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The World of Illusion Knitting

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PICKING UP THREADS

This was written in
2007
so is now very dated

There are other flexagons so we went on to create more cushions. One has 16 double-sided right-angled triangles. Another has six double-sided squares. Others have 12 double-sided rectangles and squares. There are other versions but we gave up after these. They were becoming a book called Twists and Turns and there were other objects to investigate.

Another fun lesson for school, and workshops, was dealing with Mobius bands. These can also be made from strips of paper and amaze anyone who has not seen them before. The simplest version is a strip joined into a ring after putting a half twist in it.  The result is a piece of paper that has only one side. This can be demonstrated by drawing a line along the centre of the paper. The unbroken line continues until it has travelled twice the length of the paper and can be seen on ‘both sides’ of the paper. This works even better if it is done on some sort of transparent plastic strip as it can be seen through from one side to the other and it is obvious that the two parts of the line are being drawn back-to-back. Cutting the strip in half along the line results in one large loop not two separate pieces as might be expected.

One of the problems of cutting the paper strip is that once it is cut you can’t put it back together to see what happened. We came up with a neat solution to this problem by using open-ended zip fasteners.

Near to where we live we happen to have a large well-known supplier of threads and other haberdashery. The staff there give us some very strange looks when we try to explain what we want and what we are using it for. We used their longest, and most noticeable, fluorescent zips to demonstrate what happens to Mobius bands. There are other variations of the bands, having more twists, and most spectacular of all, a cross that magically becomes a square. The zips are good for older children and adults but younger children get very excited by the square emerging from the cross when working with paper strips. We have ended many workshops with a troupe of children proudly leaving with paper squares round their necks.

We also made lots of Mobius scarves, in a variety of materials. This is a wonderful use of such a simple idea though we can’t claim to have invented it having read about it, and the Mobius waistcoat, in the works of the American knitter Elizabeth Zimmerman. The addition of the half twist, and joining the ends of the scarf, mean that you can wear it flat around your neck without the least danger of ever losing it. In addition it can be worn as a stole around the shoulders or wrapped snugly around the head and neck.

The ideas of Elizabeth Zimmermann and others have been taken to extreme artistic lengths by another American knitter, Cat Bordhi. She has written a book about a stunning new method of knitting a Mobius and we have very recently been inspired by her method to do a similar, but simpler, thing in crochet.

Closely related to these bands is the Klein bottle, which is another topological object that has only one surface. It has no inside and no outside. What do you keep inside a Klein bottle? The same thing as you keep outside! It isn’t possible to make the bottle in real life but a very close representation can be made, so we did it with zips. Making this Klein bottle prompted me to find the knitted version Ben had made many years before.

He had knitted it at the age of eighteen or nineteen. It was a few days before Christmas and he was dressed in his best suit, having just been to some seasonal lunchtime function. By now he was a keen rower and had the physique to match. It was an unforgettable sight seeing him sitting there all afternoon knitting a bright red representation of a Klein bottle.

Click here to see more about Flexagon cushions
Click here to see more about Zipped Mobius

23b. THINGS THAT MOVE continued