Presents excerpts from the travel diary of a Japanese mathematician, Yamaguchi Kanzan, who journeyed on foot throughout Japan to collect temple geometry problems. This book explains the sacred and devotional aspects of sangaku, and reveals how Japanese folk mathematicians discovered many theorems independently of mathematicians in the West.

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

"An enchanting history of Japanese geometry—of a time and place where 'geometers did not cede place to poets.' This intersection of science and culture, of the mathematical, the artistic, and the spiritual, is packed, like circles within circles, with rewarding Aha! epiphanies that drive a mathematician's curiosity."—Siobhan Roberts, author of King of Infinite Space

"Teachers will welcome this remarkable collection of mathematical problems, history, and art, which will enrich their curriculum and promote both logical thinking and critical evaluation. It is especially important that we maintain an interest in geometry, which needs, and for once gets, more than its share."—Richard Guy, coauthor of The Book of Numbers

"This remarkable book provides a novel insight into the Japanese mathematics of the past few hundred years. It is fascinating to see the difference in mathematical style from that which we are used to in the Western world, but the book also elegantly illustrates the cross-cultural Platonic nature and profound beauty of mathematics itself."—Roger Penrose, author of The Road to Reality

"A significant contribution to the history of mathematics. The wealth of mathematical problems—from the very simple to quite complex ones—will keep the interested reader busy for years. And the beautiful illustrations make this book a work of art as much as of science. Destined to become a classic!"—Eli Maor, author of The Pythagorean Theorem: A 4,000-Year History

"A pleasure to read. Sacred Mathematics brings to light the unique style and character of geometry in the traditional Japanese sources—in particular the sangaku problems. These problems range from trivial to utterly devilish. I found myself captivated by them, and regularly astounded by the ingenuity and sophistication of many of the traditional solutions."—Glen Van Brummelen, coeditor of Mathematics and the Historian's Craft

An enchanting history of Japanese geometry--of a time and place where 'geometers did not cede place to poets.' This intersection of science and culture, of the mathematical, the artistic, and the spiritual, is packed, like circles within circles, with rewarding Aha! epiphanies that drive a mathematician's curiosity. -- Siobhan Roberts, author of "King of Infinite Space" Teachers will welcome this remarkable collection of mathematical problems, history, and art, which will enrich their curriculum and promote both logical thinking and critical evaluation. It is especially important that we maintain an interest in geometry, which needs, and for once gets, more than its share. -- Richard Guy, coauthor of "The Book of Numbers" This remarkable book provides a novel insight into the Japanese mathematics of the past few hundred years. It is fascinating to see the difference in mathematical style from that which we are used to in the Western world, but the book also elegantly illustrates the cross-cultural Platonic nature and profound beauty of mathematics itself. -- Roger Penrose, author of "The Road to Reality" A significant contribution to the history of mathematics. The wealth of mathematical problems--from the very simple to quite complex ones--will keep the interested reader busy for years. And the beautiful illustrations make this book a work of art as much as of science. Destined to become a classic! -- Eli Maor, author of "The Pythagorean Theorem: A 4,000-Year History" A pleasure to read. Sacred Mathematics brings to light the unique style and character of geometry in the traditional Japanese sources--in particular the sangaku problems. These problems range from trivial to utterly devilish. I found myself captivated by them, and regularly astounded by the ingenuity and sophistication of many of the traditional solutions. -- Glen Van Brummelen, coeditor of "Mathematics and the Historian's Craft"