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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 ...
Blaise Pascal [a] (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic writer.. Pascal was a child prodigy who was educated by his father, a tax collector in Rouen.
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 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.
In 1665 Pascal posthumously published his results on the eponymous Pascal's triangle, an important combinatorial concept. He referred to the triangle in his work Traité du triangle arithmétique (Traits of the Arithmetic Triangle) as the "arithmetic triangle". [4] In 1662, the book La Logique ou l’Art de Penser was published anonymously in ...
He is also known for naming Pascal's triangle after Blaise Pascal, calling it "Table de M. Pascal pour les combinaisons." Another of de Montmort's interests was the subject of finite differences. He determined in 1713 the sum of n terms of a finite series of the form
Blaise Pascal influenced mathematics throughout his life; for instance, his Traité du triangle arithmétique ("Treatise on the Arithmetical Triangle") (1653) described a convenient tabular presentation for binomial coefficients, now called Pascal's triangle.
Pascal was born in Clermont to Martin Pascal, the treasurer of France, and Marguerite Pascal de Mons. [1] He had three daughters, two of whom survived past childhood: Gilberte (1620–1687) and Jacqueline (1625–1661). His wife Antoinette Begon died in 1626.