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| Acknowledgments | ix | |
| Prologue | xi | |
| 1. | The Journey Begins | 1 |
| 2. | On the Banks of the Luo River: The Chinese Origins of the Luoshu | 9 |
| Mystical Beginnings on the Shell of a Tortoise | 9 | |
| The Earliest References to the Luoshu | 12 | |
| The Traditional Method of Constructing the Luoshu | 16 | |
| 3. | Yinyang, Wuxing, and Key Numbers in the Luoshu | 19 |
| "Nineness" and "Fiveness" in the Luoshu | 20 | |
| Yinyang: The Potential to Become | 27 | |
| Wuxing: Directions for Change | 31 | |
| 4. | The Luoshu in Cosmic Ritual, Fortune-Telling, and Fengshui | 39 |
| Talking to the Sky God in Mingtang Temples | 40 | |
| Taiyi and the Daoist Dance | 48 | |
| Divination Enters the Picture: The Eight Trigrams | 53 | |
| Cycles of Time and the Flying Star System of Fengshui | 56 | |
| Fortune-Telling with the Luoshu | 59 | |
| Variations on the Luoshu | 61 | |
| 5. | Chinese Variations on the Luoshu Theme | 65 |
| Other Magic Squares of Order Three? | 65 | |
| Higher Order Magic Squares | 68 | |
| Later Work with Magic Number Arrangements | 77 | |
| 6. | The Magic Square of Order Three in Other Cultures | 79 |
| Who Didn't Know about Magic Squares? | 79 | |
| Babylonia | 79 | |
| Greece | 80 | |
| Egypt | 82 | |
| Who Else Knew about Magic Squares? | 82 | |
| India | 83 | |
| Tibet | 89 | |
| Japan | 90 | |
| The Islamic World | 93 | |
| Magic Squares in Latin Europe | 107 | |
| A Mathematical Interest in Magic Squares | 116 | |
| 7. | Luoshu Miscellanea | 121 |
| Some Mathematical Considerations | 121 | |
| Luoshu Puzzles | 128 | |
| Another Time, Another Place, Another Legend | 134 | |
| Mr. Browne's Illustrious Magic Square | 135 | |
| Feel the Rhythm | 140 | |
| Taijiquan, the Luoshu, and Immortality | 145 | |
| 8. | Some Final Thoughts | 151 |
| Why Did the Magic Square Originate and Flourish in China Rather Than in the West? | 152 | |
| What Happened to the Luoshu as a Visible Symbol of Harmony? | 155 | |
| What is the Ultimate Significance of the Luoshu? | 156 | |
| Epilogue | 161 | |
| Notes | 165 | |
| Bibliography | 193 | |
| Illustration Acknowledgments | 207 | |
| Index | 209 |
Anonymous
Posted April 22, 2002
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.
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