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gptkbp:instance_of
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gptkb:Mathematics
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gptkbp:analyzes
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a triangle of numbers
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gptkbp:can_be_extended_by
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downwards
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gptkbp:can_be_generated_using
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recursive formulas
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gptkbp:can_be_represented_visually_as
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a triangular array
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gptkbp:constructed_in
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adding the two numbers above
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gptkbp:developed_by
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the binomial theorem
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gptkbp:example
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mathematical induction
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gptkbp:has_a_row_for_n=0_that_is
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gptkb:1
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gptkbp:has_a_row_for_n=1_that_is
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1, 1
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gptkbp:has_a_row_for_n=2_that_is
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1, 2, 1
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gptkbp:has_a_row_for_n=3_that_is
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1, 3, 3, 1
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gptkbp:has_a_row_for_n=4_that_is
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1, 4, 6, 4, 1
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gptkbp:has_a_row_for_n=5_that_is
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1, 5, 10, 10, 5, 1
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gptkbp:has_applications_in
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gptkb:computer_science
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gptkbp:has_rows_that_represent
|
binomial coefficients
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https://www.w3.org/2000/01/rdf-schema#label
|
Pascal's Triangle
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gptkbp:is_a_source_of
|
combinatorial proofs
patterns in mathematics
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gptkbp:is_a_tool_for
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solving problems in combinatorics
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gptkbp:is_analyzed_in
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the number of subsets
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gptkbp:is_associated_with
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the concept of binomial expansion
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gptkbp:is_connected_to
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binomial distributions
the concept of lattice paths
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gptkbp:is_evaluated_by
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combinations
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gptkbp:is_fundamental_to
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gptkb:Mathematics
|
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gptkbp:is_part_of
|
discrete mathematics
mathematical history
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gptkbp:is_related_to
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Fibonacci sequence
combinatorial identities
triangular numbers
the concept of permutations
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gptkbp:is_represented_in
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modular arithmetic
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gptkbp:is_studied_for
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properties and patterns
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gptkbp:is_studied_in
|
number theory
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gptkbp:is_symmetric
|
about the center
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gptkbp:is_taught_in
|
mathematics education
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gptkbp:is_used_in
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gptkb:Mathematics
gptkb:strategy
statistical analysis
probability theory
combinatorics
binomial theorem
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gptkbp:named_after
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gptkb:Blaise_Pascal
Blaise Pascal's work
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gptkbp:represents
|
coefficients in polynomial expansion
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gptkbp:starts_at
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1 at the top
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gptkbp:bfsParent
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gptkb:Blaise_Pascal
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gptkbp:bfsLayer
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5
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