Horn

MB44

How is it that the surface area of the horn is infinite while the
volume is finite?

Chucky

Looking at a horn you can clearly see that it's surface area is not infinite. Where did you get your information from?

breadmonkey

Have a look here

http://en.wikipedia.org/wiki/Gabriel%27s_Horn

Chucky

Haha, that's very interesting.

It's just one of those pieces of Math that results in an anomaly in reality. It reminds me of the Half-Life of Radionuclides. The theory suggests that the Radionuclide will never completely decay but will always get smaller and smaller in mass. Eventually it has to come to a point where only one atom remains, however. The Math at that point suggests that it continually decays even from the single atom stage!


Grr! Infinities appear to cause problems everywhere - From Horns to Black Holes to simply getting from A to B.

Funkstard

"he apparent paradox has been described informally by noting that it seems it would take an infinite amount of paint to coat the interior surface, but it also seems that it would be possible to simply fill the interior volume with a finite amount of paint and so coat the interior surface. The resolution of the paradox is that the implication, that an infinite surface area requires an infinite amount of paint, presupposes that a layer of paint is of constant thickness; this is not true in theory in the interior of the horn, and in practice much of the length of the horn is inaccessible to paint, especially where the diameter of the horn is less than that of a paint molecule. - If the paint is considered without thickness, it would further take infinitely long time for the paint to run all the way down to the "end" of the horn."