Sacred Mathematics: Japanese Temple Geometry

by Fukagawa Hidetoshi, Tony Rothman, Freeman Dyson (Foreword)

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.

Genres: History, Mathematics, Japan, Architecture, Geometry, Science, Philosophy

392 pages, Hardcover

First published July 27, 2008

Reviews

[Jean Constant · Rating 5 out of 5]

I set the date to today because this is the kind of book I go back again and again - for my work, to relax, or just to enjoy a precious minute out of my world. Sometimes I look at the line geometry as art, sometimes I try to solve the problems, sometimes I just read a page or two on the very rich cultural background. T.Rothman & H. Kukagawa collaboration goes many years back, they are passionate about their subject. It shows!
I owe the authors my discovery of the Sangaku tradition - or geometry inscribed wooden tablets. They were the inspiration for several of my published work. Even my students in Visual Communication owe them some gratitude, sailing through some complex and challenging technical practices and using this fun and creative way to deliver both sound mathematics and colorful, inspirational messages.
Here are two monographs I did exploring some of the book's geometry examples.
https://www.amazon.com/s/ref=nb_sb_no...

[Yofish]

This is the book John got for Joanna when she left our team.

It reports on some of the math that came out of Japan during the long period when Japan was having no contact with the Western world. Very cool stuff in the problems, and there are lots of them---not really for reading straight through. Some of the prose is just a little weird. Turns out that while Japan was isolating itself from the world (maybe 1400--1850), it was developing its own quirky math. They sort of almost got calculus. They had a lot of geometry. The thing to do in those days was to write down your exciiting problems (and solutions), and post them at the local temple.

[Nate · Rating 4 out of 5]

I was briefly obsessed with Sangaku for a time and this book was a wonderful addition to my fixation.

[Tim Robinson · Rating 3 out of 5]

This is a topic that interests me greatly, yet the book is very bland. Disappointing.

[Sangaku]

good