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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.)
Reason, don't guess | Comment 9 of 13 |
(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.
  Posted by David Shin on 2004-09-14 16:47:37

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