My problem for Free Think Friday was Pascal’s Triangle. In this problem there is a triangle with 16 rows inside it. Each number is created by the two numbers added above it. For example, if two was at the top the two bottom spots underneath would be 2 because 2+0 is 2. Then underneath the two spots with two it would be 2, 4, 2. This pattern continues throughout every row and can be expanded to infinity. There is one equation that can solve the row and tell you the highest number.
The first step we did was fill out the triangle. The reason why we did this was to see if there were any patterns throughout the triangle. Next we were trying to figure out a rule for the equation. We knew that it was a recursive formula (which was told by Carlee Hollenbeck) which helped us figure out the numbers in the triangle. We bounced off each other’s ideas which helped us to get a the formula Triangle P=1 for the multiply triangle.
Our solution was not final but we figured the highest number in rows 10 and 15. Row 10 was 126 and row 15 was 3432. We also figured that there is a recursive formula. Our second question was what would the first five rows look like if you multiplied the two spaces,instead? We figured that it would end up being all 1’s. The reason why is because it starts with 1 and 1 x 1 ends up being 1 in every space.
I believe I should receive a 8 overall. I say this because I missed the first Friday we received the problem. Which meant I didn’t fill out the first 8 rows. I was there for the rest of the Fridays. I filled out the rest of the slots in the triangle. I also worked with Andrew to figure out the multiplication triangle. I filled out most of our poster and participated in the presentation.