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This was written in
2007
so is now very dated
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Chapters |
As you may remember, several years before this we had sent four designs to Brown Sheep. They had used one, and started us on this voyage of adventure. The other three had lain unused ever since. Two disappeared into obscurity but the third kept making its presence felt. Window Boxes was always Steve’s favourite so, six or seven years after it was originally drawn, we decided to make it. Maybe it had been pushed aside because there is nothing intrinsically mathematical about it that we hadn’t done before. It uses Pythagoras’ Theorem and the square root of 2. A unit can be identified that can be repeated time and time again until the surface is covered. It has squares, triangles, parallelograms and ‘windows’. It is an optical illusion.
Look at a window as the end of an open structure such as a tube and it provides opportunities for looking at 3D shapes and starting to think about what is inside and what is outside. If the windows are on the front of square tubes and we are looking into the tubes how do those ‘roofs’ or ‘church towers’ suddenly loom up? Can we be inside and outside at the same time?
We learned a long time ago that anything that forces children to use mathematical language to explain a point has to be important for mathematical development. Window Boxes certainly makes them talk and within a very short space of time they need the words to express the ideas. It proved to be as mathematically valid as any other.
Going from one extreme to the other, the next afghan was mathematics we had encountered many times in classroom situations. There are lots of nice mathematical activities for children that generate the pattern of numbers known as Pascal’s Triangle. The numbers are usually represented in a triangle which gets wider and wider. We wanted to put them onto an afghan so our triangle gets wider for seven rows but after that the side bits have been missed off and it tapers back again to form a square. The sequence of numbers is the same but ours just has some missing.
One activity asks how many ways you could go to reach a particular paving slab, on a patio, always moving forward and only one slab at a time. Using this afghan, that would mean starting at the cream coloured crochet brick in the top left corner and always moving forward towards the dark brown brick in the bottom right corner.
The answer for each brick is found by adding the numbers in the two bricks immediately above it. The first brick is numbered 1. In the second row there are two bricks with only one way to reach each of them. These can be labelled 1, 1. On the next row there is only one way of getting to the bricks at the edges but there are two different paths to get to the centre brick. This becomes 1, 2, 1. The following row has numbers 1, 3, 3, 1. The numbers start to increase dramatically after a few rows. There are 924 ways of getting to the last brick on this afghan.
I had recently been making a piece of filet crochet and, not being a crochet expert, this suddenly struck me as a way of being able to add a written message to an afghan. ‘Writing’ the numbers of Pascal’s Triangle on the bricks seemed an obvious thing to do. It is not always easy to read the numbers, particularly if you get the afghan the wrong way round, but that helps to stop the answers being too obvious. To demonstrate the mathematics the bricks could all have been the same colour but that would have been rather uninteresting so they were made in 49 different yarns, getting darker as it moves through the numbers. It was also another good use for oddments of yarn.
The name, Mere Bagatelle, has a variety of connotations. It can be thought of as something insignificant as this might be if you were taking 49 oddments of yarn with little or no value. It also reminded us of the old-
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21. MERE BAGATELLE