翻訳と辞書 Words near each other ・ Zhawar ・ Zhao Yiguang ・ Zhao Yihuan ・ Zhao Yijing ・ Zhao Yiman ・ Zhao Yin ・ Zhao Ying ・ Zhao Yingcheng ・ Zhao Yinghui ・ Zhao Yingqi ・ Zhao Yingying ・ Zhao Yong ・ Zhao Yong (politician) ・ Zhao Yongsheng ・ Zhao Youfeng ・ Zhao Youqin's π algorithm ・ Zhao Yuan ・ Zhao Yuanyan ・ Zhao Yudiao ・ Zhao Yueyu ・ Zhao Yufei ・ Zhao Yufen ・ Zhao Yuhao ・ Zhao Yun ・ Zhao Yun (volleyball) ・ Zhao Yunlei ・ Zhao Zengyi ・ Zhao Zhengyong ・ Zhao Zhiqian ・ Zhao Zhiwen Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Zhao Youqin's π algorithm ： ウィキペディア英語版 Zhao Youqin's π algorithm Zhao Youqin's algorithm was an algorithm by Yuan dynasty astronomer-mathematician Zhao Youqin (, ? – 1330) to calculate the value of in his book ''Ge Xiang Xin Shu'' (). == Algorithm == Zhao Youqin started with an inscribed square in a circle with radius r.〔Yoshio Mikami, Development of Mathematics in China and Japan, Chapter 20, The Studies about the Value of etc., pp 135–138〕 If $\backslash ell$ denotes the length of a side of the square, draw a perpendicular line d from the center of the circle to side l. Let e denotes r − d. Then from the diagram: :$d=\backslash sqrt\backslash right)^2\}$ :$e=r-d=r-\backslash sqrt\backslash right)^2\}.$ Extend the perpendicular line d to dissect the circle into an octagon; $\backslash ell\_2$ denotes the length of one side of octagon. :$\backslash ell\_2=\backslash sqrt\backslash right)^2+e^2\}$ :$\backslash ell\_2=\backslash frac\backslash sqrt\; \backslash sqrt\backslash right)^2\}$ let $l\_3$ denotes the length of a side of hexadecagon :$\backslash ell\_3=\backslash frac\backslash sqrt\backslash sqrt\backslash right)^2\; \}$ similarly :$\backslash ell\_=\backslash frac\backslash sqrt\backslash sqrt\backslash right)^2\}$ Proceeding in this way, he at last calculated the side of a 16384-gon, multiplying it by 16384 to obtain 3141.592 for a circle with diameter = 1000 units, or :$\backslash pi\; =3.141592.\; \backslash ,$ He multiplied this number by 113 and obtained 355. From this he deduced that of the traditional values of , that is 3, 3.14, and , the last is the most exact.〔Yoshio Mikami, p136〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Zhao Youqin's π algorithm」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.