Weird Shape

[Chris Daddy Cool]

For some odd reason I remembered a lecture my high school calculus teacher gave and he mentioned that there is a geometrical shape that can be found using some formulas where if you fill the shape's volume with paint, that paint would NOT be enough to cover the surface area of that shape. That doesn't seem logically possible, but I guess there must be a way to prove it. Anybody know the shape and the logic behind it?

[Mano]

Sounds like a space filling curve, like a peano curve.

[Chris Daddy Cool]

If only I knew what the hell that meant...

but aren't curves not shapes, but like, planes... that are curved? thus it couldn't have a volume since its not really a shape? unless i misunderstood the wording by my professor.

[Stu Pidasso]

I have know ideal what your talking about. However one shape I find very interesting is a Mobius strip. If you don't know how to make one, you can learn how at this link. (http://scidiv.bcc.ctc.edu/Math/Mobius.html)

Stu

[daryn]

you are talking about a thing called gabriel's horn. basically the idea if i remember correctly is you take the plot of the function e^-x and rotate it about the x-axis to form a horn shape. anyways, due to the way we calculate infinite volume and area integrals with exponential functions, the volume of said horn is FINITE, while the internal surface area is INFINITE.

like you said, you could find the amount of paint necessarry to fill the horn, but it somehow wouldn't be enough to paint the inside surface of the horn.

[daryn]

i guess i should do my research before posting. instead of e^-x it's the function 1/x. check it out here:

http://curvebank.calstatela.edu/torricelli/torricelli.htm

anyway, damn mathematicians.