POW Write Up; Just Count the Pegs
For the POW: Just Count the Pegs, I had to try and find the best formula possible for finding the area of any polygon on a geoboard. There are 3 different formulas you have to find. The first two are formulas that will combine together and help you find the best or “superformula”. In order to find the first two, you will make in and out tables. You will find the pattern and then come up with a formula for it. For the first part, you have to find a formula that works for polygons with one peg in the interior. For the second one you have to find the formula for the area of polygons with exactly four pegs on the boundary. Using both of these, you then find a formula that will work for any polygon. Process:
I started off by figuring out Freddie and Sally’s formulas. I had to find these two first in order to find the “superformula.” In | Out|
3| .5 |
5| 1.5 |
I completed Freddie’s first. Freddie’s was the easiest to find because it was a technique I had used, without really knowing it. I started out by drawing a simple in and out table. In or x was the number of pegs on the boundary of the polygon. The out or y was the area of the figure. Then I made multiple polygons on geoboard paper. I counted the pegs and calculated the area and added them to my in/out table. I used the numbers 3-5 in my table. I then looked at my table for a while and tried to find patterns in it. At first I thought it could possibly be something as simple as x plus 1 = y. Then I saw 3 was .5 and new that wouldn’t work. So I started looking at other patterns and tried out many things. Finally I came up with x/2-1=Y. I tried this for all 5 numbers and it worked for every single one of them. So, that was Freddie’s formula. In| Out|
Sarah’s formula was a lot more difficult for me because I was confused by what I...