Infinite vase? Closed vase? What's that thing called?

Does anyone know the name of the figure that connects to itself on the side of the vase? It has no opening...

/sorry
I hate non-answers too

Do you know the one I'm talking about, though?

Nice visual, btw. Thanks. Really. *gags*

On edit: Here's some more info:

"In mathematics, the Klein bottle is a certain genus-1 non-orientable surface, i.e. a surface (a two-dimensional topological space), for which there is no distinction between the "inside" and the "outside" of the surface. The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It is closely related to the Möbius strip and embeddings of the real projective plane such as Boy's surface.

Picture a bottle with a hole in the bottom. Now extend the neck. Curve the neck back on itself, insert it through the side of the bottle (a true Klein bottle in four dimensions would not require this step, but it is necessary when representing it in three-dimensional Euclidean space), and connect it to the hole in the bottom."

from wikipedia

:yourock:

:loveya:

I've been fascinated by the concept of the Klein bottle since I was a child.

I'm just glad that that was the topographical nightmare you were looking for.

I was looking up at the stars last night, thinking about the concept of infinity... that got me wondering if the symbol for infinity is somehow related to the mobius strip, and that got me thinking about this bottle (which for some reason I wanted to call a vase :eyes:).

Thanks again!

:overmyhead:

with no intersection. Thus the 3D representations are not true Klein bottles.

Can't think in 4D. :(

All the cool kids are conceptualizing in 4D these days!

I'd love to!

I just can't find anyone patient enough to try to explain it to me. :P

but this forum is not the ideal set-up to explain it.

My luck. :(

Lots of pretty pictures.

http://plus.maths.org/issue26/features/mathart/index-gifd.html

Pretty pictures, eh?

:spank:

Hehe... sorry... you were probably just sayin, but I totally read that as "hey it's got picutres!" like I'd say to my daughter to get her interested in a book. :P

Thanks. :)

Thanks for sharing! I learned something today! :)

always happy to spread a little math around.

Did you make it, or find it someplace? I played around a little with fractal programs, but never enough to make anything that cool!