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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

As I continued my knitting journey, I was producing designs with triangles, rectangles, hexagons and other geometric shapes, all using the same magic ball ideas. As the mixtures of yarns averaged themselves out, I was always working to the same tension so I knew, with a reasonable degree of accuracy, how many stitches and rows I would need to give me a particular size. The initial positioning of the design, on the number of stitches I needed to use, was a little tricky but once this was done and the first few rows were completed I had no pattern as everything was in my head. My knitting went everywhere with me and, by now, Steve had come to teach Maths in the school where I was. He made fun of me for knitting every lunchtime but when he realised that the knitting was done without a pattern, and was entirely based on geometric principles, he became totally fascinated. Although he had been brought up surrounded by knitters such as his mother and grandmother, they used commercial patterns and would not have dreamt of doing anything other than what was written in black and white.

Working with two balls of yarn was still a little tricky for me so, before long, I decided there must be an easier way to work geometrically and remove this problem. The other thing that nagged away at me was that squares were never quite as square as I wanted them to be. A flash of inspiration, from who knows where, gave me the idea to make garter stitch squares using magic balls. Many people regard garter stitch as a beginner’s stitch and don’t use it ever again once they move on to more exciting things. Although I had previously used almost every stitch and technique known to knitter, my return to basics was not to a well-worn or overgrown path but proved to be the slip road to a fast moving motorway. The beauty of garter stitch is that it is a square stitch. It forms itself into ridges, each ridge being two rows of knitting. With very few exceptions one stitch measures the same as one ridge.

I made garter stitch squares but not in the conventional way. This is the only piece of technical knitting information in this book but it is vital to everything that comes afterwards so some explanation is necessary. I certainly would not claim to have invented this method but it was not much used and I don’t know whether anyone had done it using magic balls before. Each square begins with one stitch. On each row one stitch is added, so one stitch on the first row, two on the second, three on the third, four on the fourth, and so on.

When the square gets to the width you want it to be you start taking one stitch off each row until it gets back to just one stitch. That simple arithmetic progression makes a perfect square. The method worked and all I really thought about at that stage was that the square could be the exact size needed. When it was big enough you simply stopped making it bigger and started getting smaller again. This may sound a very simple truth. In reality it was earth-shattering.

I made a long jacket of diagonally knit squares. I used all the bits of pastel yarns left over from baby items. The ball was made with a little more thought than before. Now there would only be one set of colours so they had to look planned. In a garment using two magic balls there are so many variables that it is sufficient to use yarns at random from the chosen range of colours. The results will always be unpredictable. For one ball I tried to choose every length of yarn in a shade close to the one it would join so that there would be no dramatically obvious colour changes.

There was no white in the ball as I had decided that every square was to be edged with white. This was another inspiration. I often found afterwards that if there is something to unite the pieces you can get away with all kinds of strange happenings in the pieces themselves. In this case the white edgings, along with white cuffs, hem, neck and button bands gave the jacket a sense of unity it would not otherwise have had.

After this that motorway continued. I tried to get off but the road was blocked. For some reason I wanted to make a shape that looked like a cube, in garter stitch. I wanted it to have three colours, one each for the front, top and side of the cube and I was trying to make it so that the three pieces together would form a regular hexagon and the hexagons would fit together. I know how to do it now but then I was getting very frustrated because it wasn’t as easy as I thought it should be. For some reason, and maybe for the only time, all geometric principles had been abandoned and I just couldn’t see why it wouldn’t work. It took another mathematician, looking at it more calmly, to spot the problem. As Steve pointed out I was trying to force my shapes to make 60 degree and 120 degree angles when my method was only capable of producing shapes with angles that are multiples of 45 degrees.

The hexagons were abandoned but the cubes were not. There is another way of drawing a cube – a method that could have 45 degree angles. This was a cube I could knit. The front face was a square, the top and side were parallelograms. There was one minor calculation to be done to find out how many stitches were needed for the parallelograms. It was simple. It worked. We never looked back. So many ideas came from this there weren’t enough hours in the day to use them all. We had dozens of sketches of shapes we could use. We stayed with the simplest, which were infinitely variable.

My all-time favourite design evolved from this playing with shapes. Later, when playing with words became as important to us as playing with shapes, it became known as From Square to Eternity. At this stage it was a square inside a square inside a square …. We even have this design on our wrought iron garden fence now.

Just as returning to basic knitting had taught me things about garter stitch that had previously been in only the subconscious part of my mind, constant use of simple mathematical shapes brought into sharp focus the properties of those shapes which we had taught so often but only now stopped to think seriously about. By a straightforward application of Pythagoras Theorem it suddenly became crystal clear that the diagonal of a square is always the length of the side of the square multiplied by the square root of 2. Working out the square root of two gives you an answer with lots of numbers after the decimal point. Knitting can’t be that accurate so we happily worked with an answer of 1.4. This means that if the side of the square was the size of 10 stitches the diagonal would be 14 stitches. Conversely, a diagonal of 14 stitches meant that 10 stitches would give the right length for the side of the square. With our method of making squares we always knew the number of stitches on the diagonal of the square so could easily calculate the measurement, in stitches, of the side of the square.

We were able to work out the number of stitches needed and then build a triangle, like the roof of a house, onto the first square. Doing this to all four sides of the square made a larger square with the first square standing inside it on one of its points – a square in a square. Another amazing mathematical fact, that we should have known, and probably did know if we’d ever thought about it, is that when the process is repeated to add some more triangles the number of stitches needed is the number there were on the diagonal of the first square. After the very first calculation there is no more calculating to be done and the process could go on and on. It was beautiful because it was so simple and absolutely foolproof.

I love knitting these shapes. In addition to the delight of the maths involved, all the triangles begin at their widest point and consequently, every row has one less stitch than the row before. Instead of knitting that seems to last for ever as it gets wider these stitches disappear like magic. Over the years I have knitted many designs with this motif and it was to become the backbone of much of our work with other knitters.

Click here for some Square To Eternity photos

5d. HANGING BY A THREAD continued