Following the commission from Brown Sheep we were struck by the idea of using an afghan as a canvas. Some of our earlier ideas were too big to fit onto a sweater or jacket and here was an opportunity to put them onto a large flat surface. From Square to Eternity had always been one of our favourite designs for using on sweaters so was an obvious choice for our first afghan. It creates simple yet dramatic patterns and is technically pleasing in its construction and Mathematics.
The construction is very appealing because the number of stitches on the needles is always decreasing. You have to pick up stitches for the long edge of each triangle and work them off until they have all disappeared which is much more encouraging than working on a piece that gets wider and wider.
Mathematically, it is evident from the photo that one large unit is the same width as two medium units and the same width as four small units. The small units are exactly the same as the centres of the larger units. This wonderful relationship means they can be fitted together in many different combinations. The relationship between the light and dark areas is even more magical. The length of one is root 2 times the other. This is the direct result of all the shapes being right angled triangles and being able to use Pythagoras’ Theorem on them.
When sides are in the ratio of 1 to root 2 the area of the new shape is exactly double the area of the first. Each new ‘round’ of triangles doubles the area of what has gone before. The overall size can easily be calculated once one small piece has been worked.
In the classroom the shapes can easily be drawn on squared paper, or by careful measuring.
The proof for the doubling of the area is self-
It needed a lot of yarn so I unearthed two bags of similar yarn, one in dark green, the other in bluish grey. I didn’t like either colour but I went ahead with them. I was happy with the result and it taught me a lesson. I didn’t need to like the colours in the same way I had to like them if I was going to wear them. They could be chosen for the effect they created together, not whether they suited me personally.
Why From Square to Eternity? Because the design doesn’t end here. It can continue for ever ... and the possibilities are endless.
