Here's a fun one: it is possible to divide a (circular) pizza with n cuts into more than 2n pieces (not necessarily equal, and the cuts do not all go through the center or bisect the pizza).
- the ordinary way, n cuts all through the center gives 2n uniform pieces and it is trivial to make them equal size.
However the MAXIMUM number of pieces p(n) for n cuts is called the lazy caterer's sequence and goes like this: 1, 2, 4, 7, 11, 16, 22, 29...
See e.g. the Wikipedia picture of the pancake cut into 7 pieces by 3 cuts (the middle piece is a (possibly equilateral) triangle)
http://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence
Note: "equal-area" does NOT imply "uniform"!
So anyway my questions are these:
a) for n cuts, define the general algorithm to make the cuts
b) what is the ratio r(n) of largest to smallest pieces area?
Try e.g. computing r(3) and r(4)
c) is there a more useful sequence of cuts such that 2n
2007-11-18
16:41:24
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2 answers
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asked by
smci
7