Pascal's triangle
Pascal's triangle is like a special pyramid of numbers where every number above is the sum of the two numbers below it. It is named after Blaise Pascal, a famous mathematician.
Imagine a triangle with one on top, and then below it are two ones. Then, under those two ones, there are two numbers that were created by adding the two ones directly above them. For example, the first box in the row below has a 1 (from the left) and a 1 (from the right) which have been added together to make 2.
This goes on and on for as many rows as you want. In each row, there are one more box than the row above. And you always add the two numbers directly above to make the new number.
The cool thing about the triangle is that it has some really special patterns. For one thing, every row has the same sum of numbers. And every other row can be made by multiplying each number in the row above it with a number that is one less than the number of that box in that row above it. This is called the "choose" operation, which is a fancy way of saying "how many ways there are to choose some things from a group."
People use Pascal's triangle for lots of things, like counting how many ways you can arrange a set of objects, or figuring out the coefficients in algebraic equations. It's a pretty neat tool in math!
Imagine a triangle with one on top, and then below it are two ones. Then, under those two ones, there are two numbers that were created by adding the two ones directly above them. For example, the first box in the row below has a 1 (from the left) and a 1 (from the right) which have been added together to make 2.
This goes on and on for as many rows as you want. In each row, there are one more box than the row above. And you always add the two numbers directly above to make the new number.
The cool thing about the triangle is that it has some really special patterns. For one thing, every row has the same sum of numbers. And every other row can be made by multiplying each number in the row above it with a number that is one less than the number of that box in that row above it. This is called the "choose" operation, which is a fancy way of saying "how many ways there are to choose some things from a group."
People use Pascal's triangle for lots of things, like counting how many ways you can arrange a set of objects, or figuring out the coefficients in algebraic equations. It's a pretty neat tool in math!
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