3 ms·
It's not really paradoxical [1], but I've always thought Gabriel's Horn was pretty cool. It's a (non-fractal) object with finite volume and infinite surface ar
by mnemonicsloth 19y ago
It's not really paradoxical [1], but I've always thought Gabriel's Horn was pretty cool. It's a (non-fractal) object with finite volume and infinite surface area.
http://en.wikipedia.org/wiki/Gabriel%27s_Horn http://en.wikipedia.org/wiki/Gabriel%27s_Horn
- wallflower 19y agoReminds me of Klein's bottle
- tlrobinson 19y agoFinite volume and infinite surface area, eh? For example, volume grows as the cube of linear dimension, but surface area only as the square. So as animals get bigger they have trouble radiating heat. http://www.paulgraham.com/ycombinator.html http://www.paulgraham.com/ycombinator.html Perhaps large animals should make themselves into the shape of Gabriel's Horn. Of course then they'll radiate too much heat.
- mercurio 19y agoI read the wiki article and it turns out the horn uses precisely that dimensional difference in a very clever way. The radius varies as 1/x along the x-axis, so the volume grows as 1/x^2 while the surface area grows as 1/x. This means the growth rate of volume goes to zero much faster than that of the surface area. As a result the volume integral converges, while the surface area diverges.