This afternoon I was talking to my brother and somehow we began discussing the theoretical behavior of a perfectly flat, two dimensional object that exists in a three dimensional world.

Here's a few of the conclusions I came to:
-The surface of the object would be perfectly flat, therefore the object would experience no friction along its two sides. There might be friction along its edges, but this is negligable since nothing would ever meet the edge of the object head on.
-You could stack the objects face to face infinitely without taking up any amount of space.
-The objects, being perfectly thin, could move through anything their "edges" come into contact with. Dropping such an object into the ground would cause it to fly "through" the ground, straight to the Earth's core.

But what kind of behavior would you predict from a perfectly flat two dimensional object in three dimensional space?