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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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A glimpse at japanese temple geometry l.jpg

A Glimpse at Japanese Temple Geometry

OML Conference

August 6-8, 2006

McMinnville, Oregon


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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


Japanese temple geometry l.jpg

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


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Japanese Temple Geometry Continued

  • Euclidean geometric problems with emphasis on circles and ellipses

  • Simple to nearly impossible to solve


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Japanese Temple Geometry Continued

  • Educational or recreational mathematics

  • Results predicate known Western Results about tangent circles


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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


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Sangaku from Kyoto


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More Sangaku History

  • Oldest one found from 1668

  • 1751 First collection of problems published—handwritten or printed with wooden blocks

  • Uniformly distributed throughout Japan


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More Sangaku History Continued

  • Influenced by work of Mori, Yoshida and Seki

  • Art form practiced by all


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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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