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Sím Kuat. Shen Kuo[ a ] (Chinese : 沈括; 1031–1095) or Shen Gua[ b ], courtesy name Cunzhong (存中) and pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪翁), [ 1 ] was a Chinese polymath, scientist, and statesman of the Song dynasty (960–1279). Shen was a master in many fields of study including mathematics, optics, and ...
By era. v. t. e. The Song dynasty (Chinese: 宋朝; 960–1279 CE) witnessed many substantial scientific and technological advances in Chinese history. Some of these advances and innovations were the products of talented statesmen and scholar-officials drafted by the government through imperial examinations. Shen Kuo (1031–1095), author of ...
Bhaskara II developed spherical trigonometry, and discovered many trigonometric results. Bhaskara II was the one of the first to discover and trigonometric results like: Madhava (c. 1400) made early strides in the analysis of trigonometric functions and their infinite series expansions.
The state of trigonometry advanced during the Song dynasty (960–1279), where Chinese mathematicians began to express greater emphasis for the need of spherical trigonometry in calendrical science and astronomical calculations. [33] Shen Kuo used trigonometric functions to solve mathematical problems of chords and arcs. [33]
[191] [192] Following a long tradition, Shen Kuo created a raised-relief map, while his other maps featured a uniform graduated scale of 1:900,000. [ 193 ] [ 194 ] A 3 ft (0.91 m) squared map of 1137—carved into a stone block—followed a uniform grid scale of 100 li for each gridded square, and accurately mapped the outline of the coasts and ...
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s (AD in the figure above) by the formula + This formula was known to the Chinese mathematician Shen Kuo, and a more accurate formula also involving the sagitta was developed two centuries later by Guo ...
The polymath and official Shen Kuo (1031–1095) used trigonometric functions to solve mathematical problems of chords and arcs. [36] Joseph W. Dauben notes that in Shen's "technique of intersecting circles" formula, he creates an approximation of the arc of a circle s by s = c + 2 v 2 / d , where d is the diameter , v is the versine , c is the ...
Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.