Geometry Puzzle

Fun conversation. Just wanted to share.

The boss sent me a geometry puzzle as revenge for one I sent him to solve. I shared it with my favorite philosopher. This conversation ensued.

ME, quoting the boss:

You have a rectangular piece of material out of which are cut two regular polygons of arbitrary number of sides, position and size. (Both holes are entirely contained within the larger rectangle.) Devise a method for dividing the remaining material into two equal areas.

Get back to work!

K: Slice it through from edge-on.

ME: The boss says “No.” He seems to think that the material can’t be split that way. Hmmmph. Where did he find cloth one atom thick? And why isn’t a nuclear blast a valid way of splitting it?

Update 8/2008:
The material is probably a monoatomic-thick graphite substance called “graphene.” No idea where he found it.

K: I like nuclear blast; you collect the fallout into two buckets of equal volume.

ME: I made an infinite number of radial folds so that it was made up of an infinite number of layers of rhombi of width zero. Then I cut it in half radially.
He didn’t like that answer either.

K: Well, isn’t he special? Isn’t it bad for engineers to be rigidly wedded to a single answer when other solutions might be available?

ME: Yeah, really. You have to think outside the box, something bipolars are really good at. LOL!!!
Did I mention that after I came up with a truly ugly solution for the trivial case he told me oops, that should have been ONE polygon? Sheesh. So I choked him. I wonder who will sign my paycheck next time?

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