Sacred Mathematics: Japanese Temple Geometry

by Fukagawa Hidetoshi and Tony Rothman; with a Foreward by Freeman Dyson
Princeton University Press, Princeton NJ, 2008
392 pp., illus., 16 col. Trade, $35.00
ISBN 978-0-691-12745-3.

Reviewed by Michael R. (Mike) Mosher
Saginaw Valley State University

mosher@svsu.edu



This certainly is a math book. Despite some plates of the painted wooden boards—sangaku—that contain geometrical problems, some related prints of Japanese mathematicians at work and photographs of notable temples, it’s not an art book. There are excerpts from the travel diary of nineteenth-century mathematician Yamaguchi Kanzan, who traipsed around Japan to view sangaku. The book is a collection of nearly 200 geometry problems, with diagrams and solutions, taken from sangaku that co-author Fukagawa Hidetoshi studied on similar travels.

From the seventeenth to the nineteenth centuries, Japan’s shogunate consciously decided to keep the islands of their nation free from foreign influence. While they were not completely successful, their isolation from foreign sciences forced Japanese mathematicians to devise many geometric methods themselves. From the book’s title, one might expect the geometry they developed to be applied in the construction of Buddhist temples and Shinto shrines. If that was the case, it’s a bit disappointing to find that it isn’t explored in this book. Temples were notable sites of learning, where the learned in the region and in transit would meet, and the long wooden sangaku were displayed in the temple to be seen, solved and discussed by visitors. To this reviewer the story problems and geometry (to the Greeks, “measurement of the earth”, remember) seem down-to-earth and functional, rather than “sacred”, metaphysical or mystical.

Noted scientist and polymath (here the term seems most appropriate) Freeman Dyson provides a foreword to the book, where he says “It is a work of art as well as a mathematical statement”. That exaggeration is unnecessary, for this book of problems would be a good gift for a math teacher; Fukagawa Hidetoshi retired from a career teaching in high schools, and Tony Rothman teaches Physics at Princeton University. A less expensive—perhaps smaller—paperback edition of Sangaku: The Sacred Mathematics of Japan could prove useful to dedicated high school or college geometry students.