G'day all.
Quoting Adrian Neumann <[EMAIL PROTECTED]>:
I often wonder how many cuts you need to divide a steak in n pieces.
One, if the cut is allowed to be curved and self-intersecting.
I think that the spirit of the problem, though is encapsulated in this
question: Given a circle, what is the maximum number of pieces that you
can divide it into by performing n straight cuts?
This is a great problem to set undergraduates, because if you work out
some small values of n on paper, you get:
n #pieces
0 1
1 2
2 4
3 7
Most undergrads will stall at this point trying to work out how to
place the third line to get 8 pieces, and probably come up with an
incorrect justification for why it should be 2^n.
The details are here:
http://www.research.att.com/~njas/sequences/A000124
Cheers,
Andrew Bromage
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