What is pascal's triangle?
It is a triangular pattern of binomial coefficients (Click here)
The triangle starts with a 1 at the top and carries on with 1s all along the outer sides of the triangle as shown in the image to the right. To build upon the triangle, the number below will just be the sum of the two numbers above. The numbers will keeping falling into place below as a triangular pattern. Don't forget to place the 1s on the sides of the triangle! |
Who created it?
None other than mathematician Blaise Pascal (Click here)!
What can it be used for?
1. Algebra
When raising a binomial to any power, you can use Pascal's Triangle to get the coefficients of your expansion. This is called binomial expansion (Click here)
2. Probability & Combinatorics
You can use the triangle to find Combinations (Click here)
Let's say you have 12 pencils and you want to know how many ways you can pick 4 of them. It doesn't matter which order you pick the pencils in, it just matters which ones you pick.
So the question becomes, How many different ways can you pick 4 objects from a set of 12 objects?
The answer is in the 12th row and 4th place of pascal's triangle. Twelve choose four.
When raising a binomial to any power, you can use Pascal's Triangle to get the coefficients of your expansion. This is called binomial expansion (Click here)
2. Probability & Combinatorics
You can use the triangle to find Combinations (Click here)
Let's say you have 12 pencils and you want to know how many ways you can pick 4 of them. It doesn't matter which order you pick the pencils in, it just matters which ones you pick.
So the question becomes, How many different ways can you pick 4 objects from a set of 12 objects?
The answer is in the 12th row and 4th place of pascal's triangle. Twelve choose four.