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Pascal's triangle

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 India, Persia, China, Germany…

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Overview

Formula

History

Binomial expansions

Combinations

Relation to binomial distribution and convolutions

Patterns and properties

Extensions

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Map overview Semantic statistics

Pascal's triangle

Nodes118
Edges117
Triples150
Avg. degree1.98
Density0.016949
Components1

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Pascal's triangle

Top relations

related to history · 31
Pascal's triangle → Algebra, Ancient Indian, BC, Chandaḥśāstra, Demonstration, Halāyudha, His, In India, Indian, Iran, Islamic, Karaji, Karajian, Khayyam, Khayyam's, Khayyám Nishapuri, Khayyám's, Nishapur, Omar Khayyám, Owing
related to Rows · 23
Pascal's triangle → A001142, Catalan, Every, For, Gould's, In, Let, Lozanić's, Nilakantha, OEIS, Parity, Pascal's, Polarity, Since, Some, Specifically, Taking, The, Then, These
related to External links · 14
Pascal's triangle → Arithmetic Triangle, Chu Shi-Chieh, EMS Press, Encyclopedia, Eric, Mathematics, MathWorld, Pascal, Pascal's, Pascal's Treatise, Seven Multiplying Squares, Ssu Yuan Yü Chien, The Old Method Chart, Weisstein
related to To arbitrary bases · 12
Pascal's triangle → For, He, If, In, Isaac Newton, More, Morton, Pascal's, Robert, The, Thus, To
related to Relation to geometry of polytopes · 10
Pascal's triangle → Each, For, In, Pascal's, Proceed, The, Then, There, This, To
related to Construction of Clifford algebra using simplices · 9
Pascal's triangle → Clifford, Geometric, Geometric Algebra, Just, Labelling, Pascal's, Recognising, The, This
related to Relation to binomial distribution and convolutions · 8
Pascal's triangle → By, First, Pascal's, Second, Stirling's, The, This, When
see also · 8
Pascal's triangle → Bean, Bell, David, Francis Galton's, NMR, Pascal, Pascal's, Singmaster's
related to Formula · 7
Pascal's triangle → An, For, In, Pascal's, Row, This, With
related to Combinations · 6
Pascal's triangle → For, Other, Pascal's, Rather, The, This

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Important terminology

triangle row displaystyle pascal's number binomial numbers elements example entry sum coefficients left rows one entries equal corresponds tbinom choose

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Pascal's triangleis ainfinite triangular array of the binomial coefficients which play a crucial role in probability theory0.90text
Pascal's triangleis aexponential of the matrix which has the sequence 10.90text
Pascal's trianglerelated to Binomial expansionsPascal's0.60section
Pascal's trianglerelated to Binomial expansionsFor0.60section
Pascal's trianglerelated to Binomial expansionsIn0.60section
Pascal's trianglerelated to CombinationsPascal's0.60section
Pascal's trianglerelated to CombinationsThe0.60section
Pascal's trianglerelated to CombinationsOther0.60section
Pascal's trianglerelated to CombinationsThis0.60section
Pascal's trianglerelated to CombinationsRather0.60section
Pascal's trianglerelated to CombinationsFor0.60section
Pascal's trianglerelated to Construction as matrix exponentialDue0.60section

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    Min side: 3
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