- 著者
-
小林 龍彦
田中 薫
- 出版者
- 日本科学史学会
- 雑誌
- 科学史研究 (ISSN:21887535)
- 巻号頁・発行日
- vol.22, no.148, pp.206, 1983 (Released:2021-09-24)
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 2¹⁵ -sided polygon. And he got π=3.141592648777698869248 from this conclusion.
Similarly Takakazu Seki (1640?〜1708) wrote the Katsuyȏ-Sanpȏ in 1712, in which he showed his measurement of the circle. From the perimeter of an inscribed 2¹⁷-sided polygon, he let the circumferences of a regular 2¹⁵ sided polygon be a, that of a regular 2¹⁶-sided polygon be b, and that of a regular 2¹⁷-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 2³⁵-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.