Klein bottle

[PrincessJuJuBear]

My Brain hurts. It feels gooooood

[TheBluntedKid]

fascinating

[thejakenixon]

what would happen if you were to focus small beams of coherent light (like a laser pointer type dealio) into the shape of a giant klein bottle and had some type of extreme force holding the light into the shape while you were to sit inside of one of the klein chambers?

[nebbit1]

OMMFG! i want to make one! Not sure if i would wear it as a hat though. From reading the other comments, if this Klein bottle was in 4-dimensions, it wouldn't intersect itself in any place? Wow. If i met a genie and got a wish, i'd visit the 4th dimension, somehow...

[FlamingPope]

What if we did it to a cube? Seeing how the pattern so far is # pairs of parallel sides + 2, we would get some weird 5th dimensional object right? But then we could have 2 sides connect alternatively while holding one down or will that cancel each other out, no it wouldn't be solid then.

[Escort1990x]

you seem like such a good teacher :)

[RandomNinjaOfEvil]

haha, people get crazy when they've run out of things to say. Great explanation! I didn't know you could split it to get a Moebius strip!

[plasmaants]

soo...this is really interesting. i'm not big on the whole math thing, but this is really really interesting. what sort of math is this? or if it's not math, what is it? i figured since you were doing shapes, it would be geometry or something. :)

i'd like to find out a little more about this sorta stuff.

[Elendegro]

It made me sad when you said you were going to cut it :(

[benett2]

Very simply explained. If my teacher had explained that in this way :)

[isomorphictoyoursoul]

Sweet, I am so making myself a pipe-cleaner klein bottle, post-finals. And I love your youtube lectures by the way. Subscribed.

[TheCatsters]

Thanks!

[LiteWaiter]

The surface is disturbed by itself, so it is not continuous at al times, at all places.

So, what's the point of a Klein bottle?

[TheCatsters]

This surface only intersects itself because we're trying to make it in 3-dimensional space. In fact in 4-dimensional space, it wouldn't have to intersect itself. A Klein bottle is an important example of a "non-orientable surface". These are basically surfaces on which you can't put a sensible coordinate system, and none of them can be built in 3-dimensions without intersecting themselves.

[shawnmctizzle]

what is the name of this kind of science....or mathematics...or whatever. my geometry teacher was showing me the different ways to cut up a mobius strip and in my research, i came accross the klein bottle and other intruiging shapes. is this some kind of super advanced geometry? i was thinking of majoring in astronomy, but i have to admit that this also keeps my interest longer that any video game has before =]

[TheCatsters]

I'm glad to hear you're interested!

Klein bottles and other surfaces (and many other things!) are studied in a field of mathematics called Topology - the Klein bottle is an example of a "topological space". There are also things called "manifolds" which are a bit like surfaces where you particularly want them to be smooth, whereas in topology a Klein bottle with pointy corners is still a Klein bottle! Manifolds are studied in a field called Differential geometry.

[karadan100]

Could the universe be one big hyper Klein shape?

That could kind of explain its seeming ability to go on forever.

[mathex1982]

Yes, of course. Having done experiments only in such a tiny bit of the universe as the earth, it is impossible to tell what the topology of the universe is. However I think the idea of a hyper sphere is more common. But a hyper Klein shape would be cool, if one would go around it (equivalent of going from outside to inside for Klein Bottle) one could find the left and the right side of oneself exchanged!

[yellowfellow]

klien bottles seem like pure speculation

it looks too sloppy the way it goes into itself

if you made a rounded tube wouldn't you still find yourself painting both sides, thinking that there was 2?

just seems like someone wasn't satisfied with with a tube and how common it was, so they had to make up the "klien bottle" to make it seem more complicated then it really is...

[TheCatsters]

The Klein bottle model made out of pipe cleaners is indeed sloppy - it's just a visual aid. The Klein bottle as defined mathematically is extremely precise and is crucial when classifying all the different forms that smooth surfaces can take: it's one of the non-orientable ones, which means, basically, the ones that are hard to visualise. When things are hard to visualise that's often the moment when mathematics steps in.

[yellowfellow]

so theres actually an equation that plots the 3d area of a klein bottle?

[TheCatsters]

We can specifiy the points of a Klein bottle using a formula, yes.

What do you mean by "3d area"? Do you mean 3d volume? The Klein bottle doesn't enclose a volume, as its inside turns into its outside.

[yellowfellow]

why would you say "what do you mean" if you already answered my question with "the points of a klein bottle" sounds like you're just trying to insult me now...

[TheCatsters]

I didn't know if I had answered your question, as I wasn't sure what your question was so I had to guess. When I have to guess like that, I prefer to ask people if that answered their question, in case it didn't. I'm still not sure if I answered the question you were asking.

[MockStoneLLC]

Dimmension needs a better definition, as now there is so many theorys of 4th, 5th, etc dimmensions

[TheCatsters]

"Dimension" has a completely rigorous definition in mathematics; indeed, one of the roles of mathematics is to make this sort of notion precise.

[Language81]

like mind and matter, there is no begin and no end

[Davidweiser]

I don't see how this represents 4 D's since the fourth is time itself. Or any D's actually. Since any physical object could represent 3 D's, and any flat surface could represent 2, any line could represent 1, and any point could represent 0. So I don't see the signficance of this model. Sorry.

[TheCatsters]

This isn't trying to represent 4 dimensions - it just needs 4-dimensional space in order to embed; it can't be embedded in 3-space because it has to go "through" itself as in this model. Physical objects don't "represent" dimensions. Incidentally it's not true that "the" fourth dimension is time; that's just one example of *a* fourth dimension that can be added to ordinary 3-dimensional space.

[Laveintain]

if you look up illusion stairstep, you can get the pretty same effect. Its never ending. illusions are the closest things we can get to 4 dimensional objects. I think so.

[zenSk28]

is this 4D object ?

[TheCatsters]

This is a surface, so in that sense it is only 2-dimensional. The pipe-cleaner model is an attempt to build it in 3 dimensions, but in 3 dimensions it has to go "through" itself in a rather unsatisfactory way, unlike an inflatable ball which is also a "surface" but sits in 3-dimensional space perfectly well. To build a model of the Klein bottle that did not go "through" itself, we would have to go into 4-dimensional space, yes. But this doesn't mean the Klein bottle is 4D.

[torchick163]

that is so cool XD!!!!!!!!!!!!!

[TheCatsters]

Actually the fact that it holds water sort of shows that the surface has only one side. A doughnut (torus) does not hold water - you wouldn't actually be able to get the water inside in the first place! We have to be careful though - holding water is not a rigorous definition of whether something has an inside and an outside. You could make a dent in your doughnut and then it would hold water too, but that doesn't count...

[Seanhawk23]

Well, another way to put it is that if an ant can go from any point to any other point by making a path along the surface, then it only has one side. We cannot do that for a doughnut, the ant must dig through the surface to reach the inside.

[miru021]

that was great!! thanks! :O

[scidamenge]

Is there actually an opening where you can fill it and rain it or would it permanently filled? Thanx.

[connabonz]

i do find it fascinating how its kindof only got one side, wouldnt that make it 1D? anyway.. .. ..Thanks for posting and i will be finding one for a hat!!! WOO!!

[TheCatsters]

It's actually 2D - it's a kind of surface. A 1D thing would just be some kind of line, eg a circle.

[agentolshki]

so what happens if you pour water inside?

[tripmancometh]

explain this to me please it has an inside and an outside it holds water how is a klein bottle like a mobius strip

[Concoorr]

Thanks by the explaining

[ink942]

pretty cool

[bushfingers]

This was quite interesting actually. Thanks