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The Paul Mach Blog - I Play with Balls - Part 3
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Living life on the edge... of the road

I Play with Balls - Part 3
Wednesday, September 10, 2008 - Research
What does the Inclusion-Exclusion formula applied to balls look like?

If Set of Balls is a set of balls and | . | denotes the volume of an object, then this is the formula.

Full Formula
You just add and subtract more and more intersections till you run out. The same applies for surface area of spheres. If you're interested, here is a way too detailed proof.

This method is simple to understand. The problem is that if you have more than 4 balls you run into trouble. You are stuck with figuring out if all the intersections exists and what they are.

Conclusion: This method is great if you have a small number of balls or if you know you don't have any intersections of 4 or more balls.
If you do, then you're going to have to think a little harder.

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Todd Manley
Wednesday, September 10, 2008, 10:19 am
Ouch, my eyes are hurting and my head is throbbing.

Thursday, September 11, 2008, 9:13 pm
blah blah blah. When are you going to get to the MHG (Metropolis-Hastings-Green) part?