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.
7 thoughts on “A Klein Bottle”
Hello – Thank you for the amazing ideal sphere pattern – I have one question:
– in 10 Row Sphere:
– Row 10) 4 scdec
In the end of row 9 I end up (according to pattern) with 12 stitches. What does 4 sc dec mean – do I have to crochet 4 times sc dec and ending up with a total of 8 stitches to be sewn toghether?
Thank you in advance
Susanne – Denmark
Hi Susanne, In the last row, you should sc dec 4 times, which should use up 8 of the 12 stitches in the last row (4 stitches from row 9 will be unworked). Then, you should weave a loose end of yarn through each of the open stitches and pull tightly to close. This keeps the bottom of the sphere from looking pointy.
Hope this helps!
Hey, that’s the gretseat! So with ll this brain power AWHFY?
Reblogged this on Punk Math.
Do you have a pattern for this Klein bottle?
Unfortunately, I don’t! It’s definitely on the list of things I need to get on though.