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Sacred Mathematics: Japanese Temple Geometry

Frank J. Swetz (Pennsylvania State Univ. )


Sacred Mathematics: Japanese Temple Geometry, Fukagawa Hidetoshi and Tony Rothman, 2008, 348 pp, illustrations, hardback $35, ISBN  978-0-691-12745-3, Princeton University Press, 41 William Street, Princeton, NJ, 0850


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 focus of this work is sangaku, Japanese temple problems.  These problems emerged during the Endo Period (1603-1867) of Japanese history when the country retreated into an imperially imposed state of isolationism.  During this period of cultural introspection, the mathematician Yoshida Kōyu published a collection of twelve unsolved challenge problems.  These problems were taken up and solved by readers who, in turn, posed their own challenge problems.  Thus, a popular wave of problem solving and posing developed, based mainly on the solutions of complex geometric configurations and situations involving circles, ellipses and other common geometric curves.  These problems were solved by people from all social strata who in their pride of accomplishment posted their solutions and problems on inscribed wooden tablets and hung them in local Buddhist temples or Shinto shrines.  These problem collections stand as a testimony to the climate of mathematical creativity and problem-solving ingenuity that existed in Japan at that time.

It is only recently that knowledge of sangaku has reached a western audience.  This knowledge is mainly due to the efforts of Fukagawa Hidetoshi, a retired Japanese high school teacher and a sangaku scholar.  In teaming up with a series of western co-authors: D. Pedoe, Japanese Temple Geometry Problems, 1989; D. Rigby, Traditional Japanese Mathematics Problems of the 18th and 19th Centuries, 1992; and now Tony Rothman, Fukagawa has exposed a large audience to this fascinating mathematical tradition.  The authors of Sacred Mathematics examine a wide selection of sangaku problems and their solutions.  A retrospective understanding of these problems and their intellectual milieu is provided by brief considerations about the history of Japanese and Chinese mathematics and diary excerpts from the nineteenth century wandering Japanese mathematician, Yamaguchi Kanzan, who actively collected temple problems.  Sixteen colorful illustrations and 150 diagrams enrich the presentation.  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, Professor Emeritus, The Pennsylvania State University

See also the MAA Review by Marvin Schaefer.

Frank J. Swetz (Pennsylvania State Univ. ), "Sacred Mathematics: Japanese Temple Geometry," Convergence (February 2010), DOI:10.4169/loci002864