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Tâi-lô. 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 ...
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 ...
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]
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 ...
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.
Image mnemonic to help remember the ratios of sides of a right triangle. The sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, for instance SOH-CAH-TOA in English: S ine = O pposite ÷ H ypotenuse. C osine = A djacent ÷ H ypotenuse.
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused in compass and straightedge constructions.
Shen Kuo's written work of 1088 also contains the first written description of the magnetic needle compass, the first description in China of experiments with camera obscura, the invention of movable type printing by the artisan Bi Sheng (990–1051), a method of repeated forging of cast iron under a cold blast similar to the modern Bessemer ...