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Sangaku (Japanese votive tablets featuring mathematical puzzles)

kanji: Sangaku 算額

Japanese mathematical votive tablet

What are sangaku ?

Sangaku (算額) are votive tablets offered in shinto shrines (and sometimes in buddhist temples) in Japan. The earliest sangaku found date back to the beginning of the 17th century (a few years before the beginning of the japanese Edo period).
The problems featured on the sangaku are typical problems of japanese mathematics (wasan 和算) and often involve many circles which is uncommon in western mathematics. These problems can often be seen as amusing mathematic puzzles (such as the modern Sudoku).

Examples of sangaku

Pictures Year Number of figures Description Shrine name
City Prefecture

1847 (Koka 4) 1 Circles in a rectangle Hachiman
Uchiko Ehime (Shikoku)

1686 (Jokyo 3) 11 An old sangaku in Kyoto Kitano-tenman-gu
Kyoto Kyoto

1989 (Heisei 1) 2x1 Two small sangaku recently dedicated to the yasui shrine in Kyoto. Yasui
Kyoto Kyoto

1893 (Meiji 26 ) + 1920 (Taisho 9) 17 + 0 A sangaku (or even 2) found in a temple ???
Fukushima Fukushima

1846 (Koka 3) 2x7 Two old sangakus in a shrine Ichi no seki Hachiman
Ichi no seki Miyagi
More sangaku

Where to find a sangaku?

You can find a catalog (in Japanese) of existing sangaku at http://www.morikita.co.jp/soft/0164/genzon.pdf. But some of the shrines mentionned in this catalogue do not have their sangaku anymore...

Links and references

In English:
An article about Sangaku published by Princeton University
A website dedicated to japanese mathematics (wasan) with pictures of sangaku.
The website made by the author of the article article published in Scientific american (with a link to the article).
About a sangaku found in Isaniwa.

In French:
Two articles have been published in Tangente.

In Hungarian:
Szabó Péter Gábor has written two articles One article has been published in Szaku and the other in the Hungarian Mathematical Journal. He has gathered some links on his web page.

In Dutch:
Zsófia Ruttkay wrote two articles in Dutch here and here.

In Japanese:
A book about japanese mathematics (wasan) and sangaku.

Web delerue.org
sangaku.info photographies.ws

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