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Chapter 3
Plate 3.8. In the 1778 Fuhki Jinko¯-ki, or Riches of Jinko¯- ki, the anonymous author suggests weighing an elephant by bringing it onto a boat and marking the water line, removing the elephant, then bringing on stones of known weight until the water line reaches the same level it did with the elephant. (Collection of Fukagawa Hidetoshi.)
Using a 1,024- sided regular polygon inscribed in a circle, Takebe gave in the Taisei Sankei the approximation π =
5, 419, 351 , 1, 725, 033
from which he calculated that π = 3.141592653589815383241944, noting that this value is bigger than the real π by 0.000000000000022144779300. The reader can verify on a computer that 5,419,351/1,725,033 − π = 0.0000 00000000022144779300394, which demonstrates that Takebe’s calculations were extraordinarily accurate.