History
This French mathematician gave his name to the triangle of numbers used in probability and algebra.
Blaise Pascal
This theorem lets you expand expressions like (a + b)^n into a sum of terms using coefficients from Pascal’s Triangle.
the Binomial Theorem
This type of pattern adds or subtracts the same number each time, like 2, 4, 6, 8...
arithmetic pattern (or arithmetic sequence)
This property states that changing the order of numbers in addition or multiplication doesn’t change the result.
commutative property
Pascal’s Triangle can be used to find the coefficients when expanding powers of a binomial, like (a + b)^3.
binomial expansion
Centuries before Pascal, this group of ancient mathematicians in China had already studied the same triangle, calling it the “Yang Hui’s Triangle.”
the Chinese mathematicians
In the binomial expansion of (x + y)^n, the exponents of x and y in each term always add up to this number.
n
In this type of pattern, each term is multiplied by the same number to get the next one, like 3, 6, 12, 24...
geometric pattern (or geometric sequence)
This property says that when adding or multiplying, you can group numbers differently and still get the same answer.
associative property
This branch of mathematics uses Pascal’s Triangle to calculate combinations, such as how many ways you can choose 3 students from a group of 10.
probability (or combinatorics)
Before Pascal and Yang Hui, this Persian mathematician from the 11th century described the triangle in his work The Book of Instruction on Algebra.
Omar Khayyam
The general term in the binomial expansion is written as (n/r)a^n−r b^r. The expression (n/r) is known by this name.
binomial coefficient
The sequence 1, 1, 2, 3, 5, 8, 13... is a famous pattern where each term is the sum of the two before it.
Fibonacci sequence
This property allows you to multiply a number outside parentheses by each term inside, like 3(a+b)=3a+3b.
distributive property
Patterns from Pascal’s Triangle can also represent how light bounces in a mirror or the number of paths through a grid — topics often studied in this field.
geometry (or mathematical modeling)