Saturday 5 September 2009

Pi and the 47 Ronin

If you take the Asakusa Line from Shinagawa, just one stop away you will come to one of the most famous shrines in all of Tokyo, the Sengakuji Temple. It isn't the biggest, prettiest, or most ornate, but it is rich with the kind of history the Japanese love. This is the resting place of the 47 Ronin, one of Japan's most popular samurai stories.

"The story has all the elements for a Hollywood production: a good, noble guy who dies unfairly; a corrupt court official and cunning villain who is disliked by everyone but seems to be always ahead of the game; the good guy’s loyal subordinates who are totally determined to avenge their master’s death at whatever price, even with their own lives... In the end, the story has sparked the imagination and inspired the utmost respect from an entire nation for over 300 years."[Luis Estrada's Travel Blog]

I came across a mathematical reference to the story in a March 1908 article in the American Mathematical Monthly I received recently from Dave Renfro.

"In Tokyo, at the Buddhist temple of Sengakuji lie buried the forty-seven Ronin, the national heroes of feudal Japan. Just within the gate, in a two-storied building, swords, armor and other relics of these heroes are shown on payment of a fee. By the side of the path leading to the tombs is a well with the inscription, 'Here they washed it.' No one in Japan needs to be told that it was the bloody head they were bringing to the grave of their lord, that dead master for whom they considered it the highest privilege thus to forfeit all their lives. The popular reverence for these heroes is still attested not only by the incense perpetually kept burning before their tombs but in stranger fashion by the fresh visiting cards constantly left upon their graves. [To someone who is still there, do the Japanese still leave these visiting cards?]"

"All the world knows their exploit, but who knows that one of them, Shigekiyo Matsumura, was the greatest Asiatic mathematician of his age, who in his work
, published in 1663, calculated the length of one side of a regular inscribed polygon of 32768 or 215 sides, obtaining 0.000095873798655313483 and thence for the value of pi 3.141592648, which is accurate to seven places of decimals, to eight significant figures..."

I would be thrilled if any of the folks who still read this in the Tokyo area would send a digital picture of the tomb of Matsumura so that I can add it to this note.

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