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The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book Xiángjiě Jiǔzhāng Suànfǎ (詳解九章算法) [1] of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's Triangle" was invented by mathematician Jia Xian [2] who expounded it around 1100 AD, about 500 years before Pascal.
Anders Hejlsberg (/ ˈ h aɪ l z b ɜːr ɡ /, born 2 December 1960) [2] is a Danish software engineer who co-designed several programming languages and development tools. He was the original author of Turbo Pascal and the chief architect of Delphi.
Jia Xian triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD. Yang Hui referred to Jia Xian's Shi Suo Suan Shu in the Yongle Encyclopedia Jia Xian ( simplified Chinese : 贾宪 ; traditional Chinese : 賈憲 ; pinyin : Jiǎ Xiàn ; Wade–Giles : Chia Hsien ; ca. 1010–1070) was a Chinese ...
Pascal's wager is a philosophical argument advanced by Blaise Pascal (1623–1662), seventeenth-century French mathematician, philosopher, physicist, and theologian. [1] This argument posits that individuals essentially engage in a life-defining gamble regarding the belief in the existence of God.
This algorithm draws all eight octants simultaneously, starting from each cardinal direction (0°, 90°, 180°, 270°) and extends both ways to reach the nearest multiple of 45° (45°, 135°, 225°, 315°).
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.
The Wang and Landau algorithm, proposed by Fugao Wang and David P. Landau, [1] is a Monte Carlo method designed to estimate the density of states of a system. The method performs a non-Markovian random walk to build the density of states by quickly visiting all the available energy spectrum.
Pascal was born in Clermont-Ferrand, which is in France's Auvergne region, by the Massif Central. He lost his mother, Antoinette Begon, at the age of three. [14] His father, Étienne Pascal, also an amateur mathematician, was a local judge and member of the "Noblesse de Robe". Pascal had two sisters, the younger Jacqueline and the elder Gilberte.