1. Pascal’s Triangle By Jessica Yaemmongkol

2. History Pascal was not the first to study the patterns on the triangle. The reason the triangle was named after him was because he was able to discover the importance of the entire pattern, with the help of a French mathematician, Pierre de Fermat. Al-Karaji of Persia Yanh Hui of Ancient China Yanh Hui’s Triangle

3. Building the Triangle To create the triangle start with the number 1. To get the bottom number, add the top two numbers.

4. Sequences and Patterns Diagonals

5. Sequences and Patterns Odd and Even If you color all the odd numbers in the triangle you will get a pattern that similar to Sierpinski

6. Sequences and Patterns As you go down the triangle the sum of the horizontal numbers doubles Power of 2

7. Sequences and Patterns Start at a 1 on the left side, go up and to the right. Add up the numbers and you get the Fibonacci sequence

8. Purpose of Pascal’s Triangle To determine the probability of a coin landing on heads or tails. ◦ For example, if you toss a coin twice you can have four different combinations Probability HH HTTH TT Or 1,2,2,1on Pascal’s triangle Formula for combination

9. Purpose of Pascal’s Triangle (x+4) 4 = 1x 4 + 4x 3 + 6x 2 + 4x + 1 Binomial Expansion

10. Credits Pictures credited by “Pascal’s Triangle.” Math is Fun. 2011 Mathisfun.com. 13 March 2011..http://www.mathsisfun.com/pascals- triangle.html