# Thread: A piece of the pie

1. ## A piece of the pie

What is the maximum number of regions into which you can divide the area of a circle using 3, 4 and 5 straight lines?
What about for n straight lines?
How many pieces of pie can you get from 21 cuts?

Alan

2. ## Re: A piece of the pie

I assume these are 3 seperate questions???
Q3 = 42!
As for the other 2, I haven't the foggiest idea what u mean! <img src=/S/scratch.gif border=0 alt=scratch width=25 height=29>

3. ## Re: A piece of the pie

Is that 42 or factorial(42)? In either case, not correct for 21 cuts.
With one cut, you can get 2 pieces of pie. With 2 cuts - 4, with 3 cuts - 7 (giving away the first part of the first question). I'm asking how many pieces you could get with "n" number of cuts. For instance 21 cuts.

Alan

4. ## Re: A piece of the pie

I make it <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">9</span hide> for 4 cuts and <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">15</span hide> for 5?

5. ## Re: A piece of the pie

Close, but no cigar <img src=/S/sad.gif border=0 alt=sad width=15 height=15>. You're selling yourself sort on pie pieces.

IMPORTANTLY - I should have qualified, stating that the pie is circular and the pieces need not be of equal sizes.

Alan

6. ## Re: A piece of the pie

I'm guessing 3 = <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">7</span hide>; 4 = <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">11</span hide>; 5 = <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">16</span hide> - unless you can include one cut horizontally where it would be 3 = <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">8</span hide>; 4 = <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">14</span hide>; 5 = <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">22</span hide>.

But I've been wrong before.... <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

7. ## Re: A piece of the pie

Correct Leif. And no, I didn't think about a horizontal cut between the face and the base. Now all that's left is to determine how many pieces for <font color=blue>n</font color=blue> cuts.

Alan

8. ## Re: A piece of the pie

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1 + (1 + 2 + 3 + 4 ... + n)</span hide> ?

If so, 21 cuts would be <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">232</span hide> or <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">422</span hide> if you allow for a horizontal cut.

9. ## Re: A piece of the pie

I concur <img src=/S/yep.gif border=0 alt=yep width=15 height=15>. But it's interesting how you expressed the formula, showing you must have thought about it differently from me. I can see your answer making perfect sense from a physical viewpoint. I took the analytical approach, trying to deduce the formula from the first few (relatively) easily determined results:
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2, 4, 7, 11, 16
The first order differences between successive terms are:
2, 3, 4, 5
The second order differences between successive terms are:
1, 1, 1

This indicated a quadratic dependence: Pieces = an

10. ## Re: A piece of the pie

"On behalf of HansV, who fortunately couldn't be with us this evening ........"

<img src=/S/grin.gif border=0 alt=grin width=15 height=15>

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