Knitted from the finest leather, which in turn is harvested
from the private emu herd of Gianni Versace, this dainty
yet bold handbag makes the perfect statement.

Inbeknownst to the casual observer, what appears to be a
handle is actually a tubular extension of the handbag's
body, which loops
around only to re-enter the body and
then open out again on the underside of the bag.

Anyone familiar with Klein bottles will of course recognise
this as a Klein bottle.

Because of this clever design, it becomes not only possible
but inevitable that all items will be present in the handbag
at all times, thus solving one of the most pressing
problems facing mankind.

That's because product R&D are hard at work on another topological paradox item; a möbius strip gag...

// all items will be present in the handbag at all times //

So women can drag the entire Universe round with them. Great. Just great. You must be SO proud.

// mankind //

One of the numerous pressing problems facing womankind, along with "Where are my car keys ?", "I haven't got anything to wear", "But I can't walk in these shoes" and "Does my bum look big in this ?"

The thing is, [8th], that when you find yourself fifty
miles from nowhere on a unicycle in the desert, and
you discover that the 13/23rds-of-an-inch cotter pin
has worked lose from the crank and got lost, as long
as there's a woman with a handbag nearby you can
pretty much guarantee that she'll have a spare one in
there.

//The mathematical Klein bottle contains all Klein
bottles.//

Ah. That may explain the problem that our sales
team have had. We sold one to a lady in
Wikhampstead, and immediately afterwards our
computer system told us that we had none left in
stock.

I know some pretty advanced knitters, but I have yet to
meet any that can manage the 4th dimension required to
keep the 2d surface from intersecting in the 3rd dimension.
Where did you
find them?

//I though you already were employing every
qualified mathematician in the world?//

Exactly. None of them would want to be known as an
"assistant" topologist. And, since the implications of
the Kleinbag became known to senior management,
we find ourselves with a vacant position.

The task: Find the shortest possible rope to enclose this
herd of sheep.

The physicist sets a 100 meter rope in a perfect circle
around the herd and claims that scientifically this is the
shortest rope possible with which to enclose the herd with.

The engineer builds a contraption whereby some of the
sheep get to stand above the others, after some trial and
error claims that from an engineering perspective this
length of rope, almost half of the physicist's rope, is the
shortest rope possible with which to enclose the herd with.

The mathematician takes a small piece of rope ties it
around himself and proclaims: I'm outside.