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# Pie

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If n cuts are made in a pie, what is the largest number of pieces that may be obtained?

Feb 12, 2018

#1
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If n cuts are made in a pie, what is the largest number of pieces that may be obtained?

I draw some pictures and decided that the number is maximum if all the former cuts have been crossed (not at any point of intersections.

This is the pattern that I found.

 number of cuts  n 1 2 3 4 5 6 7 number of peices   P 2 4 7 11 16 22 29

Now I looked to find the pattern,, with each cut the increaded number of peices  is 1 more than last time.

i mean 2+2=4, 4+3=7, 7+4=11

it will be a quadratic function.

 nunber of cuts  n 1 2 3 4 5 6 7 n(n+1) 2 6 12 20 30 42 n(n+1)+2 = n^2+n+2 4 8 14 22 32 44 (n^2+n+2) /2 2 4 7 11 16 22 number of peices   P 2 4 7 11 16 22 29

So the maximum number of peices if the cake is cut linearly n times is  (n^2+n+2)/2

Feb 12, 2018

#1
+2

If n cuts are made in a pie, what is the largest number of pieces that may be obtained?

I draw some pictures and decided that the number is maximum if all the former cuts have been crossed (not at any point of intersections.

This is the pattern that I found.

 number of cuts  n 1 2 3 4 5 6 7 number of peices   P 2 4 7 11 16 22 29

Now I looked to find the pattern,, with each cut the increaded number of peices  is 1 more than last time.

i mean 2+2=4, 4+3=7, 7+4=11

it will be a quadratic function.

 nunber of cuts  n 1 2 3 4 5 6 7 n(n+1) 2 6 12 20 30 42 n(n+1)+2 = n^2+n+2 4 8 14 22 32 44 (n^2+n+2) /2 2 4 7 11 16 22 number of peices   P 2 4 7 11 16 22 29

So the maximum number of peices if the cake is cut linearly n times is  (n^2+n+2)/2

Melody Feb 12, 2018