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A Glimpse at Japanese Temple Geometry

A Glimpse at Japanese Temple Geometry. OML Conference August 6-8, 2006 McMinnville, Oregon. Japan’s period of national seclusion (1639-1854). Japanese mathematics (Wasan) versus Western mathematics (Yosan) Exponential notation similar to that of Archimedes (pre-Buddhism)

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A Glimpse at Japanese Temple Geometry

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  1. A Glimpse at Japanese Temple Geometry OML Conference August 6-8, 2006 McMinnville, Oregon

  2. Japan’s period of national seclusion (1639-1854) • Japanese mathematics (Wasan) versus Western mathematics (Yosan) • Exponential notation similar to that of Archimedes (pre-Buddhism) • Imported Chinese classics on arithmetic, algebra, and geometry • Pythagorean theorem, area methods for circles, polygons

  3. Japanese Temple Geometry • Sangaku (mathematical tablet) offered in shrines and temples • Colorful solutions to a variety of problems, with a geometric focus • Samurai, merchants and farmers as devotees of math

  4. Japanese Temple Geometry Continued • Euclidean geometric problems with emphasis on circles and ellipses • Simple to nearly impossible to solve

  5. Japanese Temple Geometry Continued • Educational or recreational mathematics • Results predicate known Western Results about tangent circles

  6. Japanese Temple Geometry Rediscovered • Hidetoshi Fukagawa’s idea to improve his math classes • Dedicated his life to the study of sangaku • Learned Kambun (archaic Japanese language) • Published a collection of sangaku problems

  7. Sangaku from Kyoto

  8. More Sangaku History • Oldest one found from 1668 • 1751 First collection of problems published—handwritten or printed with wooden blocks • Uniformly distributed throughout Japan

  9. More Sangaku History Continued • Influenced by work of Mori, Yoshida and Seki • Art form practiced by all

  10. References • A HISTORY OF JAPANESE MATHEMATICS. David E. Smith and Yoshio Mikami. Open Court Publishing Company, Chicago, 1914. (Also available on microfilm.) • THE DEVELOPMENT OF MATHEMATICS IN CHINA AND JAPAN. Second edition (reprint). Yoshio Mikami. Chelsea Publishing Company, New York, 1974. • JAPANESE TEMPLE GEOMETRY PROBLEMS. H. Fukagawa and D. Pedoe. Charles Babbage Research Foundation, Winnipeg, Canada, 1989. • TRADITIONAL JAPANESE MATHEMATICS PROBLEMS FROM THE 18TH AND 19TH CENTURIES. H. Fukagawa and D. Sokolowsky. Science Culture Technology Publishing, Singapore (in press).

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