Gabriel's Horn

#1

Post by wz1000 » Tue, Jun 16, 2015, 1:17 PM UTC

Re: Gabriel's Horn

#2

Post by dubin » Tue, Jun 16, 2015, 6:53 PM UTC

Also check out the Menger sponge, which has infinite surface area and zero volume: http://en.m.wikipedia.org/wiki/Menger_sponge

Re: Gabriel's Horn

#3

Post by wz1000 » Tue, Jun 16, 2015, 7:04 PM UTC

dubin wrote: post #2

Also check out the Menger sponge, which has infinite surface area and zero volume: http://en.m.wikipedia.org/wiki/Menger_sponge

Non-mobile: https://en.wikipedia.org/wiki/Menger_sponge

Re: Gabriel's Horn

#4

Post by darkmighty » Tue, Jun 16, 2015, 7:33 PM UTC

dubin wrote: post #2

Also check out the Menger sponge, which has infinite surface area and zero volume: http://en.m.wikipedia.org/wiki/Menger_sponge

Or equivalently any object with a fractal dimension between 2 and 3.

Re: Gabriel's Horn

#5

Post by mturmon » Tue, Jun 16, 2015, 7:42 PM UTC

dubin wrote: post #2

Also check out the Menger sponge, which has infinite surface area and zero volume: http://en.m.wikipedia.org/wiki/Menger_sponge

You can do the first few levels with business cards:

http://theiff.org/oexhibits/menger02.html

As you go to higher levels, that "infinite surface area" thing starts to become difficult to manage. ;-)

Re: Gabriel's Horn

#6

Post by [deleted] » Tue, Jun 16, 2015, 7:55 PM UTC

[deleted]

Re: Gabriel's Horn

#7

Post by TeMPOraL » Tue, Jun 16, 2015, 10:11 PM UTC

I wonder what sound it would make. Can we model such a horn assuming a from, say, 1cm to some value p and simulate it?

Re: Gabriel's Horn

#8

Post by currentoor » Tue, Jun 16, 2015, 10:52 PM UTC

TeMPOraL wrote: post #7

I wonder what sound it would make. Can we model such a horn assuming a from, say, 1cm to some value p and simulate it?

Depends on how many of the laws of physics you want to ignore. The horn has infinite length and sound waves have a finite speed (assuming sound is defined as the usual compression wave through a medium). So a sound wave starting at the narrow end would take an infinite amount of time to reach the other end. But the sound it self shouldn't be anything special.

Re: Gabriel's Horn

#9

Post by relicscattergun » Wed, Jun 17, 2015, 12:07 AM UTC

dubin wrote: post #2

Also check out the Menger sponge, which has infinite surface area and zero volume: http://en.m.wikipedia.org/wiki/Menger_sponge

I think Sierpinski's triangle may also be of interest here, which, contrastly, approaches zero surface area: http://en.wikipedia.org/wiki/Sierpinski_triangle

Re: Gabriel's Horn

#10

Post by jveld » Wed, Jun 17, 2015, 12:23 AM UTC

I've thought it was paradoxical that infinitely long curves could have finite integrals ever since I first took calculus. For example, the integral of 1/x is |ln x|.

I wonder why it takes three dimensions before people start getting upset.