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Legacy of the Luoshu: The 4,000 Year Search for the Meaning of the Magic Square of Order Three: The Mystical, Mathematical Meaning of the Magic Square of Order Three [Hardcover]

Frank Swetz

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Book Description

16 Jun 2008
A symbol of the Divine, a good luck charm, a cosmogram of the world order, a template for fengshui —through the ages, the luoshu, or magic squre of order three, has fascinated people of many different cultures.

In this riveting account of cultural detective work, renowned mathematics educator, Frank J. Swetz relates how he uncovered the previously hidden history of the luoshu, from its Chinese origins, shrouded in legend, through its eventual association with Chinese fortunetelling, Daoism, and fengshui, to its incorporation into Islamic astrology and alchemy and its migration into Kabbalistic lore and other occult traditions of the West.

Product details

  • Hardcover: 228 pages
  • Publisher: A K Peters/CRC Press; 2Rev Ed edition (16 Jun 2008)
  • Language: English
  • ISBN-10: 1568814275
  • ISBN-13: 978-1568814278
  • Product Dimensions: 1.8 x 15.3 x 22.8 cm
  • Amazon Bestsellers Rank: 1,351,041 in Books (See Top 100 in Books)

More About the Author

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Product Description


...an in-depth study of the diverse roles that the luoshu (a 3x3 'magic square' of numbers in a grid, where all rows, columns, and diagonals add up to the same sum) has played in metaphysical and spiritual traditions worldwide. From Chinese fortunetelling to Daoism, and fengshui, to Islamic astrology and Kabbalistic lore, the luoshu has perpetually reappeared throughout global human history. Extensively researched and illustrated with a handful of black-and-white photographs, Legacy of the Luoshu offers a unique glimpse into one aspect of the history of numerology, and is highly recommended especially for mysticism and metaphysical studies shelves.
Wisconsin Bookwatch, October 2008

I found the book very interesting and a joy to read, not least because of the many diagrams and illustrations. What makes this book especially worthwhile, however, is the attention paid to the large variation in cultural meanings, both within China as well as in other countries ... I find in this book a beautiful uncovering of this part of the history of mathematics.
—Aldine Van Der Ham-Aaten, MAA Reviews, January 2009

This fascinating book describes the luoshu (i.e. the magic square of order three) from Chinese origins and legends, its role in the development of Chinese mathematical thinking and teaching and its association with the rise of Chinese science and philosophy. It can be recommended to anybody interested in the properties of numbers, roots of number theory and the history of mathematics, as well as Chinese mathematical tradition.
EMS Newsletter, March 2009

About the Author

Frank J. Swetz, Professor Emeritus at the Pennsylvania State University, is one of America's best known mathematics educators. His interest in how society promotes mathematical knowledge led him to try to understand the cultural history of mathematics. He is co-founding editor of Convergence, an e-journal devoted to the History of Mathematics and its Teaching. He has authored over 300 articles and 20 books, including Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China (1977) and Capitalism and Arithmetic: The New Math of the Fifteenth Century (1987). He edited From Five Fingers to Infinity: A Journey through the History of Mathematics (1994).

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First Sentence
As you read this book, you will see that the cultural history of the magic square known as the luoshu is a fascinating one that touches on cosmology, mythology, philosophy, religion, occult practices, mathematics, architecture, and even music. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.8 out of 5 stars  8 reviews
6 of 7 people found the following review helpful
4.0 out of 5 stars Well Researched Yet Fun to Read 22 April 2002
By Lorraine Wilcox - Published on Amazon.com
The Legacy of the Luoshu covers the story of the luoshu in China, both in legend and using historical sources. It tells how the luoshu and the magic square came to the attention of the West in the 17th century. The book explains uses of the luoshu in traditional Chinese culture, and also examines the use of the luoshu in other cultures, including Greece, India, Tibet, Japan, and the Islamic world. This book explains the mathematics of magic squares and how they are derived.
The Legacy of the Luoshu is 214 pages with many diagrams and illustrations. This includes some beautiful drawings from old Chinese books.
The author, Frank Swetz, is a professor of mathematics, who has written many other books, including others on Chinese mathematics. Even though he is a mathematician, his writing is very readible. The book has extensive footnotes, yet does not seem stuffy at all. In fact, you can feel the authors excitement as he discovers new details about the history of the luoshu. The author has a good grasp of Chinese culture, without any feeling of condesention.
If you are curious about history and how things work, this is a wonderful book! The first four chapters were fascinating; I just wanted to lie in bed and read them. The later half of the book is a great resource to which I will refer, although the subjects were less focused on my specific areas of interest.
If you enjoy learning about the intellectual and spiritual pursuits of classical Chinese culture, you will love this book. Overall, this is a very well researched book that is serious, yet fun to read.
3 of 3 people found the following review helpful
4.0 out of 5 stars History of the first magic square 19 May 2003
By Boyer Christian - Published on Amazon.com
If you are interested by magic squares and their history, then you will be interested by this book.
It describes with a lot of nice illustrations the history of the first known magic square 3x3, constructed by the Chinese, a very very long time ago.
Well documented book, with probably long hours of research done by the author.
New valuable information, never published before.
I wish a great success to this new Swetz's book.
2 of 2 people found the following review helpful
5.0 out of 5 stars Legacy of the Luoshu 4 Aug 2003
By James F. Kiernan - Published on Amazon.com
Frank Swetz has done it again. In plain language he has given
the best description of the luoshu magic square that I have read.
The first half of his book is a detailed explanation of
how the magic square is an outgrowth of Chinese philosophy. Swetz very carefully explains the connection of the square
to the concepts of Yin/Yang, I Ching and Feng Shui. One can easily understand the cultural and mystical significance of
the square and its relation to cosmology and astrology.The
book contains excellent diagrams which are well documented
and copious endnotes.
The third quarter of the book gives an decent explanation
of why the square was not first developed in Europe. The
last quarter of the book discusses various miscellana about
the luoshu magic square. In all the Legacy of the Luoshu is
a fascinating read and a must for anyone who would care to
give a detailed explanation of its meaning.
1 of 1 people found the following review helpful
5.0 out of 5 stars More Insight into Chinese Mathematics 29 May 2003
By "tumaradanza" - Published on Amazon.com
In the Legacy Of The Luoshu, Prof. Swetz combines history with mathematics and culture to take the reader on a particular journey of understanding. He shows how mathematics evolves from human needs and provides insights into early scientific thinking.
The book is well researched and contains many interesting illustrations. Chinese beliefs concerning yin-yang forces and cosmological theories are explained and their connections with mathematics revealed. Swetz has spent many years exploring Chinese mathematics and I have enjoyed and employed his earlier research in this field.
In this latest book, he documents the Chinese discovery of the magic square of order three and traces the influence of this number square on other cultures. It is a masterfully told story by a skilled story teller.
3 of 4 people found the following review helpful
5.0 out of 5 stars Legacy of the Luoshu 1 April 2003
By M Connor Loesch - Published on Amazon.com
As a former mathematics teacher, and someone interested in the history of mathematics, I found this most recent book by Professor Swetz to be very interesting and very professionally written. There is material in this book that I have not seen in any other sources. The book provides a great resource for anyone interested in the history of mathematics.
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