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The Paul Mach Blog - I Play with Balls - Part 2
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I Play with Balls - Part 2
Wednesday, September 3, 2008 - Research
If you're new, check out part 1. First, [img=http://www.paulmach.com/math/cup.gif popup=false] means union and [img=http://www.paulmach.com/math/cap.gif popup=false] means intersections. Just so you know.

So how do you start computing the intersection of a union of balls? Lets look at some simple examples.

If you have two balls, you can start with the volume of 2 balls. But then you need to subtract their intersection because that part was added in twice. 2 Disk example The resulting formula looks like this

2 Sphere Formula
If you have three balls, you subtracted too much so you need to add in the 3-sphere intersection.

3 Sphere Formula
You may see a pattern here, and there is. The resulting formula is the Inclusion-Exclusion Formula. More on that next time.

Again, mathematical balls.


All September Entries



hernando
Wednesday, September 3, 2008, 11:31 am
<i><b>nerd alert!</i></b>

Jesse Moore
Thursday, September 4, 2008, 9:38 am
Is this as far along as you've gotten with the research?!?! Your advisor must love bikes as much as your wife. Just tell them you are out to break Jeff Angerman's record of most seasons spent racing collegiately... I'm sure they will support that pursuit :) Seriously though can we get back to making fun of Roman or the Cal Giant team? "you are a dork"

Chaz Michael Michael's Dad
Thursday, September 4, 2008, 9:56 am
Jesse,

The reason we love Paul is because he is a dork. And it makes all cyclists feel better about themselves because we are all dorks, too.

Dorks with incredible athletic ability, maybe. And that have no upper body muscles (unless you are a good track racer) and are worried about their weight. And wearing spandex. All=Dorky!

C'mon, cyclists are dorky. Especially T-Bag Dibble (But then again, he does ride for Cal Giant, so naturally). Embrace your dorkiness. It's sexxxxy!

zach
Thursday, September 4, 2008, 4:37 pm
cooooooooooooooooooooooooooooool!

Adam
Thursday, September 4, 2008, 7:31 pm
Ok, wow, way too many two ball, three ball jokes here. System overload

Wife
Friday, September 5, 2008, 12:12 pm
There sure are a lot of people going NUTS about this blog post.

mark
Saturday, September 6, 2008, 11:22 am
Just be happy that paulmachdotcom is not a Topology student, because if he were, he'd be posting about The Hairy Ball theorem. (There really is such a theorem you know.)





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