Legacy of the Luoshu

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).

...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 2008I 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 2009This 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

• Acknowledgments, Prologue, 1. THE JOURNEY BEGINS, 2. ON THE BANKS OF THE LUO RIVER: THE CHINESE ORIGINS OF THE LUOSHU, 3. YINYANG, WUXING, AND KEY NUMBERS IN THE LUOSHU, 4. THE LUOSHU IN COSMIC RITUAL, FORTUNE-TELLING, AND FENGSHUI, 5. CHINESE VARIATIONS ON THE LUOSHU THEME, 6. THE MAGIC SQUARE OF ORDER THREE IN OTHER CULTURES, 7. LUOSHU MISCELLANEA, 8. SOME FINAL THOUGHTS, Epilogue, Notes, Bibliography, Illustration Acknowledgments