Japanese Temple Geometry Problems Sangaku [Paperback]

Fukagawa (Author)

Product Details

• Paperback: 206 pages
• Publisher: Charles Babbage Research Ctr (December 1989)
• Language: English
• ISBN-10: 0919611214
• ISBN-13: 978-0919611214
• Product Dimensions: 9.2 x 6.1 x 0.6 inches
• Shipping Weight: 10.4 ounces
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,606,693 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

9 of 9 people found the following review helpful:

5.0 out of 5 stars A truely mind-opening little book., March 4, 2006

By 

Joshua Milgram - See all my reviews

This review is from: Japanese Temple Geometry Problems Sangaku (Paperback)

This book is a valuable resource for anyone looking for a sense of wonder in the geometrical world. It is a small treasure trove of facts and ideas that no one seems to care about in Euclidville.

Did you know that if you take two non-parallel tangents to a circle and make a line going through both of the tangent points, the largest circle that can fit inside that triangle has its center on the curve of the original circle? I sure didn't.

The book is intriguing from the very first page. It does not give equations for all relationships that it illustrates, but is nevertheless a wonderful resource, if you can manage to find a copy. The book's largest asset will be the thought that it inspires, and if you are not looking for a thought-provocer, you will find you book very useless.

2 of 2 people found the following review helpful:

5.0 out of 5 stars A very interesting and very fun book, October 29, 2007

By 

David Bakin "David" (Seattle) - See all my reviews
(REAL NAME)   

This review is from: Japanese Temple Geometry Problems Sangaku (Paperback)

This is a terrific book of problems - many with solutions - of plane geometry. The problems are divided into categories: Circles, Circles and Triangles, Circles and Polygons, Polygons, Ellipses, etc. The problems are all given with diagrams.

Most of these problems are unusual from the "western" point of view: They were formulated and solved by Japanese mathematicans (of all social classes) in the years when Japan isolated itself from the western world (1600-1867). They are called "Japanese Temple Geometry Problems" because when one of these problems was posed and solved, the happy theorem prover inscribed the problem on a wooden tablet and took it to a temple or shrine to be hung up and displayed as an offering. (And also, as a challenge to other mathematicians - as the proof was only rarely given!)

The book also has a short description of the problems - from which I took the information I gave in the previous paragraph, a couple of photographs of actual tablets that still exist, and the reproductions of the solutions of two of the problems as they were given in woodblock-printed texts.

Then there is an appendix that is as much fun as the rest of the book: 100 problems, given only as diagrams (no words), all of which concern circles inscribed in square of side a, all involving at least one circle of radius a/16. The question in all cases is the same: prove that the given circles marked as radius a/16 are actually and truely of radius a/16, given the constructions as indicated. The constructions vary from simple to complex, some are very pretty. No solutions are given. I have no idea how hard these problems are - I'm still working my way through them - but they vary.

This book is a gem! If you can't get it from a bookseller (here, via Amazon) then it is well worth the effort to get it via inter-library loan from your local college or public library: That's how I first saw it. But then an Amazon Marketplace seller came through for me!

To get an idea of what these probems are like you might like to look at http://www.sangaku.info and http://www.cut-the-knot.org/Curriculum/Geometry/SquaresAndTrianglesFromJapan.shtml - both pages also have links to other sites of Japanese Temple problems. As the latter site shows, you can have a lot of fun with this book in conjunction with some dynamic geometry software like Cinderella or Geometry Expressions.

UPDATE July 21 2008: Excellent news! Fukagawa Hidetoshi has written a very much updated version of this book, with Tony Rothman, and it is now available in a beautiful book: Sacred Mathematics: Japanese Temple Geometry. It is not a reprint, but a brand new book that includes sections on the history of San Gaku problems and East v. West styles of mathematics, along with good descriptions of the San Gaku problems with solutions and explanations. Plus beautiful photographs, some in color.