Suppose we are to cut a unit circle into n equal area pieces. We can cut curves if we wish. What is the minimum distance we must cut? What strategy minimises this distance? Note: The shape of the pieces doesn't matter, nor does the number of cuts.
When n=2, clearly we simply cut a diameter, yielding a distance cut (C) of 2.
When n=3 and n=4, it seems that the optimal cutting method is simply to make equally spaced n radial cuts.
However, there must be a different strategy for some higher n. For instance, with n=10, it would be better to cut a second circle, of area Pi/2, and circumference Pi*sqrt 2, and 5 radial cuts; rather than 10 radial cuts.
So, what is the relationship between n and the distance, and what is the general optimal strategy?