From Pizza Cut, we know the formula for maximum partitioning (pieces) of the circle, given n straight lines (cuts).
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1. Determine the maximum number of regions of the plane produced by n intersecting circles.

2. Determine the maximum number of regions of the plane produced by n intersecting ellipses.

3. Determine the maximum number of regions of space produced by n intersecting spheres.

If the ellipses each have the same center but each has a greater hoizontal axis and smaller minor axis than the next the formula is

2nē - 2n - 2

I don't know if this is the maximum.

but its time to go so I won't tackle the others now

-Jer

Posted by Jer on 2004-09-13 14:11:37