 (n!)3 125
n=0 
(where Poch(n)refers to the Pochhammer notation
described in chapter 2)
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“Truly the gods have not from the beginning
revealed all things to mortals, but by long seeking,
mortals make progress in discovery.”
—Xenophanes of Colophon (c. 500 B.C.)
“Every blade of grass has its angel
that bends over it and whispers, ‘grow, grow.’”
—Talmudic commentary Midrash
Bereishis Rabbah, 10:6