A Passion for Mathematics

Clifford A. Pickover

Description

A Passion for Mathematics is an educational, entertaining trip through the curiosities of the math world, blending an eclectic mix of history, biography, philosophy, number theory, geometry, probability, huge numbers, and mind-bending problems into a delightfully compelling collection that is sure to please math buffs, students, and experienced mathematicians alike. In each chapter, Clifford Pickover provides factoids, anecdotes, definitions, quotations, and captivating challenges that range from fun, quirky puzzles to insanely difficult problems. Readers will encounter mad mathematicians, strange number sequences, obstinate numbers, curious constants, magic squares, fractal geese, monkeys typing Hamlet, infinity, and much, much more. A Passion for Mathematics will feed readers’ fascination while giving them problem-solving skills a great workout!
Acknowledgments.

Introduction.

1. Numbers, History, Society, and People.

2. Cool Numbers.

3. Algebra, Percentages, Weird Puzzles, and Marvelous Mathematical Manipulations.

4. Geometry, Games, and Beyond.

5. Probability: Take Your Chances.

6. Big Numbers and Infinity.

7. Mathematics and Beauty.

Answers.

References.

Index.

Sujets

• Sciences formelles
• Guides de référence et manuels mathématiques
• Références et manuels de mathématiques
• Clifford Pickover
• Mathematics
• Clifford A. Pickover
• Study
• Sciences et techniques
• Teaching

Informations

• Publié par: Turner Publishing Company
• Date de parution: 25 février 2011
• Nombre de lectures: 0
• EAN13: 9781118046074
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Table of Contents
 
Works by Clifford A. Pickover
Title Page
Copyright Page
Epigraph
Acknowledgments
Introduction
The Ramanujan Code
Blood Dreams and God’s Mathematicians
The Mathematical Smorgasbord
Explanation of Symbols
Cultivating Perpetual Mystery
 
Chapter 1 - Numbers, History, Society, and People
 
Chapter 2 - Cool Numbers
Chapter 3 - Algebra, Percentages, Weird Puzzles, and Marvelous Mathematical Manipulations
Chapter 4 - Geometry, Games, and Beyond
Chapter 5 - Probability:Take Your Chances
Chapter 6 - Big Numbers and Infinity
Chapter 7 - Mathematics and Beauty
 
Answers
References
Index
About the Author
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

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. Mansfield; 113, 114, 115, 145, 146, 332, 333, and 334 by Sam Loyd; 139 courtesy of Peter Hamburger and 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 Cubes by 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.
 
Design and composition by Navta Associates, Inc.
 
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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
 

 
Ramanujan said that he received his formulas from God. This book is dedicated to all those who find Ramanujan’s π formulas beautiful to look at:
(where Poch(n) refers to the Pochhammer notation described in chapter 2)
“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
Acknowledgments
I thank Brian Mansfield for his wonderful cartoon diagrams that appear throughout the book. Over the years, Brian has been helpful beyond compare.
Numerous people have provided useful feedback and information relating to the solutions to my puzzles; these individuals include Dennis Gordon, Robert Stong, Paul Moskowitz, Joseph Pe, Daniel Dockery, Mark Nandor, Mark Ganson, Nick Hobson, Chuck Gaydos, Graham Cleverley, Jeffrey Carr, Jon Anderson, “Jaymz” James Salter, Chris Meyers, Pete Barnes, Steve Brazzell, Steve Blattnig, Edith Rudy, Eric Baise, Martie Saxenmeyer, Bob Ewell, Teja Krasek, and many more. I discussed some of the original puzzles in this book at my Pickover Discussion Group, located on the Web at groups.yahoo.com/group/CliffordPickover , and I thank the group members for their wonderful discussions and comments.
Many of the fancy formulas derived by the Indian mathematician Srinivasa Ramanujan come from Calvin Clawson’s Mathematical Mysteries , Bruce Berndt’s Ramanujan’s Notebooks (volumes 1 and 2), and various Internet sources. With respect to some of the elegant prime number formulas, Clawson cites Paulo Ribenboim’s The Book of Prime Number Records , second edition (New York: Springer, 1989), and The Little Book of Big Primes (New York: Springer, 1991). Calvin Clawson’s Mathematical Mysteries and David Wells’s various Penguin dictionaries provide a gold mine of mathematical concepts. A few problems in this book draw on, update, or revise problems in my earlier books, with information provided by countless readers who spend their lives tirelessly tackling mathematical conundrums.
Other interesting sources and recommended reading are given in the reference section. Numerous Web sites are proliferating that give comprehensive mathematical information, and my favorites include Wikipedia, the Free Encyclopedia ( wikipedia.com ), Ask Dr. Math ( mathforum.org/dr.math/ ), The MacTutor History of Mathematics Archive ( www.gap-system.org/~history/ ), The Published Data of Robert Munafo ( www.mrob.com/pub/index.html ), and MathWorld ( mathworld.wolfram.com ).
Introduction
“An equation means nothing to me unless it expresses a thought of God.”
—Srinivasa Ramanujan (1887-1920)

The Ramanujan Code
“An intelligent observer seeing mathematicians at work might conclude that they are devotees of exotic sects, pursuers of esoteric keys to the universe.”
—Philip Davis and Reuben Hersh, The Mathematical Experience , 1981
 
Readers of my popular mathematics books already know how I feel about numbers. Numbers are portals to other universes. Numbers help us glimpse a greater universe that’s normally shielded from our small brains, which have not evolved enough to fully comprehend the mathematical fabric of the universe. Higher mathematical discussions are a little like poetry. The Danish physicist Niels Bohr felt similarly about physics when he said, “We must be clear that, when it comes to atoms, language can be used only as in poetry.”
When I think about the vast ocean of numbers that humans have scooped from the shoreless sea of reality, I get a little shiver. I hope you’ll shiver, too, as you glimpse numbers that range from integers, fractions, and radicals to stranger beasts like transcendental numbers, transfinite numbers, hyperreal numbers, surreal numbers, “nimbers,” quaternions, biquaternions, sedenions, and octonions. Of course, we have a hard time thinking of such queer entities, but from time to time, God places in our midst visionaries who function like the biblical prophets, those individuals who touched a universe inches away that most of us can barely perceive.
Srinivasa Ramanujan was such a prophet. He plucked mathematical ideas from the ether, out of his dreams. Ramanujan was one of India’s greatest mathematical geniuses, and he believed that the gods gave him insights. These came in a flash. He could read the codes in the mathematical matrix in the same way that Neo, the lead character in the movie The Matrix , could access mathematical symbols that formed the infrastructure of reality as they cascaded about him. I don’t know if God is a cryptographer, but codes are all around us waiting to be deciphered. Some may take a thousand years for us to understand. Some may always b