From Pizza Cut
, we know the formula for maximum partitioning (pieces) of the circle, given n
straight lines (cuts).
- Determine the maximum number of regions of the plane produced by n intersecting circles.
- Determine the maximum number of regions of the plane produced by n intersecting ellipses.
- Determine the maximum number of regions of space produced by n intersecting spheres.
(In reply to re: Reason, don't guess
Sorry, I did not mean to sound harsh in my tone in my previous comment. I apologize if it sounded so. I do think that hiding the formula from people who want to discover it themselves is a good idea.
I was more concerned that some people may think that putting a single formula that others cannot find a counter-example for suffices to solve a problem like this. It did seem that your first post entitled "Parts 1 and 2" claimed to solve the problem (i.e., "then the answer is..."). In that sense, perhaps a title like, "Possible formula" with Comment Type "Some Thoughts" would be more appropriate.
As far as "improper approach", I actually think that your approach is correct - one should draw small examples and conjecture a formula to fit the initial data. But that is only (the easier) half of the problem. The other half of this problem seems exceedingly difficult to me...