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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 term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise. [31] [32] Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified ...
Diagram illustrating three basic geometric sequences of the pattern 1(r n−1) up to 6 iterations deep.The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively.
Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers , variables , and polynomials , along with their factorization and determining their roots .
a. If the 3 coins balance, then the odd coin is among the remaining population of 2 coins. Test one of the 2 coins against any other coin; if they balance, the odd coin is the last untested coin, if they do not balance, the odd coin is the current test coin. b. If the 3 coins do not balance, then the odd coin is from this population of 3 coins.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
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Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns.It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language.
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