pumpkin or key lime?

## Problem of the week 4: Cutting the pie

In this problem you have to figure out how to cut a circle in the way that will give you the single most slices possible. After this find the number of slices with ten cuts and explain the pattern. After you do this, you have to find an equation to that can create the most amount of slices by inputting the number of cuts you make.

My process for this problem began by find the best way to make the cuts in the circle to create the greatest amount of slices in the circle. Eventually I found that the best way to make the cuts was by having all the cuts intersecting, but not at the same spot. That way you create the most slices possible. After that I cut circles until I got to eight cuts and began looking for a pattern.

# of Cuts Max # of Pieces Max # of Intersections

1 2 0

2 4 1

3 7 3

4 11 6

5 16 10

6 22 15

7 29 21

8 37 28

Eventually I found that the almost all number of slices compared to cuts is the double plus one. After experimenting with multiple equations I found the universal equations for the number maximum number of slices and the maximum number for intersections. After identifying the pattern I stated in the paragraph above I began to experiment with equations and eventually found the equation:

x

n = ( ∑ k) + 1 for: n = Max pieces, x = # of cuts

k=0

Using that equation I found that the maximum number of pieces that you can get from cutting a circle ten times is 56 pieces with 45 intersections.

An extensions that you could make with this problem is by changing the shape that you are cutting to see if the information is the same, similar or completely different.

During my progress for the the problem I think the habit of the mathematician that I used the most was being Patient and Persistent because I was constantly cutting the circles trying to get the most cuts possible. Eventually I would get it and input it to my data table. After that stage I used Trial and Error as I went through multiple different equations trying to find the formula that could fit all of the data.

My process for this problem began by find the best way to make the cuts in the circle to create the greatest amount of slices in the circle. Eventually I found that the best way to make the cuts was by having all the cuts intersecting, but not at the same spot. That way you create the most slices possible. After that I cut circles until I got to eight cuts and began looking for a pattern.

# of Cuts Max # of Pieces Max # of Intersections

1 2 0

2 4 1

3 7 3

4 11 6

5 16 10

6 22 15

7 29 21

8 37 28

Eventually I found that the almost all number of slices compared to cuts is the double plus one. After experimenting with multiple equations I found the universal equations for the number maximum number of slices and the maximum number for intersections. After identifying the pattern I stated in the paragraph above I began to experiment with equations and eventually found the equation:

x

n = ( ∑ k) + 1 for: n = Max pieces, x = # of cuts

k=0

Using that equation I found that the maximum number of pieces that you can get from cutting a circle ten times is 56 pieces with 45 intersections.

An extensions that you could make with this problem is by changing the shape that you are cutting to see if the information is the same, similar or completely different.

During my progress for the the problem I think the habit of the mathematician that I used the most was being Patient and Persistent because I was constantly cutting the circles trying to get the most cuts possible. Eventually I would get it and input it to my data table. After that stage I used Trial and Error as I went through multiple different equations trying to find the formula that could fit all of the data.

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