What is Pascal's Triangle?

What is Pascal's Triangle?
Pascal's Triangle is an arithmetical triangle we can use for some great purposes in maths. It is made up of staggered rows of numbers. There are many patterns that can be found in the triangle and it looks something like that:

How To Construct Pascal's Triangle

At the tip of Pascal's Triangle is the number 1, which makes up the Row 0. The Row 1 (1 & 1) contains two 1's, both formed by adding the two numbers above them(on the left and the right), in this case 1 + 0 (all numbers outside the Triangle are 0's).

1 Row 0
1 1 Row 1
1 2 1 Row 2
1 3 3 1 Row 3

Do the same to create the 2nd row: 0+1=1; 1+1=2; 1+0=1.
And the third: 0+1=1; 1+2=3; 2+1=3; 1+0=1.

A number in the triangle can also be found by nCr (n Choose r) where n is the number of the row and r is the element in that row. For example, in row 3, 1 is the zeroth element, 3 is element number 1, the next three is the 2nd element, and the last 1 is the 3rd element. The formula for nCr is:
n!
--------
r!(n-r)!

! means factorial, or the number multiplied by all the positive integers that are smaller than the number.
For example, 5! = 5 � 4 � 3 � 2 � 1 = 120 and...
3! = 3 � 2 � 1 = 6

To learn more about it's origin and patterns etc., navigate around with the menu bar below;).