Friday, January 20, 2012

The Impossible Vuvuzela

Mathematicians can describe a very strange theoretical object, which has two very paradoxic properties.

It looks like a horn, or maybe a trumpet. Hmmm, I guess it resembles one of those dreaded vuvuzelas most. It becomes thinner and thinner along its length — which, by the way, is infinite. You know what? Here's a picture:

On the one hand this vuvuzela has an infinite surface area. Because as the vuvuzela becomes longer, its exterior and interior become bigger, thus this vuvuzela of infinite length has an infinite surface.

On the other hand, its volume approaches π. That's right, a finite value. Surprisingly, this vuvuzela of infinite length has an exact finite volume.