Sacred Mathematics: Japanese Temple Geometry by Fukagawa Hidetoshi (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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.

⭐I am using this book for an independent study course and it has been perfect. I love the history it includes and the pictures of the equations as they were in Japan. I also liked that it included several chapters of text book style equations with examples of how to solve them, it helped me in my course work a lot.

⭐College math research paper.

⭐If you are interested in both mathematics and japanese history and culture, this is a treasure. The selection of problems is excellent. The historical and cultural background to the problems is well elucidated,

⭐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…

⭐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.

⭐I am always interested in what Tony Rothman has to say. He is the real deal, teaches physics at Princeton, Harvard, etc., who comes up with revolutionary insights you just can’t find anywhere else. SACRED MATHEMATICS is a revelation and a tremendous challenge, another brilliant one in this writer’s repertoire.I began my Rothman studies after reading INSTANT PHYSICS, which pretty much brought me up to speed in what had always intrigued yet baffled me. Then I was amazed with his majestic DOUBT AND CERTAINTY followed by the jaw-dropping, myth-busting EVERYTHING’S RELATIVE. I couldn’t get enough so I started backtracking and discovered the Pulitzer Prize nominated A PHYSICIST ON MADISON AVENUE and SCIENCE A LA MODE, where he maybe first established his continual theme of treating science with the skeptical irreverence it often deserves. In between, I discovered articles in SCIENTIFIC AMERICAN, DISCOVER, ISAAC ASIMOV’S SCIENCE FICTION MAGAZINE and THE NEW REPUBLIC, not to mention some weighty scientific papers and reports. Finally, I found his science fiction novel, THE WORLD IS ROUND, with which the movie industry might finally have the tools to do justice.Tony Rothman is a great and gifted writer and SACRED MATHEMATICS is a beautifully illustrated book of art, religion, history and geometry. I see from his web site that a novel about The Great Seige of Malta is next. I anxiously anticipate that and hope that both APOCHRYPHA and the plays there mentioned will soon be published.I strongly recommend SACRED MATHEMATICS and, in fact, everything written by Tony Rothman to anyone, who in a world too often full of nonsense and lies, cherishes instead reality and truth. Rothman’s voice is beautiful and unique.

⭐Questo interessantissimo e leggibilissimo volume è al contempo:un belissimo libro d’arte, con fotografie stupende di opere uniche della tradizione iconografica giapponese;un libro di storia della matematica che affronta il campo dei Sangaku, poco esplorato e ancora ricco di spunti da studiare;un repertorio di problemi interessantissimi, tali da suscitare l’entusiasmo di studenti ed appassionati.Peccato che difficilmnete ne vedremo un’edizione italiana.

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⭐If you like Sangakus, and mathematics in general, this is your book. Greetings from Colombia

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