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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] |
Yuan Dynasty
The Yuan dynasty ( ; zh, c=元朝, p=Yuáncháo), officially the Great Yuan (; Mongolian language, Mongolian: , , literally 'Great Yuan State'), was a Mongol-led imperial dynasty of China and a successor state to the Mongol Empire after Division of the Mongol Empire, its division. It was established by Kublai (Emperor Shizu or Setsen Khan), the fifth khagan-emperor of the Mongol Empire from the Borjigin clan, and lasted from 1271 to 1368. In Chinese history, the Yuan dynasty followed the Song dynasty and preceded the Ming dynasty. Although Genghis Khan's enthronement as Khagan in 1206 was described in Chinese language, Chinese as the Han Chinese, Han-style title of Emperor of China, Emperor and the Mongol Empire had ruled territories including modern-day northern China for decades, it was not until 1271 that Kublai Khan officially proclaimed the dynasty in the traditional Han style, and the conquest was not complete until 1279 when the Southern Song dynasty was defeated in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zhao Youqin
Zhao Youqin (趙友欽 1271-?) was a Chinese mathematician, astronomer, alchemist, and Taoist monk. He is most well known for his book ''Ge xiang xin shu (革象新书),'' translated either as ''New Elucidation of the Heavenly Bodies'' or ''New Writing on the Image of Alteration,'' wherein he described a new method to calculate pi. Biography Zhao was born on July 26, 1271. Most information about Zhao comes from three, slightly conflicting, sources: a Daoist biography ''Shangyangzi jindan dayao liexianzhi'' by Chen Zhixu, and two biographies in different editions of Zhao's own book ''Ge xiang xin shu (革象新书),'' one written by Wang Wei and the other by Song Lian (宋濂). All biographies agree that Zhao was gifted in astronomy from a young age and that he was born in Jiangxi province. The ''Shangyangzi jindan dayao'' says that, as a child, he was injured during the war between Mongol leader Kublai Khan and the Song dynasty. Zhixu's biography says that Zhao was a Daoist h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius
In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is the line segment or distance from its center to any of its Vertex (geometry), vertices. The name comes from the Latin ''radius'', meaning ray but also the spoke of a chariot wheel.Definition of Radius at dictionary.reference.com. Accessed on 2009-08-08. The typical abbreviation and mathematical symbol for radius is ''R'' or ''r''. By extension, the diameter ''D'' is defined as twice the radius:Definition of radius at mathwords.com. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yoshio Mikami
was a Japanese mathematician and historian of ''Japanese mathematics''. He was born February 16, 1875, in Kotachi, Hiroshima prefecture. He attended the High School of Tohoku University, and in 1911 was admitted to the Imperial University of Tokyo. He studied history of Japanese and Chinese mathematics. In 1913, he published "The Development of Mathematics in China and Japan" in Leipzig.Yoshio Mikami, The Development of Mathematics in China and Japan, 1913, Library of Congress 61-13497 This book consisted of two parts with 47 chapters. Part one has 21 chapters that describe in depth several important Chinese mathematicians and mathematical classics including Liu Hui, Shen Kuo, Qin Jiushao, Sun Tzu (mathematician), Sun Tzu, The Nine Chapters on the Mathematical Art, Mathematical Treatise in Nine Sections, Li Zhi (mathematician), Li Ye, Zhu Shijie and study on π. Part II deals with important ''wasan'' mathematicians and their works, including Kambei Mori, Yoshida Koyu, Kowa Seki, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perpendicular
In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', ⟂. Perpendicular intersections can happen between two lines (or two line segments), between a line and a plane, and between two planes. ''Perpendicular'' is also used as a noun: a perpendicular is a line which is perpendicular to a given line or plane. Perpendicularity is one particular instance of the more general mathematical concept of '' orthogonality''; perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the word "perpendicular" is sometimes used to describe much more complicated geometric orthogonality conditions, such as that between a surface and its '' normal vector''. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octagon
In geometry, an octagon () is an eight-sided polygon or 8-gon. A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, which alternates two types of edges. A truncated octagon, t is a hexadecagon, . A 3D analog of the octagon can be the rhombicuboctahedron with the triangular faces on it like the replaced edges, if one considers the octagon to be a truncated square. Properties The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°. If squares are constructed all internally or all externally on the sides of an octagon, then the midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other).Dao Thanh Oai (2015), "Equilateral triangles and Kiepert perspectors in complex numbers", ''Forum Geometricorum'' 15, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexadecagon
In mathematics, a hexadecagon (sometimes called a hexakaidecagon or 16-gon) is a sixteen-sided polygon. Regular hexadecagon A ''regular polygon, regular hexadecagon'' is a hexadecagon in which all angles are equal and all sides are congruent. Its Schläfli symbol is and can be constructed as a Truncation (geometry), truncated octagon, t, and a twice-truncated square tt. A truncated hexadecagon, t, is a triacontadigon, . Construction As 16 = 24 (a power of two), a regular hexadecagon is constructible polygon, constructible using compass and straightedge: this was already known to ancient Greek mathematicians. Measurements Each angle of a regular hexadecagon is 157.5 Degree (angle), degrees, and the total angle measure of any hexadecagon is 2520 degrees. The area of a regular hexadecagon with edge length ''t'' is :\begin A = 4t^2 \cot \frac =& 4t^2 \left(1+\sqrt+\sqrt\right)\\ =& 4t^2 (\sqrt+1)(\sqrt+1) .\end Because the hexadecagon has a number of sides that is a power of tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liu Hui's π Algorithm
Liu Hui's algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei. Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter of the earth, ) or as \pi \approx \sqrt \approx 3.162. Liu Hui was not satisfied with this value. He commented that it was too large and overshot the mark. Another mathematician Wang Fan (219–257) provided . All these empirical values were accurate to two digits (i.e. one decimal place). Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of to any accuracy. Liu Hui's own calculation with a 96-gon provided an accuracy of five digits ie . Liu Hui remarked in his commentary to ''The Nine Chapters on the Mathematical Art'', that the ratio of the circumference of an inscribed hexagon to the diamet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Mathematical Discoveries
Chinese may refer to: * Something related to China * Chinese people, people identified with China, through nationality, citizenship, and/or ethnicity **Han Chinese, East Asian ethnic group native to China. **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of various ethnicities in contemporary China ** Ethnic minorities in China, people of non-Han Chinese ethnicities in modern China ** Ethnic groups in Chinese history, people of various ethnicities in historical China ** Nationals of the People's Republic of China ** Nationals of the Republic of China ** Overseas Chinese, Chinese people residing outside the territories of mainland China, Hong Kong, Macau, and Taiwan * Sinitic languages, the major branch of the Sino-Tibetan language family ** Chinese language, a group of related languages spoken predominantly in China, sharing a written script (Chinese characters in traditional and simplified forms) *** Standard Chines ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
