Origami Klein Bottle

[matty]

I just got this email from Diamond:

origami Klein Bottle- a theoretical 1 sided 3-dimensional shape with only 1 side... think 3-d mobius strip. The interesting thing about the klein bottle can't actually exist in 3-d space without intersecting itself (this the theoretical aspect) though, similarly, a mobius stril can't physically exisist in 2-d space without intersecting itself... anyway- here it is:

http://www.langorigami.com/art/objects/klein_bottle.jpg

[zero2056]

I've no fucking idea what you just said. I'm going to call it the origami Clorox Bleach Bottle.

[Diamond Vision]

that's so not what it is.

[Diamond Vision]

Here's another Klein bottle image- note that if you ran your finger continuously along the outside of the bottle (if it were possible without the obvious intersection of itself) that there is only one "side," no inside or outside.

http://www.grand-illusions.com/acatalog/wine_klein.jpg

as is similar with the mobius strip- seen here as illustrated by mc esher- which can be easily made in our perceptible dimensions.

http://toaud.files.wordpress.com/2007/01/escher-mobius_strip_ii.jpg

I'm working on a theory with that our universe is actually some variant of Klein bottle geometry tho I'm having some difficulty with the non-euclidean parabolic math...

[matty]

That makes more sense now.

That picture BLOWS MY MIND. I loves it.

[slam]

I'm working on a theory with that our universe is actually some variant of Klein bottle geometry tho I'm having some difficulty with the non-euclidean parabolic math...

i assume that you're remembering that the scalar curvature, written in components, is in the form http://upload.wikimedia.org/math/4/9/b/49b4aaa632cc9dea830ed56e5ba4d89c.png

right?

:p

[matty]

A little piece of my brain just blew out...

[Diamond Vision]

scalar curvature is the least of my problems...
http://www.newton.cam.ac.uk/webseminars/hartle60/2-penrose/033.jpg

[Diamond Vision]

oops.. wrong one... you get the idea...