Three dimensional visualization test

Next piece of bad news.... I can't find the solution online

The article referred to http://physicsweb.org and they have a web site, but it doesn't seem to have the article by Eric Voice.

er, excuse me....


over here;



yes behind that big potted fern!

i did it!!!

You turned an innertube inside out?

That's a brutal geek-tease, rosborne.

I found an answer, but I'm not sure it's authoritative: http://www.fortunecity.com/emachines/e11/86/klein2.html

Don't look unless you're tired of giving yourself a headache.

One that I find easier to read (pdf format).

http://www.heartofmath.com/pdfs/pg331.pdf

In the interest of preserving the mystery, I will neither gloat (aha!) or lament (huh...).

Interesting.

That's some careful stretching and deforming.

Yeah, I'd say it's some of each. (You're a better man than I...)

i must admit that i find it unnerving that people would rather continue to search for 'evidence' on the internet; while ignoring the real thing actually performed for them in 'real time', real space' or whatever non virtual term you would like to use!!!???

I would like to do it in reality, but I don't have an inner tube. I do have an internet connection however, and the ability to visualize things when explained to me (though that ability has been somewhat humbled).

None of the above answers are correct. I cheated and made a tube out of a plastic bag. What you end up is with a tube with an opening on both ends.

nor have i got an inner tube, nor do i wanna buy one just to cut a hole in it. course, the neighbor does leave his bike sitting out on the porch...

I did it in reality. :-)

Hadda find out.

Sewed a tube out of some scrap material, tried to turn it inside out. Impossible -- for that item. It wasn't a large distortable inner tube, though, it was small (about 1 foot diameter) and non-distortable (cotton twill.)

BoGoWo, are you saying that you really did it with an innertube? If so, how big (the tube and the hole), and what method?

I've got one made from a newspaper sleeve, and am hving no luck with it (damn you, bogowo -- the woman of the house thinks I'm crazy now, again).

pd, Use a plastic bag.

This is probably how it starts...

USA, Suburbs (AP) -- Authorities are at a loss to explain a sudden rash of random tire mutilations... local resident Edna Thornwhistle suspects aliens... film at 11.

Re: Three dimensional visualization test

If I were a theorist, I would approximate the tube as a torus, in which case my answer would be yes. As an experimental physicist though, I can't help noticing that the valve of an inverted tube would be pointing into its inside, leaving me with a tube that has a hole in it, but no way to pump it up. Duh. But if Sozobe's answer is still no in the torus approximation, I'm willing to take her up on it.

Here's the way I visualize it in the Torus approximiation. I stick my thumb and my index finger through the hole into the tube, which I imagine to be on the outside of the donut. I imagine that my fingers are very long, so I can reach all the way around the inside of the tube until the two fingers touch on the opposite end, fingers bending backward. I grab the inside -- call it the "donut hole" -- and pull it all out through the "nail hole". After I'm done, my fingers are now on the outside of the inverted torus. They're still touching each other's tips. The nail hole is now on the other side, near the point where the fingertips are touching each other, on the inside of the inverted donut.

Hard to describe, but the answer is yes, and I'm certain too. I think the key is to "feel" that what Sozobe called "the bottom er hard to describe part" really isn't a bottom, because you can reach all the way round on the inside of the tube..

Of course you can; the small and big torus circles get reversed though, as do the inner and outer surfaces. The circle that was the 'hole' in the doughnut now becomes the circle that is the 'outer radius' and vice versa.

The easiest to visualise this is by enlarging the hole until the hole is as big as the tube (minus a tiny strip), then extending the hole in a circular fashion until only a tiny strip of each circle remains, now turn the big circle inside out and stretch it , so the other fits inside, then shrink back the hole - and voila!

Relative

I cheat like hell.... and remember a diagram from one of Martin Gardner's Mathematical Recreations columns in Scientific American...

If you stretch the hole to the point of ridiculous, you get two joined rings of material. One going aroung the center of the torus, and one going around diameter of the circle that you rotated to get that torus.

Hey, I'm a geometer by profession...

(Damn... relative's got it... that's what I get for not reading the 2nd page of posts before posting...)

I understand that this was exactly the problem with Bush's bike, and the reason he fell off of it. Dang inside-out inner tubes....