The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures Across Dimensions

by Clifford A. Pickover

Book Overview

Humanity's love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of...

• Format: Paperback
• Language: English
• ISBN: 0691115974
• ISBN13: 9780691115979
• Release Date: June 2002
• Publisher: Princeton University Press
• Length: 413 Pages
• Weight: 1.40 lbs.
• Dimensions: 1.0" x 6.1" x 9.1"

Customer Reviews

What fun!

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.

Diverse collection

A magic square is an array of numbers in which the sums of numbers in rows, columns, and diagonals are equal. A magic square uses consecutive numbers from 1 to N. Here's an example,4 9 23 5 78 1 6This book is different from all others I've seen on the subject, and I don't know any other books that present the large range of patterns that you'll find here. The book also focuses on discoveries in the last few years. As Pickover says, the book is essentially an exhibit of magnificent forms discovered through the centuries. All sorts of historical and quirky-human aspects are also described. Centuries ago, people believed that magic squares to had special, magical powers....

Great book on pure mathematical fun

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!

A thousand hours of magical fun.

If you love numbers, magic squares, geometry and mental calisthenics, read this book. It is the most complete source of information available on this topic and the author is exceedingly thorough and precise in his treatment of it. I was thrilled to discover new gems that I never knew existed before. As a result, a few extra neurons connected in my brain! That alone was worth the price of admission.

A smorgasbord for the mind

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.