Pow 17 Cutting The Pie
POW 17- Cutting the Pie
Problem Statement-
If you were given a pie what is the maximum number of pieces you can produce from 4, 5, and 10 cuts? Keep in mind, that the slices do not have to be the same size and the cuts do not necessarily have to go through the center of the pie, but the cuts do have to be straight and go all the way across the pie. Include any diagrams you used to find the solution such as an In-Out table, or any patterns you found.
Process-
The first thing I did to try to find my solution was to finish the In-Out table given, which already told us the maximum number of pieces that could be made with 1, 2 and 3 cuts. So I drew two circles, and drew in four cuts in one and five cuts in another to find the maximum number of pieces that could …show more content…
This is because the independent variable is the number of cuts, not the maximum number of pieces. Finding the pattern was easy, but the challenging part was finding the formula. I tried finding something that had to do with the way the actual pie was cut, like how large the cuts had to be, or if it made a difference what direction the cut was in. Unfortunately, this did not help me in coming up with a solution or formula. So, I started looking at the difference between the number of cuts and the maximum number of pieces. I noticed that the range was increasing as the number of cuts increased. For a long time I plugged and chugged, playing around with multiplying, adding and squaring. I figured subtracting and dividing wouldn't really help since the numbers were increasing. Finally, I came to the conclusion that the number of cuts had to be squared and then another value had to be added. However, I realized this wouldn't work for only one cut because you couldn't add another value and have the maximum number of pieces be two. This led me to realize that at a certain point I had to divide. This had to be done after squaring the number of cuts and adding a value because
Problem Statement-
If you were given a pie what is the maximum number of pieces you can produce from 4, 5, and 10 cuts? Keep in mind, that the slices do not have to be the same size and the cuts do not necessarily have to go through the center of the pie, but the cuts do have to be straight and go all the way across the pie. Include any diagrams you used to find the solution such as an In-Out table, or any patterns you found.
Process-
The first thing I did to try to find my solution was to finish the In-Out table given, which already told us the maximum number of pieces that could be made with 1, 2 and 3 cuts. So I drew two circles, and drew in four cuts in one and five cuts in another to find the maximum number of pieces that could …show more content…
This is because the independent variable is the number of cuts, not the maximum number of pieces. Finding the pattern was easy, but the challenging part was finding the formula. I tried finding something that had to do with the way the actual pie was cut, like how large the cuts had to be, or if it made a difference what direction the cut was in. Unfortunately, this did not help me in coming up with a solution or formula. So, I started looking at the difference between the number of cuts and the maximum number of pieces. I noticed that the range was increasing as the number of cuts increased. For a long time I plugged and chugged, playing around with multiplying, adding and squaring. I figured subtracting and dividing wouldn't really help since the numbers were increasing. Finally, I came to the conclusion that the number of cuts had to be squared and then another value had to be added. However, I realized this wouldn't work for only one cut because you couldn't add another value and have the maximum number of pieces be two. This led me to realize that at a certain point I had to divide. This had to be done after squaring the number of cuts and adding a value because