Sangaku

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Sangaku or San Gaku (算額; lit. mathematical tablet) are Japanese geometrical puzzles in Euclidean geometry on wooden tablets created during the Edo period (1603-1867) by members of all social classes.

During this period Japan was completely isolated from the rest of the world so the tablets were created using Japanese mathematics, (wasan), not influenced by western mathematical thought. For example, the fundamental connection between an integral and its derivative was unknown so Sangaku problems on areas and volumes were solved by expansions in infinite series and term-by-term calculation.

The Sangaku were painted in color on wooden tablets which were hung in the precincts of temples and shrines as offerings to the gods or as challenges to the congregants. Many of these tablets were lost following during the period of modernisation that followed the Edo period but around nine hundred are known to remain.

A typical problem, which is presented on an 1824 tablet in the Gumma Prefecture, covers the relationship of three touching circles with a common tangent. Given the size of the two outer large circles, what is the size of the small circle between then? The answer is 1/sqroot(r_middle) = 1/sqroot(r_left) + 1/sqroot(r_right).

Fujita Kagen (1765-1821), a Japanese mathematician of prominence, has published his Shimpeki Sampo (Mathematical problems Suspended from the Temple) in 1790, and in 1806 a sequel, the Zoku Shimpeki Sampo.

In recent times, a Sangaku collection was published in 1989 by Hidetoshi Fukagawa and Daniel Pedoe in the book Japanese Temple Geometry Problems.

[edit] See also

Seki Takakazu (Kowa Seki)

[edit] Further reading

Fukagawa, Hidetoshi and Pedoe, Daniel. Japanese Temple Geometry Problems: Sangaku. Charles Babbage Research Centre, 1989. ISBN 0-919611-21-4.
Rothman, Tony and Fugakawa, Hidetoshi. "Japanese Temple Geometry." Scientific American, May 1998.