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This afghan started its life as a worksheet for pupils in a mathematics classroom. Some pupils were having difficulty identifying the properties of four-sided shapes so we devised a colouring-in sheet for them. Every shape in the patchwork has four sides.

The sheet became an afghan so that it could be used over and over to show the differences between the shapes.

The birth of Metafourmosis was completely different from any of the other afghans. Most of the others arose from the desire to teach a particular piece of Maths either by showing pupils a representation of a mathematical idea or by asking them to discover something from a completed afghan.

A class of 14 and 15 year olds had been having great difficulty in identifying the different four-sided shapes. Theoretically they knew the definitions for square, rectangle, rhombus, trapezium, kite and parallelogram but were unable to differentiate between them when presented with drawings.

To try to identify the problem we made a worksheet for them to colour in. It had a key where they had to show the colours they had used for each shape (Squares were brown, parallelograms were purple, etc.). This made it very easy to spot where the errors were occurring. It didn’t take long to find the source of the problem. They were seeing in 3D where they should have been applying the rules for flat shapes. Wherever there were shapes that looked as though they could be the side of a box they coloured in rectangles.

A box drawn in 3D has parallelograms on the side - like Cubism or Fibo-optic. When the pupils were asked to define a rectangle they would happily say it had to have four right angles and then continue to colour a shape which clearly did not have any right angles.

Metafourmosis is not exactly the same as the worksheet they used though it produces the same responses from many pupils.

You don’t need to know, or care, about the shapes. The afghan is spectacular whether you know its original purpose or not.



Figure of Eight

Pieces of Eight

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Pythagoras Tree

Pythagorean Ripples




Wherever possible, shapes are knitted by picking up stitches from an existing shape.

Where this is not possible the pieces have to be stitched together.

Only one yarn is used at a time.


To replicate the original you would need 19 different shades, in six different colour families.

Squares are in one colour (2 shades), parallelograms in another (4 shades), etc. You do not have to stick to this colour arrangement.

It was worked in Aran weight yarn but you can use any weight, provided you use similar weights throughout.

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