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The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions Hardcover – January 1, 2002

ISBN-13: 978-0691070414 ISBN-10: 0691070415

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Product Details

  • Hardcover: 400 pages
  • Publisher: Princeton University Press (January 1, 2002)
  • Language: English
  • ISBN-10: 0691070415
  • ISBN-13: 978-0691070414
  • Product Dimensions: 9.6 x 6.3 x 1.3 inches
  • Shipping Weight: 1.7 pounds
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #686,551 in Books (See Top 100 in Books)

Editorial Reviews

From Scientific American

"In this book," Pickover writes, "we will go far beyond ordinary magic squares and consider many unusual variations, some in higher dimensions, all with mind-boggling patterns." You do not have to reach the "miniature epiphany" he says you might have while contemplating the intriguing structures he describes, but you should get instruction and pleasure from them. Pickover, a research staff member at the IBM Thomas J. Watson Research Center, is the author of many other books on mathematical subjects.

Editors of Scientific American

Review

"A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today."--Journal of Recreational Mathematics

"Pickover just seems to exist in more dimensions than the rest of us."--Ian Stewart, Scientific American

"Clifford Pickover is many things--scientist, scholar, author, editor, and visionary. . . ."--Games

"It is a safe bet to conjecture that this is the best recreational mathematics book that will be published in this year. . . . Pickover writes with his usual style and straightforward simplicity in this book. The material is presented well and can be understood by anyone with a basic middle school mathematics background. This is a cool book!"--Charles Ashbacker, Journal of Recreational Mathematics

"Through accessible and readable prose and through detailed, highquality line illustrations, Pickover ably transports the general reader from culturally embedded traditional topics to a new and surprising frontier."--Harold Don Allen, Mathematics Teacher

"Pickover writes about his subject with contagious enthusiasm and comprehensive erudition."--Choice

"A splendid recreational book. . . . An extremely alluring page-turner."--Andrew Bremner, Notices of the American Mathematical Society

Customer Reviews

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And you will probably have a next edition, I am sure that your book will be really successful.
Boyer Christian
They appear throughout history and the most famous person to create them was the immensely talented Benjamin Franklin.
Charles Ashbacher
When I first spotted this title< I was hooked by its appeal Thus, my expectations were very high.
John Tyler Gibson

Most Helpful Customer Reviews

18 of 19 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on February 21, 2002
Format: Hardcover
While I am writing this in late February, it is still a safe bet to conjecture that this is the best recreational mathematics book that will be published this year. Magic squares are a fascinating area of mathematics, and Pickover covers a great deal of ground in bringing the field up to date. A magic square is a square grid of numbers where the row and column sums are the same. They appear throughout history and the most famous person to create them was the immensely talented Benjamin Franklin.
Magic squares can be created using many different formulas, including the moves of a knight on a board, using operations other than addition, and the embedding of magic squares inside magic squares. If you have not followed the development of the field, you will be amazed at how many different ways they can be constructed.
Magic squares have also been extended to include magic cubes of three and four dimensions. The star of the book is John Hendrick, an incredible person who seems blessed with some form of magic as he creates ever more complicated magic structures. Hendrick uses only a programmable calculator in his searches for larger and more complex magic figures, which makes his work all the more remarkable. Additional magic structures are the star and circle, where the points of intersection are marked with numbers and the sums of the points along lines are equal.
Pickover writes with his usual style and straightforward simplicity in this book. The material is presented well and can be understood by anyone with a basic middle school mathematics background. This is a cool book!
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23 of 26 people found the following review helpful By Archimedes2 on January 9, 2004
Format: Hardcover
This is a book about mathematical artifacts, but it has practically no mathematical content of its own. A casual reader who wants to gaze at these beautiful objects and come away impressed but with little understanding will find this a marvellous book. However, a mathematically inclined reader is not satisfied with someone declaring that an object has such-and-such a property, he wants to know WHY.
Chapter 1 of this book gives dozens of fascinating constructions, but for most of them not a shred of proof is offered that the arrays produced are the magic squares Pickover claims. It leaves me wondering whether or not Pickover could produce such proofs himself, even for the more simple constructions in the book.
Pickover describes some interesting computer experiments at the end of the chapter but seems completely stymied as to why they work. The demonstration is a lovely, but simple, piece of matrix theory that I would expect my first or second year Linear Algebra students to be able to perform.
He shows two "brute-force" proofs for the order 3 case, one by Hendricks and "another" by Johnson (at least here is an attempt at including a proof), but annoyingly seems unaware that the second is just a minor variation on the first. I wonder if Pickover actually tried to follow these proofs himself or if he just copied them for his book.
Mathematics is not a collection of statements that the hearer must accept on "authority", it is a systematic development of theory in which every statement can be, at least in principle, demonstrated by a logical argument. The mathematics is in understanding "why", not in the acceptance of fact. Without demonstration of the claims, all that is left is the shell with no life.
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10 of 11 people found the following review helpful By Emily Rosen on January 17, 2002
Format: Hardcover
This book is awesome! It seems as if Cliff Pickover has journeyed around the world to find unusual people and their fascinating magic squares, circles, stars, and other mathematical wonders. Topics include: Benjamin Franklin's "most magical" magic square, John Hendricks' four-dimensional magic tesseracts and other gems from prisoners, scientists, little-known artists, and computer programmers. Just last year, Pickover came across a wonderful collection of magic figures designed by the late, great Fubine. Fubine, whose real name was Cipriano Ferraris, died in 1958. Fubine's designs ranged from simple squares through a wide variety of linear geometric shapes and three-dimensional figures. Rows, columns, spokes, and diameters consisted of lines of numbers, no single one of which was repeated and whose totals were always the same. Pickover say that in 1929, Fubine lost all his money in the great stock market crash. He found himself in near suicidal state and distracted himself by creating ever-larger magic squares.
What a smorgasbord for children, laypeople, and even seasoned mathematicians! In this book, you'll find information on magic square creation, classification, and history, and graphical representations that can be quite beautiful. The book contains math and art. Although, the literature on magic squares is vast, this book contains some magnificent structures discovered in the last few years. I don't think there is any other book that presents such a huge range of patterns.
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10 of 11 people found the following review helpful By "kmwwrench" on December 28, 2002
Format: Hardcover
OK, there were a couple of typos -- keeps you on your toes. Lots and lots of examples of different variations on the magic square theme -- and puzzles for the reader to solve. Some of those puzzles are quite easy and some are quite difficult and have yet to be solved by anyone. You can't be a mathphobe to read this book, but you don't need to be a math whiz either. Anybody who likes the challenge of a good crossword or crossnumber puzzle should like this.
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Most Recent Customer Reviews


More About the Author

From my publisher:

Clifford A. Pickover received his Ph.D. from Yale University and is the author of over 30 books on such topics as computers and creativity, art, mathematics, black holes, religion, human behavior and intelligence, time travel, alien life, and science fiction.

Pickover is a prolific inventor with dozens of patents, is the associate editor for several journals, the author of colorful puzzle calendars, and puzzle contributor to magazines geared to children and adults.

WIRED magazine writes, "Bucky Fuller thought big, Arthur C. Clarke thinks big, but Cliff Pickover outdoes them both." According to The Los Angeles Times, "Pickover has published nearly a book a year in which he stretches the limits of computers, art and thought."
The Christian Science Monitor writes, "Pickover inspires a new generation of da Vincis to build unknown flying machines and create new Mona Lisas." Pickover's computer graphics have been featured on the cover of many popular magazines and on TV shows.

His web site, Pickover.Com, has received millions of visits. His Blog RealityCarnival.Com is one of his most popular sites.

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