The Pea and the Sun: A Mathematical Paradox [Paperback]

Leonard M. Wapner (Author)

Book Description

ISBN-10: 1568813279 | ISBN-13: 978-1568813271 | Publication Date: January 20, 2007

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski s magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

Editorial Reviews

Review

A marvelous book --Martin Gardner, The New Criterion

What is presented in this book is math for its own sake: beautiful, elegant, artistic, astonishing. --Helen Joyce, Plus Magazine

This book is sure to intrigue, fascinate, and challenge the mathematically inclined reader. --Charles W. Mitchell Jr., Mathematics Teacher

About the Author

Leonard M. Wapner is Professor of Mathematics at El Camino College in Torrance, CA. He received his BA and MAT degrees in mathematics from the University of California, Los Angeles. During his thirty-year tenure at El Camino, his writings on mathematics education have appeared in The Mathematics Teacher and The AMATYC Review. This is his first book.

Product Details

• Paperback: 232 pages
• Publisher: A K Peters (January 20, 2007)
• Language: English
• ISBN-10: 1568813279
• ISBN-13: 978-1568813271
• Product Dimensions: 8.9 x 6 x 0.6 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #794,897 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

30 of 31 people found the following review helpful:

5.0 out of 5 stars A fascinating introduction to the Banach-Tarski Paradox, October 11, 2005

By 

Midwest Book Review (Oregon, WI USA) - See all my reviews

This review is from: The Pea and the Sun: A Mathematical Paradox (Hardcover)

The Pea And The Sun: A Mathematical Paradox is a fascinating introduction to the Banach-Tarski Paradox, a mathematical riddle that asserts it could be possible to create something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again. Written to be accessible to lay readers and non-mathematicians, The Pea And The Sun outlines the history of the paradox, introduces readers to the basics of such matters as set theory, isometrics, scissors congruence and equidecomposability, and walks the reader through the theorem and proof that object duplication is indeed mathematically possible. But just because it is mathematically possible, is it physically possible? The highly counterintuitive nature of the mathematical theorem demands a critical response. A final chapter dwells on speculation as to how the Banach-Tarski Paradox may apply to the modern and future world. Written in a fresh, captivating, friendly style, The Pea And The Sun is remarkably engaging and will appeal to any reader with a discerning, inquisitive mind into the nature of the so-called impossible, regardless of their particular mathematical background.

26 of 27 people found the following review helpful:

5.0 out of 5 stars It made my top ten list of best popular mathematics books, January 13, 2007

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: The Pea and the Sun: A Mathematical Paradox (Hardcover)

The Banach-Tarski paradox is a candidate for the most counter-intuitive mathematical result ever published. Basically, the conclusion of the theorem is that it is possible to decompose a small object into a finite number of pieces and then reconstruct the pieces a certain way to make two objects identical to the original. Phrased another way, it means that an object the size of a pea can be deconstructed into a finite set of objects that can be reconstructed in a manner to make an object the size of the sun. As bizarre as this sounds, the proof has stood up against all manner of assaults until there is no doubt that it is in fact true.
Wapner does an excellent job in setting the mathematical, historical and philosophical groundwork for explaining the theorem. The book starts with a brief explanation of the lives of Alfred Tarski and Stefan Banach as well as others such as Georg Canto and Kurt Godel who helped create the mathematical framework. This is followed by a lengthy and thorough discussion of the mathematical background needed to understand the theorem and the proof. It begins at the very basic level, so very little mathematical knowledge is needed before you begin.
The next step is the proof of the theorem, which by this time is very easy to understand. It is done step-by-step with not even the slightest "leap of faith." The final chapters deal with the consequences of the theorem. I found these chapters to be the most interesting in the book. In "Resolution", Wapner discussions the possible reactions to the theorem. They are:

*) Declare the result fallacious.
*) Accept the theorem at face value.
*) Reinterpret the result.

The first is not realistic as there is no longer any doubt that the theorem is true and the second is self-evident. Performing the mental gyrations necessary to accept the third option is the most interesting. Wapner resolves it by saying, "Yes, the theorem is true, but the actions needed to do something like duplicating a gold bar are not possible." Chapter 7, called "Real world" mentions some of the principles of quantum mechanics and how they can be related to the Banach-Tarski paradox.
This book is one that will fascinate you, it proves in the mathematical sense what you "know" cannot be true in the real sense. It also demonstrates a fundamental problem of philosophy, which is to consider to what extent a mathematical result can be applied in the real world. I loved this book, it made my top ten list of best popular mathematics books.

Published in Journal of Recreational Mathematics, reprinted with permission.

21 of 25 people found the following review helpful:

5.0 out of 5 stars Actually proves the theorem, October 20, 2005

By 

Mark Weitzman (USA) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: The Pea and the Sun: A Mathematical Paradox (Hardcover)

The book is wonderful because it actually proves the theorem in a way that a non-expert in mathematical foundations can actually understand. I wish all popular mathematics books were written at this level where the goal is to educate and entertain. Now as I suggested to the author all we need is a book like this one that will explain Godel's and Cohen's results on the independence of the continuum hypothesis.