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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.)
Some Thoughts Part 2 solution? | Comment 1 of 13

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
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