Half Measures was the result of a workshop at a Mathematics Conference in 1998. The delegates were challenged to design a series of eight squares to fit particular criteria.
Each set of eight had to show some form of progression and every square had to be exactly half pink and half blue. Each square also had to have 20 stitches, if knitted in the conventional way, and 28 stitches on the diagonal, if knitted from corner to corner.
The ‘rules’ for Half Measures were that the squares should be in groups of eight and each group of eight must show some kind of progression or movement. Each individual square must have exactly the same amount of pink and blue but they could be in any number of pieces. (In knitting terms this means that there are equal numbers of pink stitches and blue stitches in each square.) The squares could be knitted straight or diagonally. Those that were straight would have twenty stitches across and twenty ridges of garter stitch. Those knitted diagonally would start at a point and work up to twenty-eight stitches on the diagonal. This would mean that all the squares would be the same size.
We made four of the sections then added the borders to separate them from each other. The borders looked very like window frames so it soon looked as though we were making panels for a wall or window. We took the half completed afghan to a conference of the Association of Teachers of Mathematics and asked the participants in a workshop to design the other sections. Four of their designs were used for the remaining sections.
The eight squares for each block are made individually. They are then stitched together and edged with a border created by picking up stitches from the edge of the squares.
Two main colours, and a background colour, were used in the original. Any type of yarn can be used. The thickness of the yarn may affect the overall size of the afghan.
Each block of eight squares could be made in different colours to use up any oddments of yarn.
How many different ways can a square be coloured so that half of it is one colour and half another?
The answer to the question is that (theoretically) an infinite number of ways could be found. In knitting, the answer is a finite number because the number of stitches in the square is fixed and, in reality, only whole stitches can be coloured in a particular colour. The answer would, however, be a very large number and would change according to the number of stitches in the square.