A Klein bottle is an interesting closed surface that comes up in certain areas of mathematics. After our wonderful librarian at school hooked me up (no pun intended, but I will leave it) with a paper on a knitted version of a Klein bottle, I thought I should really try to crochet one someday. Enter: summer holidays and free time.
So, what the heck is it? Unlike a Mobius strip, it doesn’t have an edge, but, like a Mobius strip, it is referred to as a ‘non-orientable’ surface. This means that if you were to run your finger along the entire length of the surface (starting anywhere) you would wind up back where you started, but with your finger on the opposite side of the surface. Trippy.
It’s a cylinder that intersects with itself and then the ends get attached together. Here’s a diagram to help you visualize what it looks like on the inside:
I ended up adding some stuffing in mine to give it some shape (this may be considered cheating, but oh well). Also, I had to switch the direction of my stitches (‘V’ side out to ‘V’ side in) on the inside the Klein bottle so that my stitches would all be ‘V’ side out (or right side out) once I attached it to where I started crocheting.
The intersection point was a little tricky; I had to start and stop crocheting as I worked my way around the smaller ‘neck’ tube as it passed through the larger bowl part.
Finally, while I was searching for information on the Klein bottle, I found this adorable limerick by a mathematician named Leo Moser:
A mathematician named Klein
Thought the Möbius band was divine.
Said he: “If you glue
The edges of two,
You’ll get a weird bottle like mine.”
Mathematicians are awesome.