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(3): Part 3?? what was I thinking? by nikki)

Guessing formulas to match the first few experimental values is not the
right way to go. The aim should be to geometrically reason about
the problem and give a proof. If you have a guess of a formula,
it should be labeled as such, not as a solution.