h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

A mathematician named Klein
Thought the Mobius strip was divine.
He said "If you glue
The edges of two
You'll get a weird bottle like mine".

Actually you CAN get a real Klein bottle ... http://www.kleinbottle.com/

Mathematicians try hard to floor us

With a non-orientable torus

The bottle of Klein
They say is divine

But it is so exceedingly porus.

Erm. No you can. Not in only three dimensions - they always cross over themselves, and that's not technically allowed. You can only have a klein bottle in 4 dimensional space, so if you put that cross-over therough hyperspace, you'll have done it!

A mathematician named Stein
Went to sea in a bottle by Klein
Since the sea was entirely inside the hull
The scenery seen was exceedingly dull.

'Kay, I thought I was somewhat intelligent, but I can't seem to figure out the whole Klein bottle thing. It boggles me.

Yeah - 4 dimensional objects make my head hurt. How come so many people know so much about mobius and klein? when I wrote the article I figured it would never get approved, let alone that anyone would read it!

Lets just stick to 3 dimensions, anyone for a hexaflexagon...

Now, does anyone know where I left the Nephroid of Freeth.

P.S. As far as I know this thread is the only place where cutting a mobius strip into thirds (rather than in half) has been suggested (by me) but I'd be glad to be proved wrong.
Cutting strips into smaller divisions is very tricky and doesn't do much, the interest is all in the move from even to odd divisions.

Okay, Maybe it was the thread next door.