Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appearsIn |
mathematics education
number theory algebra textbooks combinatorics textbooks |
| gptkbp:describes |
binomial coefficients
|
| gptkbp:firstDescribed |
gptkb:Chinese_mathematicians
gptkb:Persian_mathematicians |
| gptkbp:firstRow |
1
|
| gptkbp:hasApplication |
probability
algebraic expansions combinatorial problems |
| gptkbp:hasEntry |
C(n, k) at row n and position k
|
| https://www.w3.org/2000/01/rdf-schema#label |
Pascal's Triangle
|
| gptkbp:knownInChinaAs |
gptkb:Yang_Hui's_Triangle
|
| gptkbp:knownInPersiaAs |
gptkb:Khayyam_Triangle
|
| gptkbp:namedAfter |
gptkb:Blaise_Pascal
|
| gptkbp:popularizedBy |
gptkb:Blaise_Pascal
|
| gptkbp:property |
appears in binomial theorem
appears in combinatorial identities appears in probability calculations contains tetrahedral numbers contains triangular numbers each number is the sum of the two numbers directly above it can be constructed recursively can be generalized to other number systems contains Fibonacci numbers along shallow diagonals diagonals correspond to figurate numbers entries are non-negative integers modulo 2 forms Sierpinski triangle rows are symmetric sum of elements in nth row is 2^n used to expand binomials |
| gptkbp:relatedTo |
gptkb:Lucas_numbers
gptkb:binomial_theorem gptkb:Catalan_numbers gptkb:Sierpinski_triangle gptkb:Fibonacci_sequence binomial coefficients combinatorial mathematics probability distributions algebraic identities |
| gptkbp:rowN |
contains coefficients of (a+b)^n
|
| gptkbp:secondRow |
1, 1
|
| gptkbp:shape |
triangular array
|
| gptkbp:thirdRow |
1, 2, 1
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:probability_theory combinatorics |
| gptkbp:bfsParent |
gptkb:Blaise_Pascal
|
| gptkbp:bfsLayer |
5
|