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Sangaku Problem

Sangaku problems, often written "san gaku," are geometric problems of the type found on devotional mathematical wooden tablets ("sangaku") which were hung under the roofs of shrines or temples in Japan during two centuries of schism from the West (Fukagawa and Pedoe 1989). During the time of isolation, Japanese mathematicians developed their own "traditional mathematics," which, in the 1850s, began giving way to Western methods. There were also changes in the script in which mathematics was written and, as a result, few people now living know how to interpret the historic tablets (Kimberling).

Japanese mathematicians represented in sangaku include Seki Kowa (1642-1708), Ajima Chokuen (also called Naonobu; 1732-1798), and Shoto Kenmotu (1790-1871).

Sangaku problems typically involve mutually tangent circles or tangent spheres, with specific examples including the properties of the Ajima-Malfatti points, Japanese theorem, and Kenmotu point.

See also

Ajima-Malfatti Points, Casey's Theorem, Circle Inscribing, Cylinder-Sphere Intersection, Descartes Circle Theorem, Ellipse Tangent, Hexlet, Japanese Theorem, Kenmotu Point, Right Triangle, Tangent Circles, Tangent Spheres

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References

Bogomolny, A. "Sangaku: Reflections on the Phenomenon." http://www.cut-the-knot.org/pythagoras/Sangaku.shtml.Fukagawa, H. and Pedoe, D. Japanese Temple Geometry Problems. Winnipeg, Manitoba, Canada: Charles Babbage Research Foundation, 1989.Fukagawa, H. and Rigby, J. F. Traditional Japanese Mathematics Problems from the 18th and 19th Centuries. Singapore: Science Culture Technology Press, 2002.Hidetoshi, F. and Rothman, T. Sacred Mathematics: Japanese Temple Geometry. Princeton, NJ: Princeton University Press, 2008.Huvent, G. Sangaku: Le mystère des énigmes géométriques japonaises. Dunod, 2008.Kimberling, C. "Review: Traditional Japanese Mathematics Problems from the 18th and 19th Centuries and Japanese Temple Geometry Problems.Kotera, H. "Japanese Temple Geometry Problem: Sangaku." http://www.wasan.jp/english/.Mikami, Y. The Development of Mathematics in China and Japan, 2nd ed. New York: Chelsea, 1974.Rothman, T. "Japanese Temple Geometry." Sci. Amer. 278, 85-91, May 1998.Rothman, T. "Japanese Temple Geometry." http://www2.gol.com/users/coynerhm/0598rothman.html.Ruttkay, S. "Sangaku--Wiskunde als Kunst." http://www.arsetmathesis.nl/sangatekst.htm.Smith, D. E. and Mikami, Y. A History of Japanese Mathematics. Chicago: Open Court, 1914.

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Sangaku Problem

Cite this as:

Weisstein, Eric W. "Sangaku Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SangakuProblem.html

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