Pascal's Triangle

In my workshop, Prove It or Lose It, we have been working on what combinations are and what the Pascals's Triangle is. We have been working on finding different ways to go from point A to point B. We learned about the equation on how to tell if the triangle equals each other.  A combination is something that deals with letters or numbers, and you can find a different ways to mix the letters or numbers, so that each letter/ number ends up in a different place each time. For example, if we use the word CAT. I can make 6 different words from this 3 letter word. I figured this out because I used a math term called Factorials. Factorials are when you take a number and put an exclaimation mark next to it. That basically means that you are taking this numer and multiplying it by each number that is smaller than this number. For example, 9!= 9x8x7x6x5x4x3x2x1. This is what factorials and combinations looks like.  This is an example of using a three letter word and using factorials to find how many ways there are to rearrange the word CAT, 3 letters= 3!= 3x2x1= 6.  Here is a gif of what a Pascal Triangle is and it will show you the steps on what to do and how you figure out where to put the numbers.



As you can see, as the numbers add up with each other it becomes a bigger number each time. Pascal's Triangle is a triangle that shows numbers getting bigger and bigger based off of what the number has on it. It was named after Blaise Pascal. He was a "French mathematician, physicist, inventor, writer and Catholic theologian." based off of google. 

Another interesting thing I learned in Prove It or Lose It was, how to find different ways to get from one point to another, without going backwards or going away from the second destination that you are trying to reach. I thought that it was really interesting when I found out that there were more than one option to get to the other destination. 

In conlcusion, I am happy that this class is over and I hope that I get a better knowledge in math. 

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