Suppose we have to cut a pie into n pieces, using only straight cuts. What is the fewest number of cuts we can do it in?
When n is even, it is always possible to do it in n/2 cuts: with each cut being a diameter. When n is odd, a similar technique makes it possible to cut it in (n+1)/2 cuts. Can the n/2 bound ever be beaten?
For instance, it is possible to cut a pie into 7 pieces with 3 cuts, but impossible for these pieces to be equal.
Any thoughts on whether the n/2 bound can be beaten to create equi-area peices? Note: the cuts need not go from one edge of the circle to another.