Preface by Rothman
as acts of worship, thanks to the gods for being able to solve a difficult problem. In this sense, temple geometry is indeed sacred mathematics. Finally, in the years since the article appeared, Hidetoshi has succeeded in organizing a large exhibit of over 100 sangaku at the Nagoya Science Museum, which took place in 2005 under sponsorship of the daily newspaper Asahi Shinbun. We are fortunate to be able to publish here some of the original photographs from the exhibit catalog. Readers cannot but be struck by the beauty of the tablets and we are certain it will add to the artistic aspect of the book. To that end, we have attempted to include contemporary drawings and illustrations that will put the mathematical art in the context of the prevailing art of the times. We have also included some of the original drawings of temple geometry problems from rare seventeenth-nineteenth century rice-paper books. We hope that they help make Sacred Mathematics as much an artistic creation as an historical and mathematical one.
The authors’ collaboration for this project has been unusual. To this day Hidetoshi and I have never met and the work has taken place entirely by email. Hidetoshi has been the primary author. His collection of rare books on traditional Japanese mathematics, consisting of several hundred volumes, dwarfs anything available in Western libraries, and by now he has been studying the subject for forty years. My role has been to a large degree editorial. Hidetoshi’s native language is far from English, and I speak no Japanese. Fortunately, mathematics is universal. I have taken Hidetoshi’s drafts and attempted to render them in reasonably fluent English. I have also added substantial material, redrawn the diagrams, and gone through all the proofs, attempting to simplify them slightly. Hidetoshi’s solutions are those of a professional mathematician, and I have frequently felt a few more steps and diagrams were needed to make them accessible to American students (or at least their teachers!), who we certainly hope will try the problems. In the more difficult exercises I have added more explanation, in the easier ones less, sometimes none at all; one or two of the solutions are my own. My only guide in this procedure has been my experience of having taught many university students, often freshmen, from whom I have learned that if I have difficulty with a problem, they sometimes will. In Sacred Mathematics we often present traditional solutions. However, these are frequently translations from Kanbun to Japanese to English with modern mathematical notation, whereas traditional solutions did not use trigonometric functions, lacked indications of angles, and so forth. The “traditional” proofs in this
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