Application of mathematics

I linked to a video explaining the Banach Taski Paradox to the layman (in this branch of math, I am also a layman). If you didn't watch it, the paradox said that a sphere could be partitioned into two identical spheres without missing any points. 1=1+1

I'm still a trifle dubious about algorithms that step through uncountable numbers of points (or maybe I misunderstood that), but after we brushed the rabbit tonight I'm fairly sure that the assertion must be true--there's enough fur to constitute an entire new rabbit, and the old rabbit is still shedding.