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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

From this time on there was always at least one large item hanging on the wall in my classroom.  I was very fortunate that I had a very large old-fashioned classroom with a picture rail all round. Steve frequently commented that I had the largest room in the school because I had the loudest voice! Not so! It was always the most impressive-looking room and was frequently commandeered for meetings and when visitors needed a room. By a strange set of circumstances it was apart from the rest of the Maths Department and was situated between two Art rooms. Visitors were often confused as to where they were, especially as there was a connecting door to one of the Art rooms.

The reaction to Have It All Ways surpassed anything I had expected. We had made it because it seemed a good idea. There were no big plans about its long time use and no suggestion of where it might be leading us. It looked good. It was a piece of textile art and some might never realise it had another purpose. It was so large, bright and colourful it attracted attention and no class could come into the room without someone saying ‘What’s that?’.  The scale factor was something I hadn’t accounted for. The children I was teaching often had a poor command of English and this tactile item did more to encourage them to express themselves than any formal lesson would ever have done. They could touch and point and show exactly which part they were referring to. When it was put down on the floor ten or twenty of them could prod and poke and explain to each other in a mixture of languages. This just isn’t possible with pictures on a normal-sized piece of paper.

At various times during the day, heads would appear round the door (which was very rarely closed) and children would creep in to see these things they had heard about. It wasn’t only children. Some members of staff were the same – but more of that later.

Beryl’s first afghan was The Long and Winding Road. I don’t think Mum would have been able to stick with this one. It was an experiment with technique and very valuable for the information and inspiration it provided but I have to admit it has never been one of my favourites. It is a large rectangular spiral constructed in four  sections. It didn’t have the same excitement but it was still an essential stepping stone to other designs.

Basketweave followed and, looking back now, I have much the same feeling about that one. It proved that various modules could be knitted, in three shades, and fitted together to make something that resembled a large-scale piece of weaving but there wasn’t a lot of maths to be derived from it. They were exciting at the time because they worked and we were still at the stage when we could only truly believe it worked if we saw it done.

The captive knitters went on to three more, all of which were mainly to do with fitting mathematical shapes together. Figure of Eight was an octagon that started with eight narrow radiating spokes of knitting. The spokes could be any length and they determined the overall size of the octagon. Everything else was done by simple counting related to these spokes. It was nice to make because it was so simple to adapt though it looked quite complex but, once the shapes had been identified, it didn’t have a lot to say for itself in a Maths lesson. Confusingly, there was also Pieces of Eight. None of these names existed at the time. They only became necessary when items had to be identified for some purpose.

We had calculated an easy way to knit an octagon, based on knowing the length of one side, when we had made hats years before. You might expect a hat to be round but, technically, it is not possible to knit a perfect circle. The nearest approximation is a polygon with many sides. Because knitting is easily stretched and deformed, an octagon can easily take on the form of a circle. Pieces of Eight was made from similar octagons but these were not allowed to deform. Octagons will not fit together on their own. When they are placed edge-to-edge square holes are left and these would be easy to fill with small squares. If they are placed point-to-point the holes are stars and, with a bit of planning, these were shapes we could knit, in sections, with 45 degree angles. The octagons were lilac, the stars were purplish-red.

Every design was eventually drawn on the computer and printed out. What you see on the paper is not necessarily what you see when it is reproduced at a larger scale. Pieces of Eight prompted arguments we had not expected. To us, it was a tessellation of stars and octagons. It completely covered the area, as a tessellation should. Very few pupils saw it that way until it was pointed out to them. This inevitably produced oohs, ahs and grins and an end to the arguments that had arisen from the different ways they saw it. Some had seen octagons with holes in between, others had seen only stars and did not recognise that a regular octagon filled the space between them. We all think that what we see is the same as what everyone else sees. This was obviously not true. As teachers, we could never again assume that pupils were seeing what we thought was obvious.

The final contribution from the knitters was Making Waves. This was a deliberate attempt at creating an optical illusion using octagons. Or hexagons? It worked! It used the method we had devised for knitting octagons, with some minor amendments to create lines of knitting in different directions to create a slight shading effect. It had columns of alternating light and dark shapes. The top of each column was a hexagon. This was not a regular hexagon. It was a section of an octagon and it had the effect of turning 2D octagons into 3D hexagonal columns. To confuse the eye even further the columns were joined alternate ways up so when the completed afghan was viewed they all appeared to taper, some at the top and some at the bottom.

Click here to see more about The Long And Winding Road
Click here to see more about Basketweave
Click here to see more about Figure Of Eight
Click here to see more about Pieces Of Eight
Click here to see more about Making Waves

8b. SHEEP AND OTHER ANIMALS continued