Keys to Infinity (Paperback)

~ (Author) "How many numbers contain the digit 3?..." (more)
Key Phrases: infinity worms, narcissistic numbers, vampire numbers, New York, Infinity World, Cancer Game (more...)

Editorial Reviews

Amazon.com Review

Clifford Pickover is by most standards a mathematics geek (Ph.D. research scientist for IBM, associate editor for two computer journals), but he is the coolest math geek you might ever meet. For this book he has compiled 30 chapters of mathematical puzzles (and one short story), all having some connection to the concept of infinity. These problems are open-ended; in the event that the reader actually solves the main puzzle, there are enough digressions, diversions, and tangents to keep even the fastest computer running for hours. Computer modelers will be happy to find that instructive BASIC and C language has been provided for most of the problems. Many puzzles have been previously posted on the Internet, and the best or weirdest replies have been included in this book.

If phrases like "Monte Carlo bootstrapping approximation" send you off the deep end, not to worry. These are not dry, dusty puzzles. In problems such as "The Loom of Creation," "Grid of the Gods," "Alien Abduction Algebra," and "The Infinity Worms of Callisto," Pickover has couched mathematical puzzles in bizarre science fiction scenarios to make them both fun and challenging. --Eric Warner

Review

"In this the latest of Dr. Pickover's marvelous books, he breaks all finite chains to soar into the transcendental, mind-boggling regions of mathematical infinity. Written in the author's informal, clear style, it is a treasure trove of recreational problems, many published here for the first time, with special emphasis on computer programs and riveting graphics. As you soar, fasten your seat belt."-Martin Gardner, author of The Magic Numbers of Dr. Matrix "Inventive, quirky, fun! Pickover presents an engaging, inspiring romp in the realm of number and mathematical thought."-Ivars Peterson, author of The Mathematical Tourist "Join Pickover on his wonderful merry-go-round of ideas, and reach for the infinite. Keys to Infinity is an engaging book...a must for those wishing to explore the infinite in all its manifestations."-Theoni Pappas, author of The Joy of Mathematics "Keys to Infinity contains a near infinity of absorbing themes: from stepladders to the moon and spiral earths, to worm worlds, random chords, and self-similar curlicues. Fascinating!"-Manfred Schroeder, author of Fractals, Chaos, Power Laws "What could be more appropriate to the subject of infinity than a book like this one, so dense with wonderful puzzles, anecdotes, images, and computer programs that you could pore over it forever? In Keys to Infinity, Pickover has once again assembled a mathematical feast."-Carl Zimmer, Senior Editor Discover "Cliff Pickover has produced yet another book of mathematical puzzles, weird facts, computer art, and simple programs to challenge our minds and enthrall us with the beauty of the infinite mathematical world in which we live."-Dr. Julien C. Sprott, author of Strange Attractors

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Product Details

• Paperback: 352 pages
• Publisher: Wiley (August 29, 1997)
• Language: English
• ISBN-10: 0471193348
• ISBN-13: 978-0471193340
• Product Dimensions: 8.5 x 5.6 x 0.7 inches
• Shipping Weight: 1 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon.com Sales Rank: #1,085,477 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars A truly entertaining book on numbers, February 25, 2000

By	Charles Ashbacher "([e-mail])" (Marion, Iowa United States([e-mail])) - See all my reviews (TOP 50 REVIEWER)

A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today. In most cases using only simple ideas, he follows paths that in many cases must be constructed immediately before traversal. In this, his latest installment in that trek of exploration, he is again at his best.
Each subject starts with a simple premise and the author follows it through to a basic conclusion. Many of the topics involve computer programs, and source code is provided. The programs are in several languages, including C, Pascal, BASIC and Rexx. However, most programs are quite short and represent basic algorithms, so it is not difficult to understand a program even if you are not familiar with the language.
Some of the topics include:

- 10^33, the largest power of 10 that can be represented as the product of two numbers that contain no zero digits.
- A debate as to whether there should be a national computing initiative to compute the first trillion digits of Pi.
- Fractal milkshakes, or creating a collection of fractal "bubbles."

Truly fuN with a capital N for number, this is another of the author's superb creations. A math book that is entertaining, and not just to people who find it so by nature or profession.

Published in Journal of Recreational Mathematics, reprinted with permission.

8 of 8 people found the following review helpful:

5.0 out of 5 stars A fascinating exploration of topics on infinity, July 6, 2002

By	P. Barnes "Pete B" (Nashville, TN) - See all my reviews (REAL NAME)

*The book is a collection of fascinating, thought-provoking essays on
various topics which are not necessarily all concerned with infinite
topics. Some may be discussions of really big numbers or
mathematical constructs, but these may or may not necessarily involve
infinity.

*If you absolutely cannot stand math stuff, this is not your book.
Otherwise, it has a range of math from very simple to really
advanced. I just brushed over the very advanced math stuff that I
either did not understand or had long ago forgotten, but I didn't
really feel like I missed anything.

*There are a slew of amazing visually complex and striking graphical
representations of various advanced functions, etc. All are well
worth exploring, even if they do not directly involve infinite
concepts. The book is loaded with such graphics, a real visual feast.

*The math is rather advanced in some sections but is quite elementary
in others. Best of all, a generous collection of computer programs
is included which can be used to explore almost every chapter.

*There are a few "mystery" type things, but mostly it is just very
exotic, seldom-explored areas of number theories and other areas of
mathematics.

*The chapter on Vampire numbers is really cool, I thought. I have
seen them mentioned in posts here from time to time, now I understand
what they are and why they are so interesting

*The chapter on recursion has loads of really cool pattern-type stuff
that you can easily explore with a PC. A great topic.

*The chapter near the back of the book on random numbers and random
number generators is great background for some anyone interested in quantum theory. I had never seen the RNG cloud graphics before, what a
unique and ideal way to show the effectiveness of an RNG.

As expected, this is a great book, I heartily recommend it for all.

4 of 5 people found the following review helpful:

5.0 out of 5 stars The one thing wrong with this book is that it's finite, September 14, 1997

By A Customer

This review is from: Keys to Infinity (Hardcover)

This book is not just for maths nuts like me. Its for anyone who has a passing interest in the subject.

The author has in a crisp and concise wa,y managed to introduce, and in some cases explain, both the history and the solution, to some of the most mystifying problems to confront mankind in his infinite quest to understand the Ultimate Infinity - The Universe.

The cover notes suggest that the reader requires "no specialised mathematical knowledge " but you will need to understand some maths probably to GCSE level but then you would not buy, borrow or steal this book if you can't add, subtract, multiply and divide.

The computer programs that are sprinkled throughout the book do require a lot of thought and a good knowledge of the particular language, of which there are several, to make them work but, when they do, they demonstrate the beauty of maths as well as illustrate the ideas under discussion extremely well.

In all a very good read.