European paper sizes are magical! Over the years we have done a lot of work with folding paper, to teach Maths,

We once went to a maths conference and, between sessions, I got into conversation with an American man and we got to talking about European paper, as you do! He knew almost nothing except that the most commonly used size is called A4.  I explained that joining two A4 sheets creates A3, which is exactly the same shape as the starting shape but with twice the area. Two A3 give A2; two A2 give A1; two A1 give A0; A0 is a rectangle, of the same shape, with an area of one square metre.

One of the practical advantages of metric paper sizing is that fewer envelope sizes are needed. Any size of paper can be folded in half, half again, etc. to fit in any envelope.

By one of those strange coincidences that sometimes happen, we proceeded to the next session and, at the door, we were each given an A4 sheet of paper, with some sort of symbol to find a group to join. Each group was given instructions about folding the paper and assembling it the group’s sheets in a particular way. The climax of this warm-up task was the question, ‘What is the volume of the shape you have made?’

The American started jumping up and down, like a five-year old, shouting, ‘I know! I know! That lady told me!’ It was a very simple calculation based on knowing the relationship between the paper sizes - and the necessary information was very fresh in his mind.

This system of sizing works because multiplying the length of the shorter side by the square root of two (approximately 1.4) gives the length of the longer side. Multiplying the longer side by half of root two (approximately 0.7)  gives the length of the shorter side. These numbers might not appear to make sense but it is all down to the special properties of root 2 and its reciprocal. This was the same property we had been using for many years to create our 45-degree angle shapes and we now decided to use it for a different purpose. We discovered that, using DK yarns, we could make this design work and create a small afghan that had an area of one square metre. The numbers worked out very nicely so that all the paper sizes could be made at the correct size and in the correct proportions. The rectangles are nested inside each other so they can all be seen at once. It is possible to lay sheets of paper over the rectangles to see that they do exactly match.

The one square metre size  is usually referred to as ‘A Nought’. We have corrupted the title so you might think of it by its proper name or as Ay-Oh.

The afghan is knitted using the log cabin technique so is very easy to make using only one yarn at a time.

Size

Width in mm

Height in mm

Area in sq m

A0

841

1189

1

A1

594

841

1/2

A2

420

594

1/4

A3

297

420

1/8

A4

210

297

1/16

A5

148

210

1/32

A6

105

148

1/64

A7

74

105

1/128

A8

52

74

1/256

A9

37

52

1/512

These numbers have been rounded