Sacred Mathematics

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.

Table of Contents:

Foreword by Freeman Dyson ix
Preface by Fukagawa Hidetoshi xiii
Preface by Tony Rothman xv
Acknowledg ments xix
What Do I Need to Know to Read This Book? xxi
Notation xxv
Chapter 1: Japan and Temple Geometry 1
Chapter 2: The Chinese Foundation of Japanese Mathematics 27
Chapter 3: Japa nese Mathematics and Mathematicians of the Edo Period 59
Chapter 4: Easier Temple Geometry Problems 89
Chapter 5: Harder Temple Geometry Problems 145
Chapter 6: Still Harder Temple Geometry Problems 191
Chapter 7: The Travel Diary of Mathematician Yamaguchi Kanzan 243
Chapter 8: East and West 283
Chapter 9: The Mysterious Enri 301
Chapter 10: Introduction to Inversion 313
For Further Reading 337
Index 341