Calculations of 兀 in Early Edo Period
Bibliographic Information
- Other Title
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- 江戸時代初期のπの計算について
Abstract
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.
Journal
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- Journal of History of Science, JAPAN
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Journal of History of Science, JAPAN 22 (148), 206-, 1983
History of Science Society of Japan
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Details 詳細情報について
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- CRID
- 1390852436901766528
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- NII Article ID
- 130008091447
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- ISSN
- 24350524
- 21887535
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- Text Lang
- ja
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- Data Source
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- JaLC
- CiNii Articles
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- Abstract License Flag
- Disallowed