|
Zhao Youqin's π Algorithm
Zhao Youqin's algorithm is an algorithm devised by Yuan dynasty Chinese astronomer and mathematician Zhao Youqin (, ? – 1330) to calculate the value of Pi, in his book ''Ge Xiang Xin Shu'' (). Algorithm Zhao Youqin started with an inscribed square in a circle with radius r. If \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=\sqrt :e=r-d=r-\sqrt. Extend the perpendicular line d to dissect the circle into an octagon; \ell_2 denotes the length of one side of octagon. :\ell_2=\sqrt :\ell_2=\frac\sqrt Let l_3 denotes the length of a side of hexadecagon :\ell_3=\frac\sqrt similarly :\ell_=\frac\sqrt 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 :\pi =3.141592. \, He multiplied this number by 113 and obtained 355. From this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zhao Youqin Circle Dissection Algorithm
Zhao may refer to: * Zhao (surname) (赵), a Chinese surname ** commonly spelled Chao (surname), Chao in Taiwan or up until the early 20th century in other regions ** Chiu, from the Cantonese pronunciation ** Cho (Korean surname), represent the Hanja 趙 (Chinese: Zhao) ** Triệu, a Vietnamese surname which is the equivalent of the Mandarin Chinese surname Zhao (趙) * Zhao County, in Shijiazhuang, Hebei, China * Zhao family (other) ** Zhao family (Internet slang), based on the surname Zhao, an internet term in China which refers to the ruling elite and the rich * 兆 (zhào), a Chinese numerals, Chinese numeral which usually represents 106 or 1012 **Mega-, corresponding SI prefix in China, equals to 106 **Tera-, corresponding SI prefix in Taiwan, equals to 1012 * Admiral Zhao, a List of Avatar: The Last Airbender characters#Major recurring characters, character in the animated series ''Avatar: The Last Airbender'' Chinese history * Zhao (state) (403 BC–222 BC), a Warri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
