江戸時代初期のπの計算について

概要

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In the Sanso of 1663, Shigekiyo MURAMATU (1608-1695) made calculations of the circumferences of a regular square, a regular octagon, a regular sixteen-sided polygon, …… inscribed in the circle with the diameter 1, and ended in the circumferences of regular 2^<15>-sided polygon. And he got π=3.141592648777698869248 from this conclusion. Similarly Takakazu SEKI (1640?〜1708) wrote the Katsuya-Sanpo in 1712, in which he showed his measurement of the circle. From the perimeter of an inscribed 2^<17>-sided polygon, he let the circumferences of a regular 2^<15>-sided polygon be a, that of a regular 2^<15>-sided polygon be b, and that of a regular 2^<17>-sided polygon be c, and he made calculations as follows: b+((b-a)(c-b))/((b-a)-(c-b))=3.14159265359 "extremely weak". Shu-Li-Jing-Yun was introduced into Japan in about 1723. In this book Ludolf (1540〜1610) also showed his measurement of the circle, and he got π=3.141592653589793238431541553377501511680 from the perimeter of an inscribed 2^<35>-sided polygon. In this paper we made a comparative study with the process of their measurements, which is an oblique side of rectangular triangles produced in each process.
日本科学史学会の論文
1984-02-10