Klein bottle

A Klein bottle made from pipe cleaners

Category:

Howto & Style

Tags:

• klein
• bottle
• pipe
• cleaners

[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.

[Escort1990x]

you seem like such a good teacher :)

[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.

[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!

[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 :(