a triangular array of the binomial coefficients

Pascal’s triangle is a triangular array of the binomial coefficients.

a triangular array of numbers

Pascal is also famously associated with Pascal’s triangle, a triangular array of numbers that has found many uses in mathematics, including, appropriately, probability theory.

a triangle formed by rows of numbers

Pascal’s triangle is a triangle formed by rows of numbers.

a number pattern

Pascal’s Triangle is a number pattern in the shape of a (not surprisingly!)

an arrangement of numbers in a triangular array

Pascal’s triangle is an arrangement of numbers in a triangular array.

a neat triangle formed by binomial coefficients

Pascal’s triangle is a neat triangle formed by binomial coefficients.

an arithmetic and geometric figure

Pascal's triangle is an arithmetic and geometric figure often associated with the name of Blaise Pascal, but also studied centuries earlier in India, Persia, China and elsewhere.

an infinite, equilateral triangle composed of numbers

Pascal's triangle is an infinite, equilateral triangle composed of numbers.

Binomial coefficients

Binomial coefficients are more commonly known as Pascal's triangle, named after Blaise Pascal.

polytope

Pascal's triangle can be used as a lookup table for the number of elements (such as edges and corners) within a polytope (such as a triangle, a tetrahedron, a square and a cube).

an array of numbers

As a result, Pascal devised what is called Pascal's Triangle, an array of numbers which begins as shown here.

each number is the sum of the two directly above each number

In Pascal’s triangle each number is the sum of the two directly above each number .

an arrangement of numbers where each value is the sum of the values adjacent to the values in the previous row

Pascal's triangle is an arrangement of numbers where each value is the sum of the values adjacent to the values in the previous row: ...

the exponential of the matrix which has the sequence 1, 2, 3, 4, … on Pascal’s triangle's subdiagonal and zero everywhere else

Pascal’s triangle is the exponential of the matrix which has the sequence 1, 2, 3, 4, … on Pascal’s triangle's subdiagonal and zero everywhere else.

Pascal's Arithmetical triangle

What Pascal called Pascal's Arithmetical triangle had been used in various cultures for more than 500 years.

pattern

Another mathematical prat, pattern that is directly related to n choose r, is Pascal’s triangle, named for Blaise Pascal.

this triangle

As is the case with crediting all the discoveries of Indian mathamaticians after westerners, this triangle is now called Pascal triangle named after Pascal(17th Century) mach after Pascal(17th Century's discovery and relevance 1900 years ago!

an infinite triangular matrix

The Pascal triangle is an infinite triangular matrix thats built from the edges inside 1 11 121 1331 14641 1 5 10 10 5 1.

just binomial coefficients in disguise (or vice versa)

, now we know why Pascal’s triangle is just binomial coefficients in disguise (or vice versa).

hidden patterns

Pascal’s Triangle is not only an interesting mathematical work because of not only an interesting mathematical work's hidden patterns, but its hidden patterns is also interesting because of its hidden patterns's wide expanse of applications to other areas of mathematics.