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.

(In reply to Part 3?? by nikki)

Extending your table to 5 spheres shows 2^n – 1 is not correct.

Spheres:
n      regions added      regions     
0                                    0
1               1                   1
2               2                   3
3               4                   7
4               8                 15
5             14                 29

Posted by Brian Smith on 2004-09-14 12:55:27