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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 problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.
1000th row of Pascal's triangle, arranged vertically, with grey-scale representations of decimal digits of the coefficients, right-aligned. The left boundary of the image corresponds roughly to the graph of the logarithm of the binomial coefficients, and illustrates that they form a log-concave sequence
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 ...
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The first five layers of Pascal's 3-simplex (Pascal's pyramid). Each face (orange grid) is Pascal's 2-simplex (Pascal's triangle). Arrows show derivation of two example terms. In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem.
The temperatures may be dropping as 2024 comes to an end, but this year’s sexiest movie scenes still have Us sweating. From a sports drama about three tennis superstars in a decades-long love ...
The two sets of three numbers which the Star of David theorem says have equal greatest common divisors also have equal products. [1] For example, again observing that the element 84 is surrounded by, in sequence, the elements 28, 56, 126, 210, 120, 36, and again taking alternating values, we have 28×126×120 = 2 6 ×3 3 ×5×7 2 = 56×210×36.