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Sacred Mathematics: Japanese Temple Geometry [Hardcover]

by Fukagawa Hidetoshi, Tony Rothman, Freeman Dyson
4.9 out of 5 stars  See all reviews (7 customer reviews)

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Book Description

July 21, 2008 069112745X 978-0691127453 0

Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree. During that time, a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in Western mathematics. People from all walks of life--samurai, farmers, and merchants--inscribed a wide variety of geometry problems on wooden tablets called sangaku and hung them in Buddhist temples and Shinto shrines throughout Japan. Sacred Mathematics is the first book published in the West to fully examine this tantalizing--and incredibly beautiful--mathematical tradition.

Fukagawa Hidetoshi and Tony Rothman present for the first time in English excerpts from the travel diary of a nineteenth-century Japanese mathematician, Yamaguchi Kanzan, who journeyed on foot throughout Japan to collect temple geometry problems. The authors set this fascinating travel narrative--and almost everything else that is known about temple geometry--within the broader cultural and historical context of the period. They explain the sacred and devotional aspects of sangaku, and reveal how Japanese folk mathematicians discovered many well-known theorems independently of mathematicians in the West--and in some cases much earlier. The book is generously illustrated with photographs of the tablets and stunning artwork of the period. Then there are the geometry problems themselves, nearly two hundred of them, fully illustrated and ranging from the utterly simple to the virtually impossible. Solutions for most are provided.

A unique book in every respect, Sacred Mathematics demonstrates how mathematical thinking can vary by culture yet transcend cultural and geographic boundaries.

Frequently Bought Together

Sacred Mathematics: Japanese Temple Geometry + Ruler and Compass: Practical Geometric Constructions (Wooden Books) + Sacred Geometry (Wooden Books)
Price for all three: $56.34

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Editorial Reviews


Winner of the 2008 PROSE Award in Mathematics, Association of American Publishers

"Now Fukagawa Hidetoshi, a mathematics teacher, and writer Tony Rothman present a collection of Sangaku problems in their book, Sacred Mathematics. The puzzles range from simple algebra within the grasp of any intermediate-school student, to challenging problems that require graduate-school mathematics to solve. Copious illustrations and many detailed solutions show the scope, complexity, and beauty of what was tackled in Japan during the Tokugawa shogunate."--Peter J. Lu, Nature

"Fascinating and beautiful book."--
Physics World

"This book is the most thorough (and beautiful) account of Japanese temple geometry (sangaku) available."--Paul J. Campbell, Mathematics Magazine

"The difficult problems with complete solutions and rich commentary that comprise the heart of this book will interest every mathematics student."--

"This is a marvelous book. Good books are not just written or compiled, they are crafted. Sacred Mathematics is a well crafted work that combines mathematics, history and cultural considerations into an intriguing narrative. . . . The writing style is appealing and the organization of material excellent. Princeton University Press must be congratulated on producing this quality publication and offering it at an agreeable price. This book is highly recommended for personal reading and library acquisition. It should be especially appealing to problem solvers."--Frank J. Swetz, Convergence

"A unique book in every respect. Sacred Mathematics demonstrates how mathematical thinking can vary by culture yet transcend cultural and geographic boundaries."--
International Institute for Asian Studies Newsletter

From the Inside Flap

"An enchanting history of Japanese geometry--of a time and place where 'geometers did not cede place to poets.' This intersection of science and culture, of the mathematical, the artistic, and the spiritual, is packed, like circles within circles, with rewarding Aha! epiphanies that drive a mathematician's curiosity."--Siobhan Roberts, author of King of Infinite Space

"Teachers will welcome this remarkable collection of mathematical problems, history, and art, which will enrich their curriculum and promote both logical thinking and critical evaluation. It is especially important that we maintain an interest in geometry, which needs, and for once gets, more than its share."--Richard Guy, coauthor of The Book of Numbers

"This remarkable book provides a novel insight into the Japanese mathematics of the past few hundred years. It is fascinating to see the difference in mathematical style from that which we are used to in the Western world, but the book also elegantly illustrates the cross-cultural Platonic nature and profound beauty of mathematics itself."--Roger Penrose, author of The Road to Reality

"A significant contribution to the history of mathematics. The wealth of mathematical problems--from the very simple to quite complex ones--will keep the interested reader busy for years. And the beautiful illustrations make this book a work of art as much as of science. Destined to become a classic!"--Eli Maor, author of The Pythagorean Theorem: A 4,000-Year History

"A pleasure to read. Sacred Mathematics brings to light the unique style and character of geometry in the traditional Japanese sources--in particular the sangaku problems. These problems range from trivial to utterly devilish. I found myself captivated by them, and regularly astounded by the ingenuity and sophistication of many of the traditional solutions."--Glen Van Brummelen, coeditor of Mathematics and the Historian's Craft

Product Details

  • Hardcover: 392 pages
  • Publisher: Princeton University Press (July 21, 2008)
  • Language: English
  • ISBN-10: 069112745X
  • ISBN-13: 978-0691127453
  • Product Dimensions: 9.9 x 8.4 x 1 inches
  • Shipping Weight: 2.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #889,893 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
14 of 15 people found the following review helpful
5.0 out of 5 stars Beautiful Mathematics August 4, 2008
Format:Hardcover|Verified Purchase
For anyone who truly loves mathematics, this book is a must have.
Simply put, the book tells the story of sangaku, geometry problems which were painted in color on wooden tablets and displayed at Buddhist temples and Shinto shrines throughout Japan. Most of the sangaku were composed by people from all walks of life-priests, farmers, children women, samurai, etc.-between 1600 and 1900. Approximately 900 of the old tablets have survived and even today one is occasionally found at an abandoned temple/shrine. Tony Rothman has assisted Mr. Fukagawa Hidetoshi, a retired Japanese high school teacher, who is one of the world's foremost experts in sangaku, in producing a beautiful book. Various chapters discuss Japan and temple geometry, the Chinese foundation of mathematics, Japanese mathematics and mathematicians of the Edo period. In addition, the book contains over 200 sangaku problems ranging from very elementary to extremely difficult. The book also contains extensive excerpts from the diary of Yamaguchi Kanzan, a Japanese mathematician, who treked through Japan during the 1800s collecting sangaku problems. Finally, there are chapters on East and West, Japanese attempts to handle differentiation and integration, and inversion. The book contains numerous diagrams which accompany the problems and there are 16 color plates. In summary, this book captures a beautiful form of vanished mathematics which was artistic/religious in nature. Mr. Fukagawa Hidetoshi and Mr. Rothman are to be congratulated for producing a superb book which tells the story of this vanished mathematical/religious art form. Buy your copy today. This book contains enough history, mathematics, art, and religion to keep one's intellect perplexed for years.
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12 of 13 people found the following review helpful
5.0 out of 5 stars Like pirahnas on a hapless animal December 12, 2008
Format:Hardcover|Verified Purchase
I have been using a number of the Sangakus from Sacred Geometry in my High School Pre-Calculus classes to get things rolling at the start of the class. The kids are loving them! Watching the kids last class get the problem and go to work on it reminded me of watching piranha's go after a hapless animal-- maybe a bit less graphic. The problems are just great-- they really hook the kids, really get them trying stuff, and they do a fantastic job of building up and connecting their skills. Of course I am having a great time with them too!

Further, the book is just a pleasure to read. Everything about it-- prose, graphics, mathematics, quality of production-- is just top notch.
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9 of 10 people found the following review helpful
5.0 out of 5 stars Excellent book October 9, 2008
Format:Hardcover|Verified Purchase
The last (for the moment) title of Fukagawa&Rothman is really excellent. Not only the printing is superb, but the mathematical content is also outstanding. Strongly recomended to every lover of geometry...
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8 of 9 people found the following review helpful
4.0 out of 5 stars An excellent book with just one minor thing missing April 12, 2009
It's a beautiful book, interesting and lovely. I enjoy mathematical problems and I enjoy studying Japanese culture. This book satisfies both my interests!

There is just one minor thing that's missing - the Japanese names are written entirely in Romanji. When I first started reading the book I kept wondering what is "sangaku" in Kanji. Most of my Japanese friends have not even heard of it. After much searching, I discovered the kanji for sangaku is ZZŠz, or mathematics tablets. The same romanji, "sangaku", could also have been these two kanji, ZZŠw, study of mathematics.

I hope the next edition of this book would include kanjis or at list an index of the kanji, it makes life easier for students of Japanese.

Bottom line is, this is an excellent book, and anyone interested in Japanese culture would be interested in this book.
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