Pascal's triangle

Pascal's triangle
noun Date: 1886 a system of numbers arranged in rows resembling a triangle with each row consisting of the coefficients in the expansion of (a + b)n for n = 0, 1, 2, 3, …

New Collegiate Dictionary. 2001.

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  • Pascal's triangle — The first six rows of Pascal s triangle In mathematics, Pascal s triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal. It is known as Pascal s triangle in much of the …   Wikipedia

  • Pascal's triangle — noun A geometric representation of the binomial coefficients in a triangle, each entry being the sum of the two entries above …   Wiktionary

  • Pascal's triangle — Math. a triangular arrangement of the binomial coefficients of the expansion (x + y)n for positive integral values of n. [named after PASCAL] * * * …   Universalium

  • pascal's triangle — noun Usage: usually capitalized P Etymology: after Blaise Pascal : a system of numbers triangularly arranged in rows consisting of the coefficients in the expansion of (a + b)n for n .0,1,2,3, etc …   Useful english dictionary

  • Pascal's triangle — noun Mathematics a triangular array of numbers in which those at the ends of the rows are 1 and each of the others is the sum of the nearest two numbers in the row above (the apex, 1, being at the top) …   English new terms dictionary

  • Pascal's triangle — /pæskalz ˈtraɪæŋgəl/ (say paskahlz truyangguhl) noun a triangular figure with rows of numbers, each number being obtained by adding together the two numbers on either side of it in the row above. {named after Blaise Pascal1} …   Australian English dictionary

  • Pascal's pyramid — In mathematics, Pascal s pyramid is a three dimensional generalization of Pascal s triangle. Just as Pascal s triangle gives coefficients for the terms of a binomial expansion, so Pascal s pyramid gives coefficients for a trinomial expansion.… …   Wikipedia

  • Pascal's simplex — In mathematics, Pascal s simplex is a version of Pascal s triangle of more than three dimensions. As the triangle and tetrahedron are used to show the binomial and trinomial coefficients respectively, so an n dimensional simplex is used to show… …   Wikipedia

  • Pascal's rule — In mathematics, Pascal s rule is a combinatorial identity about binomial coefficients. It states that for any natural number n we have:{n 1choose k} + {n 1choose k 1} = {nchoose k} where 1 leq k < n and {nchoose k} is a binomial… …   Wikipedia

  • Lozanić's triangle — (sometimes called Losanitsch s triangle) is a geometric arrangement of binomial coefficients in a manner very similar to that of Pascal s triangle. It is named after the Serbian chemist Sima Lozanić, who researched it in his investigation into… …   Wikipedia

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