Sangaku - mathematical picture

This refers to votive plaques dedicated to shrines and temples as a prayer for research and study of mathematics (Japanese mathematics). According to Murase Yoshimasu's Sangaku Entei-ki (1681), mathematical tablets were found all over Edo in the mid-17th century. The book introduces the problems on a mathematical tablet from Meguro Fudo. It is believed that mathematical tablets existed in Kyoto and Osaka even earlier. Since people could study not only from mathematical books but also from the questions and answers written on mathematical tablets, in the second half of the 17th century, some people began collecting problems written on mathematical tablets and composing them into mathematics books.

The first mathematical plaque collection to be published was Shinpeki Sanpo (Shinpeki Sanpo) by Fujita Sadasuke (1789), and subsequent publications of mathematical plaque collections followed suit. The oldest mathematical plaque in existence is the plaque from 1683 (Tenwa 3) at Hoshimiya Shrine in Sano City, Tochigi Prefecture, followed by Kitano Tenmangu Shrine in Kyoto City (1686), Yasaka Shrine in Kyoto City (1691), Oshio Hachimangu Shrine in Echizen City, Fukui Prefecture (1701), and Miyakojima Seikannon in Honjo City, Saitama Prefecture (1726). There are about 800 mathematical plaques in existence. The purpose of the offering is not necessarily a prayer for improvement in mathematical ability. For example, the mathematical plaque at Yasaka Shrine in Kyoto is the answer plaque from Gokonomiya Sangaku in Fushimi, which was donated in 1683, and is similar to the inheritance of mathematical themes. Questions and answers using mathematical tablets were not uncommon, and one example is the mathematical tablet dedicated to Shiba Atagoyama (Edo) by Aida Yasuaki, which developed into a debate between the Saijo and Seki schools. The dedication of mathematical tablets is a custom unique to Japan, and the purposes for which are varied, including prayers for the safety of the family, the prosperity of a private school, celebrations of the birth of a grandchild, the solving of a difficult problem, coming up with a good problem, understanding an entire mathematical book, or even just to show off.

[Shimohira Kazuo]

"The Secret History of Ema" by Hiromi Iwai (1979, Japan Broadcasting Publishing Association)

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

数学（和算）の研究や勉強の祈願のために、神社仏閣に奉納した絵馬(えま)をいう。村瀬義益(よします)の『算学淵底記(えんていき)』（1681）によれば、17世紀中ごろには江戸の各地に算額があったことがわかる。同書に、目黒不動の算額の問題が紹介されている。京、大坂にはさらに早くから算額があったと思われる。数学書ばかりでなく、算額に書かれた問答でも勉強ができたので、17世紀後半には、算額に書かれた問題を集めて数学書にする者も現れた。

　算額集の出版の最初は藤田貞資(さだすけ)の『神壁算法(しんぺきさんぽう)』（1789）で、以後これに倣って算額集の出版が続いた。現存最古の算額は栃木県佐野市の星宮神社の1683年（天和3）の額で、次に京都市の北野天満宮（1686）、同八坂神社（1691）、福井県越前(えちぜん)市の大塩八幡宮(はちまんぐう)（1701）、埼玉県本庄(ほんじょう)市の都島正観音（1726）である。現存数は約800面。奉納の目的は、かならずしも数学の力が上達する祈願とは限らない。たとえば、京都の八坂神社の算額は、1683年奉納の伏見の御香宮(ごこうのみや)算額の解答額であり、数学書の遺題継承と似ている。算額による問答も珍しくなく、なかには最上(さいじょう)流と関流の論争にまで発展した会田安明(あいだやすあき)の芝愛宕(あたご)山（江戸）奉納算額の例もある。算額奉納は日本独特の風習であるが、その目的のなかには、家内安全、塾の繁栄とか、孫の誕生を祝うもの、さらに、難問が解けた、よい問題ができたとか、数学書が全部理解できた、あるいは自慢のためなど、いろいろである。

［下平和夫］

『岩井宏実著『絵馬秘史』（1979・日本放送出版協会）』

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