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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

A Glimpse at Japanese Temple Geometry

OML Conference

August 6-8, 2006

McMinnville, Oregon

japan s period of national seclusion 1639 1854
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
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
japanese temple geometry continued
Japanese Temple Geometry Continued
  • Euclidean geometric problems with emphasis on circles and ellipses
  • Simple to nearly impossible to solve
japanese temple geometry continued5
Japanese Temple Geometry Continued
  • Educational or recreational mathematics
  • Results predicate known Western Results about tangent circles
japanese temple geometry rediscovered
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
more sangaku history
More Sangaku History
  • Oldest one found from 1668
  • 1751 First collection of problems published—handwritten or printed with wooden blocks
  • Uniformly distributed throughout Japan
more sangaku history continued
More Sangaku History Continued
  • Influenced by work of Mori, Yoshida and Seki
  • Art form practiced by all
references
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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