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Partitioning Space (Posted on 2004-09-13) Difficulty: 5 of 5
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.

No Solution Yet Submitted by SilverKnight    
Rating: 4.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Part 3?? | Comment 6 of 13 |
(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
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